Multiverse-wide Cooperation via Correlated Decision Making

explains that by sending in 'C', a participant can increase everyone else's payoff by $2. By sending in 'D', participants can increase their own payoff by $5. The letter ends by informing the participants that they were chosen for the similarity and rationality of their decision mechanisms, particularly in weird scenarios like this one. It should be noted that every participant only cares about the balance of her own bank account, and not about Hofstadter's or that of the other 19 participants. Upon receiving the letter, should you cooperate or defect? Assuming the participants' thought processes are sufficiently similar to each other, I think we should cooperate because this makes it more likely that our 19 fellow participants also cooperate (see chapter 2 and the references given therein). After all, Hofstadter stated fairly explicitly that the thought processes of the participants are strongly correlated. Thus, if we cooperate, we should expect significantly more of the other participants to cooperate as well than if we defect, which means that cooperating has higher expected utility. Alternatively, we may reason that by our choice we determine what the rational choice is for all participants. Hofstadter calls this idea of cooperation via correlated decision making superrationality. By itself, superrationality does not seem particularly action-guiding. Usually, we have other evidence about other agents' behavior and thought processes such that the evidence we gain from our own decisions is less important (see section 6.6). To apply superrationality in practice, we combine it with another intellectually stimulating but by itself inconsequential hypothesis: we probably live in a vast universe or even multiverse, most of which we cannot observe or interact with (see appendix section 6.2). In this paper, we will use the term "multiverse" in a broad sense to refer to any theory postulating multiple universes, including but not limited to Everett's many-worlds interpretation of quantum mechanics. In fact, for brevity's sake, we will use the term to refer to any theory of physics that implies the existence of a sufficiently large universe with many agents, including a merely spatially infinite universe. 1 Some parts of this multiverse are probably inhabited by intelligent beings like us, some of which surely think about scenarios like this one in the same way as we do. This is all we need to allow for the application of superrationality. The key insight of this paper is that agents in a multiverse are in a situation structurally similar to the aforementioned donation game if they care about each other's decisions in far away parts of the multiverse. Consider the following list of parallels: • The decisions between some groups of agents are correlated, just like those in the donation game. • Some agents have different goals than others -a claim for which we argue in section 3.1 -just like the agents in the donation game maximize the balances of different bank accounts. • On occasion, agents can "cooperate" by benefitting the value systems of agents in other parts of the multiverse at low costs to themselves. • As in the donation game, our actions cannot causally influence the behavior of other agents in the multiverse. As an example, imagine you have some specific value system like the reduction of involuntary suffering. You come into a situation in which involuntary suffering has already been reduced to a very low amount. You face a choice between two actions: • You can continue to reduce suffering and increase your own utility and that of other suffering reducers by 1. 2 • You can increase the utility of superrational agents in other parts of the multiverse who (also) care about things other than suffering reduction by 100, e. g. by generating a society of agents who live happily, produce interesting art, conduct science, explore technologies, trade, behave benevolently towards each other, etc. By construction of the thought experiment you care about suffering reduction only, so you would usually take the first action. But consider that many agents throughout the multiverse will face very similar decision problems. For example, there might be an agent who primarily cares about agents experiencing art and the interestingness of things and who is facing similarly diminishing returns -in her world, most things that could be of interest already exist. Other value systems, on the other hand, have been ignored in the process of making her world more interesting. Her world contains many sentient beings with very low levels of well-being, such as humans experiencing various crises (wars, loneliness, life-threatening dangers) -a common theme in art -, wild animals, or blood sports. She knows that agents in other parts of the multiverse dislike this suffering and that she could alleviate them at low opportunity costs to herself. Her decision problem is thus structurally similar to our own. If her thought process is similar to our own, superrationality applies. If we are nice and follow the heuristic "fulfill the goals of other agents in the multiverse whenever the returns are much higher than the opportunity costs for your own values", then this makes it more likely that she will be nice as well, the benefits of which are much greater than those forgone by our own friendliness. In general, if after thinking about superrationality we are nice to other value systems and relinquish opportunities to exploit them, this makes it more likely that other superrational agents with different value systems out there, or at least those who think in ways similar to our own, do the same. And if everyone is friendly in this way, we can expect to harvest gains from compromise -everyone will be better off. I will refer to this idea as multiverse-wide superrationality, or MSR for short.
 An overview of the paper Having read the above introduction, the reader is familiar with the basic idea of MSR. However, it opens up many further questions, some of which I attempt to answer in the present paper. Specifically the rest of this paper makes the following contributions: • We investigate the mechanism of superrationality (chapter 2). -After elaborating on the argument for superrationality, we survey the decision theory literature pertaining to superrational cooperation (sections 2.1 through 2.5). Among other things, we argue in favor of incorporating "updatelessness" into one's decision mechanism. -Exactly how much should we cooperate? Considering superrationality, how should we decide between actions in this universe to maximize our multiverse-wide utility? I will argue that it is best to effectively adopt a new utility function in this universe: a weighted sum of all superrationalists' utility functions that, if adopted by all superrationalists, gives every superrationalist the same gains from compromise. This function should be the same for all agents with your decision algorithm. (See sections 2.6 through 2.8.) -We show how superrational cooperation fundamentally differs from standard causal cooperation (sections 2.9 and 2.10). We will see how it requires no reciprocity -we should benefit superrationalists who cannot benefit us, because we may correlate with agents who can benefit us but whom we cannot benefit. • Cooperating superrationally with agents elsewhere in the multiverse means taking their values into account. Chapter 3 explores what these values might be and which aspects of these values are relevant for MSR. -I argue that (with regard to the decision to cooperate or not) we correlate with agents who hold values that differ from ours (section 3.1). If this were not the case, cooperating with them would be unnecessary except when it comes to coordination (see section 2.8.9). -I provide a comprehensive list of prerequisites that must be fulfilled for MSR to work (see section 3.2). For example, we cannot benefit agents who do not care about our part of the multiverse (section 3.2.2). -Which aspects of other agents' preferences should be taken into account? E.g., should it only be "moral preferences"? To which extent should we idealize their preferences, e. g. by trying to factor out cognitive biases? We motivate and answer these questions in section 3.3. -We review different approaches to hypothesizing about the values of other agents in the multiverse (section 3.4), the most important ones being evolutionary psychology and the study of cultural evolution. • How does multiverse-wide superrational cooperation shift our priorities? What does it recommend in practice? These questions are discussed in chapter 4. We first show how to make policy decisions in the absence of reliable knowledge about the values of agents elsewhere in the multiverse (section 4.1). I then recommend a few interventions, such as promoting causal cooperation (section 4.5.2) and, perhaps most importantly, ensuring that future superintelligent AIs reason correctly about decision theory (section 4.6.3). • The appendix contains various additional considerations that are either less crucial for our decisions or otherwise more tangential, yet nonetheless relevant and of interest to at least some readers. For example, I give an overview of the small amount of work that is closely related to MSR (section 6.1) and explain why I find it plausible that we live in a universe or multiverse containing many agents with whom we are correlated (section 6.2). I also argue that superrationality has few implications for the interactions between agents on Earth (section 6.6), and hence why this paper specifically concerns the application of superrationality in a multiverse-wide (as opposed to general) setting. Much more research is needed to answer some of the questions I set out to explore. This is why I focus more on outlining how these questions can be researched in the future, rather than on trying to ascertain that all my answers are correct with high confidence. The optimal outcome is the one where you defect and everyone else cooperates, yielding a payoff of 19 • $2 + $5 = $43. Conversely, the worst outcome occurs if you cooperate and everyone else defects, yielding a payoff of $0. In any case, no matter how many participants cooperate, you are always better off defecting; 'D' is the dominant strategy. Standard game-theoretical analysis would therefore suggest that 'D' is the correct choice  (Binmore, 2007a , chapter 1, Osborne, 2004 . This is quite unfortunate, because if everyone abides by this reasoning, this yields a payoff of just $5 -whereas if everyone could cooperate, you and everyone else could earn 19 • $2 = $38. Is there any way around this tragedy of the commons? If we only consider the causal implications of an action, the analysis is indeed accurate. However, it ignores that there is also a correlation between the decisions of the participants 3 . Consider a variation of the above thought experiment in which you know that the other 19 participants are all exact copies of you, deciding under the exact same environmental circumstances as yourself. You still have no causal influence over the others' decisions and 'D' is still the dominant strategy; no matter what the other copies choose, 'D' is the better option. However, this argument seems much less attractive now. No matter what you choose, your copies are guaranteed to make the same choice (assuming that they make decisions deterministically). There is no possible (deterministic) world in which two copies decide differently in the exact same situation. Thus, your decision whether to cooperate is one between two worlds: in one of them, the algorithm implemented by your brain returns 'C'; in the other, it returns 'D'. Determining the choice of all your copies to be 'C' gives you more utility, and should thus be regarded as the (instrumentally) rational choice. Of course, strong correlation is not limited to atom-by-atom copies. Imagine a variation of the donation game in which you play against near copies who differ from you in insignificant ways. One may have forgotten some particular childhood memory; another may be more skilled at playing basketball; and so forth. Similarly, the environments in which the near copies decide may differ inconsequentially. One participant may receive the letter in, say, the font "Times New Roman" and another in "Arial". In a donation game with such negligible variations, it seems clear that 'C' is still the better option. Although we cannot be absolutely certain that all 20 of the near-copies make the same choice, it is very likely that they will. With growing dissimilarities between two agents and their environments, the correlation between them decreases further, but your own decision still gives you information about the other agents' decisions. As long as the accumulating differences do not affect any of the agents' reasoning, the correlation will remain a strong one. While the participants of the two donation games are not copies of each other, both variants make clear that the participants' decision-making mechanisms resemble one another and are thus correlated. The donation game with similarity is very explicit about this similarity. The donation game with common rationality, on the other hand, is more subtle -it tells the participants that their decision mechanisms are all "rational". Of course, the individual participant does not know what the rational choice is, yet, but she knows that, if she makes her decision by abstract reasoning (rather than a whim) the result will be the rational decision. She also knows the other participants are also rational (in the same sense of the word) and will therefore arrive at the same -the rational -decision. (It seems unlikely that 'C' and 'D' are exactly equally rational.) In essence, this argument from common rationality is one from (perfect) correlation: if we are rational, we determine what the rational decision is and thus what other rational agents will do. This mechanism is what Hofstadter calls superrationality: if everyone knows that everyone is rational and has the same information, then everyone can determine everyone else's decision. Throughout this paper, I will tend to make arguments from similarity of decision algorithms rather than from common rationality, because I hold these to be more rigorous and more applicable whenever there is not authority to tell my collaborators and me about our common rationality. In any case, the argument from correlation is sufficiently general to include reasoning based on common rationality as a type of perfect correlation. Because the underlying mechanisms are similar, we use the term superrationality for both similarity and common rationality-based lines of reasoning. Assuming that we ourselves apply superrationality, we will also call an agent "superrational" if her decision correlates with ours. Similarly, we call a group of agents superrational if they use similar decision algorithms and take superrationality-type reasoning into account, sweeping the complications of thinking about individual correlations under the rug. Furthermore, we shall use the term "donation game with superrationality" for donation games with similarity or common knowledge of each other's rationality. Anticipating objections,  Hofstadter (1983)  writes: This solution depends in no way on telepathy or bizarre forms of causality. It's just that the statement "I'll choose C and then everyone will", though entirely correct, is somewhat misleadingly phrased. It involves the word "choice", which is incompatible with the compelling quality of logic. Schoolchildren do not choose what 507 divided by 13 is; they figure it out. Analogously, my letter really did not allow choice; it demanded reasoning. Thus, a better way to phrase the "voodoo" statement would be this: "If reasoning guides me to say C, then, as I am no different from anyone else as far as rational thinking is concerned, it will guide everyone to say C." [...] Likewise, the argument "Whatever I do, so will everyone else do" is simply a statement of faith that reasoning is universal, at least among rational thinkers [or those who receive the letter], not an endorsement of any mystical kind of causality. I do not think that, in practice, similarity between decision algorithms will often be as strong as assumed in the above thought experiments. Even if I received a letter of the above kind, I would not think of my decision as determining the others' decisions with near certainty (although there are circumstances under which I would cooperate). In fact, the very reason I make the superrationality argument about the multiverse in particular is that the conditions for superrationality are usually not fulfilled on Earth (see section 6.6). Nonetheless, it is useful to assume perfect and near-perfect correlations in thought experiments for illustration purposes. The rest of this section explores various theoretical considerations related to those mechanisms of superrationality that have practical implications for multiverse-wide superrationality. Most of them are not specific to the multiverse-wide application, however, and we will often illustrate them in more readily imaginable settings in a single universe.
 Lack of knowledge is evidential power, part I: the other agents One reason why some people would not cooperate in the donation game (or the prisoner's dilemma) is, I think, that they have knowledge that would break the correlation between the participants. Using their model of human psychology, they can quickly make an informed guess about what the others are likely to think about and thus decide. Put simply, you learn less from your own cooperation once you already know what the others are deciding. Consider the following variation of the donation game: The Devious postal worker. Game master Hofstadter (in this thought experiment a fictional character) has contrived another donation game. This time, you and the other participants know that you all live in the same area and are to reply by post. Having learned your lesson from Hofstadter's article in Scientific American, you write a big 'C' onto a postcard and walk to the post office. The postal worker takes your card, reads the address and says: "You're participating in one of Prof. Hofstadter's games, aren't you? And you seem to have decided to cooperate. How very noble and decision-theoretically sound of you! Well, I'll let you in on a little secret. Hofstadter has been playing his games with people in this area for years now. We used to merely distribute the letters for him, look at people's answers and then send them back to Hofstadter, but after a year or two, we started to bet on people's replies. The participants tend to use small cards rather than envelopes to save money, so it was easy to spot their replies and count the number of C's and D's among them. We eventually became almost perfect at predicting people's responses, including those from first-timers like yourself who don't necessarily correlate with past participants. But merely betting on responses got boring after a while, so we started to play a new game: we would tell all participants about our predictions of what the others would choose, giving each one a chance to reconsider their own choice. Although this obviously affected the players' behavior and forced us to readjust our methods, our predictions are now practically flawless once again. To cut a long story short, we're highly confident that 18 of your 19 fellow players will defect and only one will cooperate." The postal worker gives you back your postcard and a pen. Should you still cooperate or revise your decision? If we assume that the postal worker's prediction gives you far more reliable evidence than your own action, then the superrationality argument presented above no longer works. Once we already have reliable information about what the other participants are likely to choose (or what they have already chosen), our own choice can no longer make cooperation significantly more likely. In terms of evidential decision theory (introduced in the next section), if
 E[number of other cooperators | I cooperate & postal worker says "n others defect"] ≈ E[number of other cooperators | I defect & postal worker says "n others defect"], where E denotes conditional expectation, then the evidential role of our decision provides no reason to cooperate. That said, in section 2.4 we will see that this issue is actually a bit more complicated. After having sent in your postcard of defection and reflected on what happened, you might realize that all of the other participants were in the same situation as you were. They were also told that 18 (or, in case of the one who cooperated, 19) of the others would defect and, upon hearing this, each concluded that defection would give them a higher payout. No wonder that most players defected. Note that even if everyone had been told that all the others had cooperated, it would still be rational for all participants to defect. By merely telling the participants about their predictions, the postal workers make cooperation much less attractive and thereby less common. What is interesting about the Devious postal worker is that what makes the outcome worse for everyone than in the original Superrational donation games is that everyone receives information about the other participants' behavior. While counterfactually useful for each single player, the information is harmful overall. As Paul  Almond (2010b, chapter 4.5 ) says, "lack of knowledge is power", which I would like to refine to: lack of knowledge is evidential power. We shall revisit this concept soon. In particular, we will think about whether there is some way around the unfortunate conclusion that nobody should cooperate after receiving the respective information.
 A short survey of decision theories and their relation to superrationality Superrationality is a special application of non-causal decision theories -that is, theories of rational decision making that not only take the causal implications of an action into account but also other information that making this decision would give us.  4  In the case of superrationality, that information is always about the other agents. Conversely, causal decision theory (CDT)  (Weirich, 2016 ; J. M.  Joyce, 1999; Lewis, 1981; Skyrms, 1982; Gibbard and Harper, 1978)  neglects any such non-causal implications of an action in the Donation game with similarity. However, the best-known example of what I would view as CDT's limitations is surely Newcomb's problem, originally introduced by  Nozick (1969) . Readers who have not yet studied the problem, are encouraged to do so, although it is not required for understanding most of the present paper. Because Newcomb's problem was the first published example of a problem that (potentially) requires one to consider the non-causal implications of one's decision, all problems wherein such considerations -including superrationalitymight play a role are called Newcomb-like problems. Somewhat confusingly, the field that studies decision theories (in particular, which one we ought to use) is itself called decision theory. Besides discussions of Newcomb-like problems (i. e. whether and how correlated decision making and the like should be taken into account), decision theory is also concerned with topics like the expected utility hypothesis and deciding without assigning probabilities. For those who are unfamiliar with the field, I recommend starting with An Introduction to Decision Theory  (Peterson, 2017) . More elaborate introductions to the decision theory of Newcomb-like problems and correlated decision making include  Ahmed (2014) ,  Yudkowsky (2010) , and  Almond (2010) . Interestingly, most philosophers seem to endorse CDT. A recent survey of professional philosophers conducted by Bourget and Chalmers shows that in Newcomb's problem -one of the clearest examples of CDT's potential failure 5 -about 30% endorse CDT's recommendation 6 of two-boxing, whereas only 20% endorse one-boxing  (Bourget and Chalmers, 2014) . In fact,  Bourget and Chalmers (2014, p. 21, table 11 ) even shows that philosophers who specialize in decision theory are especially likely to endorse two-boxing. Defenses of CDT in Newcomb's problem are given by, e. g.,  Joyce (1999, chapter 5.1)  and  Eells (2016, chapter 8) . Some have also argued that Newcomb's problem cannot occur  (Ledwig, 2000, footnote 81; Binmore, 2007a, chapter 10) . Overall, I find the arguments put forward against CDT much more convincing than those in favor. Yet even among decision theorists who reject causal decision theory, there is disagreement about what the proper replacement should be. Classically, CDT is contrasted with evidential decision theory (EDT)  (Ahmed, 2014; Almond, 2010b; Price, 1986; Horgan, 1981) . However, there are also many newer, less widely known ideas. These include functional decision theory  (Soares and Levinstein, n.d.) , timeless decision theory  (Yudkowsky, 2010a) , updateless decision theory  (Benson-Tilsen, 2014; Hintze, 2014; McAllister, n.d.) , ambient decision theory, Spohn's variation of  CDT (2003; , section 2; 2012), Arntzenius' deliberational decision theory (2008) and Wedgewood's variation of causal decision theory (2013). 7 Superrationality is not based on any specific non-causal decision theory but works in most of them. Consequently, this paper is meant to adopt an impartial stance between the decision theories in which superrationality works.
 CDT would self-modify to behave like a non-causal decision theory in some Newcomb-like problems There is a class of problems wherein causal decision theorists recommend self-modifying into a new decision theory that acts as though it takes some acausal considerations into account. In both the aforementioned donation game and Newcomb's problem, the agent serves as a model for a number of (near-)copies and a prediction, respectively. Assuming that this model is captured at a particular point in time, it follows that the model represents a time-specific version of the agent. Thus, if the agent precommits to using superrationality or to one-box before the copies or simulation are made, they would causally determine all copies' choices. Consider the following thought experiment: Donation game with copies and precommitment. One morning Omega (an absolutely trustworthy, perfect predictor with various superhuman abilities) tells you that you will play the donation game on the next day. However, instead of merely recruiting other people as participants in the game, Omega will copy you atom-by-atom tonight and employ the resulting copies as tomorrow's participants. You are also told that the payouts this time around will be a thousand times higher than in previous games, so it is in your best interest to prepare well. As a final deed, Omega then leaves you a short book entitled From cold showers to chastity: How to commit to any action by self-hypnosis. What do you do? If you are already convinced of superrationality -or if you care a lot about the wealth of your copies -you would not have to do anything. You could spend the day going about your usual business, cooperate on the next day, and win a lot of money. But imagine you were a about the monetary rewards paid to the real version of the agent. 7 Many decision theories are also parameterized by some aspect of their definition. For example, causal decision theory is parameterized by the notion of causality that it uses (see, e. g.  Lewis, 1981; Hájek, 2006, page 19; Weirich, 2016, chapter 2.3; Pearl, 2009, chapter 4) . proponent of CDT and did not care about your copies. You would then want your future self and your copies to cooperate, but you know that they will not do so automatically. As soon as the copies are created, none of them -including you -will have any causal influence on what the others will do. So, if you do nothing, everyone defects and you get a very low payout. However, since you have not yet been copied, you still have a causal influence on the future version of you from which the copies will be created, and thus on the copies themselves. If you could cause the future version of you to be the kind of agent who cooperates, you could causally improve your payout in Omega's game. Given the book that Omega left you, this should be easy: read the book, precommit yourself -and thereby all your future copiesto cooperate, and everybody wins. A causal diagram representing the decision problem is given in Figure  1 .
 Precommitment Your decision Your 1st copy's decision Your 19th copy's decision Payout ... If CDT thinks that it will face some Newcomb-like problem where the copy or model for prediction is created in the future, it would precommit to make the same decision that acausal decision theories recommend (without precommitment). Does that mean that CDT would have to make one precommitment for each Newcomb-like problem (starting in the future) that it will face with non-zero probability? Rather than patching its behavior in each (future) Newcomb-like problem individually, CDT could also make a more general self-modification. At time t, it would precommit to use the following alternative decision theory in the future: do what I, at time step t, would have precommitted to do in the present situation  (Yudkowsky, 2010a, chapter 2; Soares and Fallenstein, 2015, chapter 3; Meacham, 2010) . Such precommitment is not sufficient to generate the kind of superrationality required for this paper: it does not cover Newcomb-like problems that do not start in the future. That is, if the copies are not created based on a future version of the agent, cooperation with them is not covered by precommitment. Thus, CDT's precommitment does not imply cooperation with agents in other parts of the multiverse. However, it does suffice for a weaker version if we assume the Everett interpretation of quantum physics (see section 6.8).
 Lack of knowledge is evidential power, part II: taking a step back CDT's precommitment only entails partial agreement with its rival decision theories. Still, it is worth taking a closer look at precommitment, as it leads us to another interesting dimension along which decision theories can vary. Consider Counterfactual mugging, also known as "the curious benefactor"  (Hintze, 2014, chapter   A CDT agent would, again, only precommit if Omega bases its prediction on a future version of the agent, whereas I (and many non-causal decision theorists) would argue that we should precommit as long as the result of the coin flip is unknown to us (even if Omega's model is based on a past version of us). 8 If we do so, we gain information that Omega thinks we give in, and therefore that we will receive money in expectation. However, once we learn that the coin came up tails, the "winning" move is to keep the $100. As before, the problem contains a harmful piece of information -although in this case an aspect of the environment, and not a piece of information about the behavior of other agents, causes trouble. If we got the chance, we would "protect" ourselves against this piece of information by a precommitment, which renders that piece of information harmless. A similar reasoning applies to the Devious postal worker variant of the donation game: If everyone precommits to cooperation irrespective of what the postal worker's prediction says, then a negative prediction about the other agents' behavior can no longer be self-fulfilling. Thus, if you precommit to cooperating before the postal worker tells you about the other agents' decisions, you have reason to expect more positive news (assuming you correlate with the other agents). 9 As is the case for CDT's precommitment in the previous section, this leads to a more general self-modification that can be made instead of a large number of individual precommitments for individual situations. Specifically, we would (again) precommit to basing our decision in this situation on what is good from the perspective of the state of knowledge prior to being given new information (like the result of the coin toss). This is where updateless decision theory gets its name from, and I will call this feature of decision theories updatelessness. Contrary to what the term may suggest, it does not mean that we do not react to new information at all, but rather that we do it in a different way. Instead of updating the probabilities we assign to possible states of the world and making the best decision based on that probability distribution, we think about what we would have precommitted ourselves to do in this situation. Usually, what we would have precommitted ourselves to do is the same as what is then rational for us to do. For example, if we take a bite from an apple and it tastes foul, we throw the apple away. If you had to precommit to some action before learning that the apple is foul, you would also precommit to throw the apple away if it tastes foul (and to continue eating the apple if it tastes good). Counterfactual mugging is one of the rare cases in which it does make a difference. Acausal decision theorists would precommit to be updateless about all information they receive in the future. In essence, they would switch to a decision theory that comes with updatelessness built-in (the most notable one of them currently being updateless decision theory  (Benson-Tilsen, 2014; Hintze, 2014; McAllister, n.d.)  itself). Thus, if you had been reasoning about (acausal) decision theory including the possibility of self-modification correctly all along (rather than only after learning about the experiment and its result), you would actually cooperate in the Devious postal worker and give in to Counterfactual mugging -even without having precommitted to do so in these particular problems. Some readers will no doubt already be familiar with updatelessness and the arguments in favor of it. For those who have not, this may be a good time to incorporate general updatelessness into their decision-theoretical intuitions, as it is relevant for some of MSR's implications (see sections 2.8.6 and 2.9.1). As a side note, there are justifications of updatelessness that are not based on precommitment and thus suggest that we should, e. g., give the money in counterfactual mugging even if we previously have not thought about precommitting to updatelessness. Ryan Carey lists a few in a comment on the Intelligent Agent Foundations Forum. Benja Fallenstein proposes a justification based on "logical zombies". For other ideas, see Armstrong (2011, section 3.1.2) and Drescher (2006a, chapter 6.2). 10 However, these are more complicated, non-obvious and not well-established. I thus opted for limiting myself to the more straightforward precommitment-based justification for updatelessness as discussed by  Meacham (2010) , Fallenstein on LessWrong and myself in a blog post (cf.  Ahmed and Price, 2012) .
 Reasons and correlations It is difficult to pin down the general principles of how the decisions of different agents in different situations correlate. Indeed, I suspect that the problem has no simple solution other than what is implied by the general solutions to naturalized induction (Soares and Fallenstein, 2014, section 2.1; Soares, 2015) and decision theory. 11 10 Also note that updateless behavior can sometimes result from anthropic uncertainty even when applying the more classical evidential or causal decision theories. 11 Determining correlations between actions is similar to specifying the maxim corresponding to an action in Kant's categorical imperative. It seems that nobody has a precise grasp of how the latter is supposed to be done and that this makes it difficult to apply the categorical imperative. However, the problem of specifying the maxim underlying one's action does not necessarily have a single correct solution. Determining correlations between your actions and that of others, on the other hand, follows from any solution to the problems of naturalized induction and decision theory. These solutions probably depend on priors, but it probably makes more sense to speak of them as having a correct solution. However, humans seem to have some good intuitions for how decisions correlate, in part because understanding the correlations between actions is a day-to-day activity. Imagine seeing your friend Anna being wounded in her right arm one day. She uses her left arm to apply bandages and call a doctor, who arrives a few minutes later and inspects her right arm. A few days later, you see Bob being wounded in his left arm. Based only on the experience from Anna's wound, what should you reasonably expect to happen? Will Bob use his left arm to apply bandages to his right one? Will Anna apply bandages to her right arm? Or to Bob's? Will doctors come to Anna? Even after seeing just one instance of a situation, we are often able to identify many of its causal links and use this information to infer correlations with similar situations. If we see the reasons for a decision from the inside, these correlations become even clearer. If you are Anna and you apply bandages to your right arm, you know that it is to stop the bleeding. Doing so gives you no "weird" evidence -it would not lead you to expect, say, that people are generally likely to apply bandages to things (cf.  Ahmed, 2014, chapter 4; Almond, 2010b, chapter 2.8) . In general, taking a particular action only because of some reason X tells you nothing about whether agents who do not care (or know) about X will also take that action. Importantly, superrationality itself falls under this general rule. That is, if you do something for superrationality-related reasons, then this does not tell you anything about how people who do not accept superrationality would behave. As a trivial example, consider playing a donation game against 19 people whom you all know to make fun of superrationality whenever the opportunity avails itself. Attempting to superrationally cooperate with those people seems rather fruitless. While these considerations may seem trivial, alleged refutations of acausal decision theories are often based on ignoring them or assuming that the evidential thinker ignores them (cf.  Ahmed, 2014, chapter 4; Almond, 2010b, chapter 2.8 ).
 Your back is not mine If the decisions of agents correlate or if each can determine what is rational, then why can someone -let us call him Dennis -not just determine that it is rational to benefit him or his values? Surely, if everyone just benefited Dennis, that creates the optimal outcome for him. So, in a donation game with superrationality, perhaps he should determine the rational policy to be "cooperate, unless your name is Dennis"? This is clearly absurd. The specific reasons that lead Dennis to come up with this strategy (and to abide by it) do not matter to his fellow players, although each of them probably have self-serving reasons which are analogous to those of Dennis. Dennis wants to achieve his own goals, and this is done optimally if everyone cooperates while he alone defects. However, this only makes it more likely that some other participant -let us call her Dana -would reason, "I want to maximize my payoff; if I could determine everyone's choices, I would want everyone but me (Dana) to cooperate." (cf.  Drescher, 2006a, page 298f.) .
 Does accepting superrationality commit us to irrational behavior in medical Newcomb problems? One common objection to making decisions based on what our action correlates with, rather than what our action causes, is that it seems to imply irrational behavior in some cases (e. g.  Nozick, 1969, page 135) . In particular, reasoning from correlation seems to fail in so-called medical Newcomb problems. An example is Yudkowsky's chewing gum problem (2010a, section 1.2), which he describes as follows: Suppose that a recently published medical study shows that chewing gum seems to cause throat abscesses -an outcome-tracking study showed that of people who chew gum, 90% died of throat abscesses before the age of 50 This table shows that whether you have the gene CGTA or not, your chance of dying of a throat abscess goes down if you chew gum. Why are fatalities so much higher for gum-chewers, then? Because people with the gene CGTA tend to chew gum and die of throat abscesses. The authors of the second study also present a test-tube experiment which shows that the saliva from chewing gum can kill the bacteria that form throat abscesses. The researchers hypothesize that because people with the gene CGTA are highly susceptible to throat abscesses, natural selection has produced in them a tendency to chew gum, which protects against throat abscesses. The strong correlation between chewing gum and throat abscesses is not because chewing gum causes throat abscesses, but because a third factor, CGTA, leads to chewing gum and throat abscesses. Having learned of this new study, would you choose to chew gum? The causal graph of this problem is given in Figure  2 . Similar well-known decision problems of this kind are Solomon's problem  (Gibbard and Harper, 1978, section 5; Eells, 2016, chapter 4) , the Smoking lesion  (Eells, 2016, chapter 4) , and the Psychopath button  (Egan, 2007 , section 3). Naive correlation-based reasoning suggests that we should still refrain from chewing gum, since the act of chewing gum would be evidence that we have the CGTA gene and thus throat abscesses. This strongly conflicts with our intuition that we should chew gum to protect against the abscesses. However, I will argue that this provides no convincing argument against superrationality. First, the correlation in the Chewing gum problem differs qualitatively from the correlations between similar decision algorithms  (Treutlein and Oesterherld, 2017) . In the Chewing gum problem (and medical Newcomb problems in general), the correlation stems from a causal relationship: our genes influence our decisions. Thus, the genes and the decisions are correlated. The correlations of superrationality, on the other hand, result from the similarity of the decision algorithms. The reasoning behind cooperation does not involve a common cause of all collaborators' decisions. Instead, the correlation may be viewed as logical  (Garrabrant et al., 2016) : if I cooperate, then this implies that all other implementations of my decision algorithm also cooperate. Figure  3  illustrates the difference between these two types of Newcomb-like problems. Because correlations in medical and non-medical Newcomb-like problems differ qualitatively, ignoring the correlations of our actions in the former does not mean we should ignore them in the latter. In fact, in response to medical Newcomb problems, philosophers have proposed a variety of decision theories that behave in this exact way  (Treutlein and Oesterherld, 2017) . That is, they cooperate superrationally (and one-box in Newcomb's problem) but chew gum in the Chewing gum problem. These include Spohn's variation of  CDT (2003; , section 2; 2012) and Yudkowsky's timeless decision theory (2010).
 CGTA
 Gum
 Abscess Secondly, even purely correlation-based reasoning as done by EDT may recommend chewing gum, depending on how the causal link from the CGTA gene to chewing gum is believed to work. Given that people in the study presumably did not know that chewing gum helps against throat abscesses, it is plausible that CGTA causes people to intuitively desire chewing gum. However, if learning about the study and applying EDT then causes us not to chew gum, it does not tell us anything about whether having the CGTA gene would have caused us to do the opposite. Similarly, if you know that a sprinkler has watered the lawn, observing that the grass is wet is no evidence that it has also rained (see Figure  4 ). The sprinkler already explains why the lawn is wet, so you do not need rain as an additional explanation (see  Ahmed, 2014, section 4.3  for an extensive discission of this argument).
 My decision
 Payoff
 Are the correlations strong enough? In most superrationality-related thought experiments, it is assumed that the other agents are near-copies of ours. The problems presented in this paper are no exception. However, in any real-world setting, most agents are not close copies of ours. We should therefore expect correlations to be much less than perfect. Luckily, the total number of agents in the multiverse is probably so vast 12 that the correlations between ourselves and any individual agent need not be very large 13 (see section 6.2). Because many agents probably do not know about superrationality, we may assume that 99.99% of the agents do not correlate with us at all when it comes to the decision whether to cooperate superrationally. In this case, cooperation with the rest still pays off if we believe that our correlation with the others is non-negligible and positive. It does not matter that we inadvertently benefit many "free riders". For example: if our cooperation makes it 1% more likely that each of these correlated agents also cooperates, then if there are "only" a billion of them, we can expect 10 million more to cooperate if we cooperate. 14
 Correlation only with close copies? Some might think that they are uncorrelated with everyone else apart from very close copies of themselves. Because such near-copies would likely share their utility function to a large extent, there is no need to cooperate with them (although coordination may be useful, depending on the utility function, see section 2.8.9). While the lack of formalized and agreed-upon solutions to decision theory and naturalized induction (Soares and Fallenstein, 2014, section 2.1; Soares, 2015) makes it difficult to draw definitive conclusions on such matters, I am nevertheless skeptical of this objection to MSR. It seems to me that decision theories, at least as people currently conceive of them, are compatible with very large sets of possible minds. That is, if an agent uses, say, evidential decision theory, it can still use all kinds of different mechanisms for assigning conditional probabilities and, most importantly, it can still have all kinds of values (see section 3.1).
 Negative correlations? There is another interesting objection about correlation strength that could be raised: perhaps we should expect to correlate negatively with some agents in the multiverse, such that cooperation can even do some harm (beyond the opportunity costs connected to it) as it makes some other agents more likely to defect. While interesting, I do not find this reason against superrational cooperation very convincing, either. Such a reaction seems implausible given our state of knowledge. Surely, there are a few eccentric agents who have superrationality-related algorithms similar to mine, yet choose to somehow invert the output of these algorithms. But such algorithms make little sense from an evolutionary point of view and so I do not expect them to be very common in the multiverse. It may seem that agents have an incentive to become negatively correlated (via selfmodification), thereby enabling them to defect and make everyone else cooperate. However, there are various problems with this idea. For one, to be able to correlate negatively with the other agents it seems as though one would have to find out about their decision and then do the opposite, which appears to be difficult. Furthermore, self-modification also commits us to cooperate more when the others defect -an agent committed to unconditional defection does not correlate with anyone else. The intuition underlying the self-modification idea is that by self-modifying to be negatively correlated, we can acausally determine the others' decisions. But I do not think this works in the relevant way. When you modify your decision algorithm, you lay your power into the hands of the new algorithm. This means you cannot, for example, self-modify to some decision algorithm A that does the exact opposite of what everyone else is doing, and then defect -unless A already defects on its own. Thus, you cannot determine everyone else to cooperate unless you are already correlated with them. Similarly, you cannot commit to output the 100th digit of π, and then return 6 anyway to acausally determine the value of π. However, if you are already correlated with the 100th digit of π, you can logically determine its value. For instance, if Omega predicts your behavior and then tells you that if you raise your arm, the 100th digit of π will be 7 and if you do not it will be 1, you can determine the 100th digit of π. Of course, these stop working once you know what the 100th digit of π is. As a last point, self-modification does not seem to add anything to direct defection (without self-modification). To see why, let us consider the two kinds of agents that are not yet negatively correlated with the others. The first agent is not correlated with others before self-modification, and therefore has no reason to self-modify. He can just defect directly, without adopting a weird decision theory that is about doing the opposite of what someone in some other part of the multiverse is doing. The second agent is (positively) correlated with others before self-modification. Her problem is that if she self-modifies, others will do so as well, which gives her evidence that a lot more defection is happening than if she would cooperate. Another relevant point is that there is a sharp upper bound to the amount of negative correlation that can exist within a group of agents. Imagine agents A, B, and C, whose decision to cooperate we model as a random variable with the two values 1 (for cooperation) and 0 (for defection). Let us say A is perfectly negatively correlated with B and B is perfectly negatively correlated with C. A is then perfectly positively correlated with C. So, even among just three agents, not all correlations can be perfect and negative. On the other hand, the pairwise correlations may well all be perfect and positive. To study this further, we move from correlations to covariances, because they can be meaningfully added up. In general, we can derive a lower bound of − 1 4(n−1) for the average covariance between pairs of agents from any set of n ≥ 2 agents (excluding "pairs" of one and the same physical agent), if cooperation is seen as a binary random variable. If the agents are all perfectly correlated, then all covariances are at most 1 4 , so the upper limit for the average covariance is also 1 4 . Unless we have reason to believe that we are special, i. e. that our covariance with the others falls far below the average covariance between two agents, this suggests that especially for very large numbers of agents n, our possible acausal impact under the assumption of only positive covariances can be much larger than that of negative covariances. In fact, the covariances of the average agent cannot add up to something below − 1 4 regardless of the number of agents. In contrast, they can be as high as 1 4 (n − 1) for positive covariances. If we view the covariances as uncertain, this suggests a prudential argument in favor of assuming positive covariances to dominate over negative ones, given that our acausal influence is so small under the opposite assumption. However, the details of this argument (and whether it works at all) depend on our "meta-probability distribution" over covariances.
 The relative importance of superrational cooperation: an example calculation Looking at a single decision, how do the benefits from superrational cooperation compare with the opportunity costs? Although we need to make some unrealistic assumptions (such as exact symmetry of the decisions faced by all the agents) in order to calculate this value, it is nevertheless worth an attempt, if only for the purpose of illustration. We assume that there are n superrational agents whose decisions in donation games are perfectly correlated; that is, either all of them cooperate or all of them defect. Realistically, many more agents' decisions will correlate weakly with ours, while only very few correlations will be perfect. However, the implications of many weak and a few strong correlations are similar. For simplicity, we assume that the goals of the agents are orthogonal to each other, i. e. that if someone benefits it is neutral in expectation to any other value system. All of them have values that can benefit from behavior in other universes to the same extent. The n agents face the decision between a) generating b u cardinal, interpersonally comparable utils (or utilons) for their own utility function and b) generating b other utils for k randomly chosen superrationalists. Choosing option a) makes everyone chose option a) and so only generates b u utils for us. Choosing option b) makes everyone choose option b). Whenever someone (including ourselves) chooses option b), there is a probability of k n that we are among the beneficiaries. Overall, if we and thus everyone else chooses option b), we receive n k n b other = kb other utils. Choosing option b) is therefore to be preferred if and only if kb other > b u . (1) This suggests that our own preferences have no priority over those of other superrationalists in this decision. We only decide based on "the greatest good for the greatest number". For instance, if k = 1, then we should choose option b) to help other value systems if b other > b u , i. e. as long as helping other value systems can be done more efficiently than helping your own values. This shows how important superrationality considerations can be. Whereas the non-superrational agent maximizes only for its own value system, the superrational agent maximizes for the value systems of other superrational agents just as much as for their own. Moreover, whether we cooperate depends only on the number of agents whose cooperation is correlated with ours and not at all on the number of agents that will defect. In this regard, multiverse-wide superrational cooperation differs from most causal cooperation, where we usually try to ensure that beneficiaries of our actions reciprocate (unless we care about them intrinsically). As mentioned already, this analysis is based on unrealistic assumptions of perfect symmetry to highlight the relative importance of superrationality considerations. We will now move on to more general, potentially asymmetric cases.
 Compromise strategy
 Sharing gains from compromise in the face of asymmetries We have so far only considered completely symmetrical situations, wherein other agents faced the exact same decision problem as ourselves. One could either choose to cooperate, which correlated with everyone else's cooperation; or defect, which correlated with everyone else's defection. Both cooperation and defection were associated (via the correlation between agents) with particular outcomes. Based on these correlations it was straightforward to choose the action that correlates with the best outcome for ourselves (and also for everyone else). Of course, in practice, compromise will not be this tidy. Specifically, we will have to deal with asymmetrical decision problems. Consider the following example: Superrational cake cutting. You are playing a donation game with two fellow players whose decision algorithms correlate strongly with yours. Unlike other donation games, the currency in this game is cake, of which there are two flavors -vanilla and strawberry. Each player's utility grows in linear proportion to how much cake they eat, and they all have taste preferences that affect their total utility. Let's say you, player 1, like vanilla twice as much as strawberry. Player 2, meanwhile, likes strawberry four times as much as vanilla, and player 3 likes both flavors equally. Each player currently owns different amounts of strawberry and vanilla cake. You have one strawberry cake and one vanilla cake, while player 2 has three vanilla cakes and player 3 has one strawberry cake. (See Figure  5   First note that this problem is indeed one of superrational cooperation. If causal decision theory is applied, then the dominant strategy for each player is to keep all the cake -but this would be a suboptimal outcome for everyone. The players have two strawberry and four vanilla cakes in total. If you could redistribute them so that player 1 has one strawberry and two vanilla cakes, player 2 has one strawberry cake, and player 3 has two vanilla cakes, everyone would be better off than without any redistribution. However, there are infinitely many other possible (fractional) distributions that would also be better for everyone. This makes it hard to decide among them. One part of the problem is that it is unclear what our decisions correlate with. If we send player 2 a piece of her preferred cake (strawberry), can we expect to get some of our preferred cake (vanilla) from her? If so, how much? If we could pin down the correlations and assign probabilities to each combination of strategies -i. e. to each strategy profile -conditional on any of our actions, we could choose the action that maximizes expected utility (the exact formulation of which depends, of course, on our decision theory). But even if the agents know that they have very similar (or even identical) decision algorithms, the asymmetries make it hard to assign these probabilities. Another perspective on the problem is that asymmetries make it unclear who "deserves" how much. In the symmetrical situations it was always clear that everyone should get the same, but this is different in superrational cake-cutting. It is useful to view the symmetry of a compromise problem as a non-binary property. For example, a donation game in which one player gains slightly more than the others from cooperating may still be symmetric enough to make it obvious what the right decision is.
 The compromise problem In order to solve the problem of superrational compromise in asymmetric situations, we will treat compromise as a game-theoretical problem. Note that this requires basic knowledge of game theory; for an introduction see, e. g.  Osborne (2004) . Formally, a game consists of • a finite set of players P = p 1 , . . . , p n , • for each player p i , a set of actions A i , • for each player p i a utility function u i : A 1 × • • • × A n → R, where R refers to the real numbers. Multiverse-wide superrational compromise is a game where P is the set of correlated superrationalists, the utility functions u i represent their preferences, and the sets of possible actions A i represent the set of strategies a player can pursue in their part of the multiverse. Note that the last aspect of the definition assumes that the players' preferences are von  Neumann-Morgenstern-rational (vNM-rational) , which is technically useful and mostly non-controversial 15 . Our notation indicates that utilities are calculated deterministically from action tuples. However, we will sometimes view the utilities u i (a 1 , . . . , a n ) as random variables in the Bayesian sense. This is because we are usually uncertain about the implications of the policies a 1 , . . . , a n , as well as the utility function u i itself, in the context of MSR. Now, the question is which (potentially mixed) strategy α i any player p i should choose. Note that we are not looking for the (CDT-based) Nash equilibria of the game. We will therefore have to move our focus from (Nash equilibrium-based) non-cooperative to cooperative game theory. In principle, the optimal strategy α * i can be determined by applying one's decision theory. For example, if one were to use EDT, then the optimal strategy is argmax αi E[u i (a 1 , . . . , a n ) | α i ]. As noted earlier, however, computing or optimizing the expected value conditional on one's action directly is not feasible in situations of asymmetric payoffs. To find the best action, we will therefore approximate the above expected value maximization with some new criterion, similar to how game theory has replaced expected value maximization with Nash equilibria and other concepts. We will therefore try to develop some new compromise utility function u * : A 1 × • • • × A n → R, intended as a new criterion for choosing the optimal strategy. Because the compromise utility function depends less on the specifics of the problem, it will prove to be easier to reason about what the adoption of some u * tells us about what the other agents do. The optimal u * can then, under certain assumptions, tell us what action to take. At least if our choosing u * means that everyone else chooses the same u * (which is not necessarily the case), then player p i should implement the i-th strategy entry of argmax (α1,..,αn)∈A1×•••×An E[u * (α 1 , . . . , α n )]. 15 One exception may be the axiom of continuity. It is violated by preferences with lexicality, which are commonly discussed in moral philosophy  (Knutsson, 2016) . However, if we drop the axiom of continuity, we can still represent the preferences as a lexicographic utility function  (Blume, Brandenburger, and Dekel, 1989; Fishburn, 1971) . However, a treatment that includes lexicographic utility functions is beyond the scope of the present paper. Because in uncertain situations, a lexicographic utility function is usually equivalent to only maximizing the lexically highest values, we may nonetheless apply the present results by simply omitting all lexically lower values. Once again, having a compromise utility function, as opposed to more general compromise preferences, implicitly assumes that the compromise preferences are also vNM-rational.
 Cooperation with and without coordination In a way, argmax (α1,..,αn)∈A1×•••×An E[u * (α 1 , . . . , α n )] is the optimal plan on the assumption that everyone will follow it. With practical degrees of correlations, however, we cannot assume that everyone will arrive at the same plan, especially if multiple plans have the same compromise utility. In MSR, it is especially unlikely that everyone will arrive at the same plan, as superrational collaborators have different states of knowledge about the multiverse and each others' value system. A perfect plan may have catastrophic results if it is not accurately followed by everyone involved. Specifically, plans are risky if the utility of one player's action hinges on another player's action because such plans assume the ability to coordinate. Hence, it is useful to look at a class of utility functions where coordination plays no role. We say that a utility function u i (additively) decomposes into local utility functions {u i,j : A j → R} j=1,...,n if u i (a 1 , . . . , a n ) = n j=1 u i,j (a j ). Intuitively speaking, u i decomposing into local utility functions means that any player p j has a very direct impact on p i 's utility, such that when p j attempts to benefit p i she need not think about what other players do. In game theory as it is usually applied to interactions between agents on Earth, the assumption of additive decomposition of utility functions would be a severe limitation: if agents interact with each other physically, then, of course, the impact of an action often depends on the other players' actions. As examples, consider some of the classic games studied in game theory, such as Bach or Stravinsky or Chicken. In the problem of multiverse-wide compromise, on the other hand, there is probably no causal interaction between the actions of agents in different parts of the multiverse. Additive decomposition of utility functions is thus a more natural assumption in this context. That said, issues of coordination can still arise in the utility function itself. As an example, consider a utility function that wants there to be at least one (dis-)proof of the Riemann hypothesis somewhere in the multiverse, but does not care about the existence of further, redundant proofs. This utility function does not decompose additively; whether I benefit this utility function by proving the Riemann hypothesis depends on whether someone else is already working on a proof. Other, perhaps more realistic, examples of ethical notions that do not decompose into local utility functions are (partial) average utilitarianism and potentially biodiversity. However, many other plausible utility functions (e. g., total utilitarianism) do fulfill the above condition. If some of the utility functions in a game do not decompose into local utility functions, we will call the game a coordination problem 16 . Theoretically, the following arguments also work for coordination games, but they are much more robust and practically applicable in problems that require little or no coordination. This topic will be discussed further in section 2.8.9.
 Harsanyi's aggregation theorem Although we do not yet know how and to what extent, we know that our compromise utility function u * should incorporate the utility functions u 1 , . . . , u n but not be sensitive to anything else. The following assumption captures these attitudes: Assumption A. Let P and Q be probability distributions over outcomes  17  That is, all players like P at least as much as Q. Then A 1 × • • • × A n such that E P [u i (a 1 , . . . , a n )] ≥ E Q [u i (a 1 , . . . , a n )] for i = 1, . . . , n. E P [u * (a 1 , . . . , a n )] ≥ E Q [u * (a 1 , . . . , a n )], i. e. the compromise utility function also values P at least as highly as Q. We could view this assumption as a decision to limit ourselves to a particular class of compromise utility functions -a decision that makes our superrational collaborators limit themselves to the same class. In terms of expected value for ourselves, this is a good decision. It basically does not tell us anything other than that we do not want to pay anything to switch from P to Q if everyone likes P at least as much as Q. We furthermore introduce the notion of utility function equivalence: two utility functions u and v are equivalent, written as u ∼ v, if they imply equal behavior. For the cardinal utility functions discussed here, this is the case if one arises from positive affine transformation of the other, i. e. if u = av + b for some a ∈ R >0 and b ∈ R. Assumption A does not seem especially strong, but it turns out that it suffices for a significant result regarding the shape of the compromise utility function. It is essentially a version of Harsanyi's aggregation theorem  (Harsanyi, 1955 ; see also  Peterson, 2017, section 13.4  for an introduction). 18 Theorem 1.  (Resnik, 1983; Fishburn, 1984)  Let u * be a compromise utility function for u 1 , . . . , u n that satisfies Assumption B. Then there are weights λ 1 , . . . , λ n ∈ R ≥0 such that u * ∼ n i=1 λ i u i . (2) Note that the λ i are not unique. Also, not all weight assignments consistent with Eq. (2) or Assumption A have only positive weights. In particular, if u i = u j for some i = j, we can decrease λ i by an arbitrary constant C if we correspondingly increase λ j by C, and end up with the same compromise utility function u * .  (Resnik, 1983; Fishburn, 1984) . If C > λ i , we arrive at an equivalent utility function that assigns negative weights. Theorem 2. Let u 1 , . . . , u n each decompose into local utility functions {u i,j : A j → R} j=1,...,n . Then a compromise utility function u * that satisfies Assumption A relative to u 1 , . . . , u n also decomposes into local utility functions. Proof. Because of Theorem 1, it is u * (a 1 , . . . , a n ) = b + n i=1 λ i u i (a 1 , . . . , a n ) = b + n i=1 λ i n j=1 u i,j (a j ) = b + n j=1 n i=1 λ i u i,j (a j ) = n j=1 b n + n i=1 λ i u i,j (a j ) for some b and weights λ 1 , . . . , λ n ∈ R ≥0 . Thus, u * decomposes into local utility functions u * j : A j → R : a j → b n + λ i u i,j (a j ) j=1,...,n . This is quite a convenient result. If indeed u 1 , . . . , u n each decompose into local utility functions, then each player p i can maximize u * i in her own part of the multiverse without having to think about the precise actions of other players elsewhere in the multiverse.
 How to assign the weights Having argued that we should make our decisions based on a weighted sum of the decisions of our superrational collaborators, the question is how we should optimally assign the weights. Theorem 1 does not tell us much about this. In fact, it even allows for the possibility of assigning positive weight only to our own utility function. We will differentiate two ways of assigning the weights: biased toward our own values, or impartial. We will consider the two options in turn.
 Biased compromise utility functions? We start with the option of assigning the weights in a way that is somehow biased toward our values. For example, we could assign higher weights to utility functions that are more compatible with ours, and lower weights to those that are not. Of course, this tells us that agents with other value systems will do the same, i. e. assign weights in a way that biases the resulting utility function toward their own values. I will argue against assigning weights in a biased way and in favor of impartial weights. This point is crucial for the strength of the implications of MSR, because the more weight we assign to other utility functions, the more our policies have to change in response to MSR. In a way, the reasons against biased weights are merely an extension of the reasons for cooperating in the first place. Let us say that in response to MSR we assign some weight to the other agents' utility functions but still largely maximize for our own values. Then gains from further trade are left on the table. Because we still maximize for different utility functions, we could trade again until all our compromise utility functions approach some impartially weighted sum. This line of reasoning is also supported by the standard ways in which gains from trade arise. If everyone compromises with biased weights, then this produces some gains from comparative advantages -in situations where I have a large comparative advantage to maximize for someone else's utility function, I will do so at the cost of not maximizing for my own values. In return, others do the same. But if the comparative advantages are too small, then we miss out on gains from trade. Consider an example with two superrational collaborators. For simplicity, we will assume them to be in symmetrical situations at the time of compromise, such that the only plausible neutral compromise would give the same weight to each of the two utility functions. Both may, at some point, face the choice between taking a utility of x for themselves and giving x + ε to the other, where x and ε are any positive real numbers. In such a situation both have a comparative advantage to help the other's values. But if ε is very small, the comparative advantage is very small, too. So, if they assign more weight to their own utility functions, there is some ε such that they choose to maximize their own utility functions and thus miss out on the gains from trade. While I am moderately confident that all compromises with biased weights are Paretosuboptimal, I do not, at this point, have a formal proof of this statement. That said, the above example at least shows that such compromises yield collectively vNM-irrational behavior. Furthermore, section 2.7 showed that, at least in symmetrical idealized scenarios, prioritizing one's own values does not achieve the best results. I should note that impartial weights do not imply that I should be equally likely to find myself maximizing for my own values as any of my superrational collaborators. For example, if you are very uncertain of the content of some value system, then it will not influence your decisions as much, even if you assign a high weight to that value system.
 Neutral compromise utility functions We have argued that after an optimal compromise, each player should judge their action roughly by the same impartial criteria. Hence, we now have to look for a way of assigning the weights in a neutral way. Harsanyi himself proposes -albeit in the context of social welfare rather than trade -to simply give equal weight to all utility functions, which is equivalent to removing the weights altogether  (Harsanyi, 1979 , section 2). Besides the argument of "equal treatment", it can be backed by an original position argument  (Harsanyi, 1953; Harsanyi, 1955; Freeman, 2016) . From an original position, i. e. a perspective from which we do not yet know which position in the multiverse we will take, how many resources will be at our disposal, etc., it seems reasonable to give equal weight to all utility functions. Updatelessness gives this argument some additional appeal, as it asks us to make our decisions from a similar perspective. However, there are various problems with maximizing unweighted aggregated utility. One is that it is based on interpersonal comparisons of utility. In Harsanyi's words, it assumes that "all individuals' utility functions u 1 , . . . , u n are expressed in equal utility units (as judged by individual j on the basis of interpersonal utility comparison)". 19 Such comparisons, however, are highly controversial  (Hammond, 1991; Binmore, 2007b) . Recall that the cardinal utility functions postulated by the von Neumann-Morgenstern utility theorem are only determined up to positive affine transformation. This means that if a utility function u represents an agent's preferences, then so do 100 • u and 0.01 • u. None of the three is in some way the more natural choice for representing the agent's utility function. Whereas positive affine transformations do not alter an agent's behavior in choosing lotteries, they do change the behavior implied by the aggregate of multiple such functions. In Superrational cake cutting, we specify the utility functions (or, as they are sometimes called in fair cake-cutting, subjective value functions) of each agent up to positive affine transformation by specifying the trade rates between units of strawberry and vanilla cake. For example, the third player has a 1:1 trade ratio, the second has a 4:1 trade ratio. To simplify notation, let s i and v i be amounts of strawberry and vanilla that p i receives under some action profile. Then the second player's utility function could be u 2 (s 2 , v 2 ) = 4s 2 + v 2 and the third player's utility function could be written as u 3 (s 3 , v 3 ) = s 3 + v 3 . If one wanted to maximize aggregate utility u 2 + u 3 , then u 2 would effectively receive far more weight than u 3 . If u 2 (s 2 , v 2 ) = 400s 2 + 100v 2 , this bias toward u 2 would be even worse. Because utility functions come in different versions depending on their scale, we still need to find a satisfactory way of normalizing the utility functions, i. e. to pick one out of a whole class of equivalent utility functions. This task is actually equivalent to assigning a weight to a given member of each class. Thus, removing the weights and relying on interpersonal comparison of utility can be seen as merely passing the buck from assigning weights to choosing the scale of the utility function. One common approach to interpersonal comparison of utility is range normalization  (Isbell, 1959; Hausman, 1995, section 3) . That is, the utility functions are chosen in such a way that their maximum is 1 and their minimum is 0 (using no additional weight).  20, 21  While intuitive, range normalization appears to be inappropriate for compromises. For one, it lacks a rigorous justification in this context -it is not immediately obvious that the underlying naive view of neutrality is relevant for compromise. The main problem with using range normalization for the compromise utility function is that in some cases some of the agents have no reason to accept it as it leaves them worse off than engaging in no compromise at all.  22  For example, consider the case of a compromise between a beggar and a millionaire with different sets of preferences. If the compromise gives equal weight to the preferences of the two, then this leaves the millionaire worse off as she receives little in return for dedicating half of her resources to fulfilling the beggar's wishes. Even if all agents have equal resources, a range normalization-based compromise can be unappealing to some of them. Consider two equally powerful agents with two very different value systems. The first cares about bringing about a state that is only very rarely attainable. All his other preferences pale in comparison. The second agent divides states of the world into two classes: good and bad states. Within each of those classes she is indifferent between any pair of states. Also, the division is such that in most situations, the different actions vary in how likely they are to bring about a good state. Under range-normalization, the first agent's utility function would usually be close to 0 and it would only rarely be possible to get it to 1. The second agent's utility function is 0 for some states and 1 for the others. If we maximize the sum of these two utility functions, this will mean that we will usually optimize much more for the second agent's preferences. After all, in most cases doing so significantly increases the probability of attaining 1 util. Maximizing for the first agent, on the other hand, usually only generates a small fraction of a util. Only in the rare situations in which we have an opportunity to attain the first agent's favorite state do the agents' preferences have a similar amount of control over the decision made based on the compromise. The first agent may therefore have no reason to accept this compromise. Because range normalization can drastically favor some players, it may actually be not so neutral after all. If you already knew that a range-normalized utility function would benefit you a lot, you would be biased to accept it. If you accept the range-normalized utility function on these grounds, however, it would not tell you much about the choice of agents who already know that the range-normalized sum would be harmful to them. In this sense, range-normalization is a biased compromise. Of course, if I benefit from range-normalization, I could hope that those who are disadvantaged by it nevertheless compromise in some other way that still benefits me. However, using such tricks to exclude others from our compromise is evidence that we are excluded in other ways as well (cf. section 2.9.3). Thus, without some other justification, range normalization does not appear especially promising. Many other approaches to interpersonal comparisons (see, e. g., Sen, 2014, section 7.3 23 ) suffer from the same problems. We thus need to set up more rigorous criteria for neutrality. It appears that the most directthough certainly not the only -approach is to require that the compromise is, in expectation, equally good for everyone -that is, everyone gets the same gains from compromise. This ensures that the compromise is equally attractive to everyone involved.
 Assumption B. The expected gains from adopting u * are the same for each player p i . Unfortunately, Assumption B is underspecified. The most naive view is that the gains from compromise for player p i are E[u i (α 1 , . . . , α n ) | u * ] − E[u i (α 1 , . . . , α n ) | no compromise]. (3) allow for a compromise that leaves everyone better off. However, there are some aspects of Eq. (  3 ) that should, perhaps, be revised. For one, it is unclear whether having a full compromise versus having no compromise is the appropriate counterfactual. One alternative is to choose the counterfactuals provided by one's decision theory. That is, one could compare E[u i (α 1 , . . . , α n ) | I cooperate with u * ] with E[u i (α 1 , . . . , α n ) | I defect] , where EDT's conditional expectation may be replaced by an alternative notion of the counterfactual (see  Gibbard and Harper, 1978; Hintze, 2014, section 3) . Alas, these are difficult to calculate. Perhaps one could also measure the gains from each p i 's individual participation, so that the set of cooperators in the minuend and subtrahend of Eq. (  3 ) would be the same, except that the latter does not contain p i . Moreover, the subtrahend's compromise utility function would not contain λ i u i as a summand. This resembles the notion of voting power from social choice theory  (Cotton-Barratt, 2013; Felsenthal and Machover, 1998) . A second area of revision may be that Eq. (  3 ) does not account for some value systems potentially being more common among the p i , or holding more power, than others. We would probably want the gains from trade to be proportional to the resources invested by a particular value system. Otherwise, an individual agent with a very common value system has no or less of an incentive to join the compromise. For example, if an agent already knows that at least one other agent with the same utility function is part of the compromise, then this could mean that joining the compromise produces no additional gains from trade for that agent. One way to weight different utility functions based on their power would be to divide Eq. (  3 ) by some measure of the resources invested by u j . The Shapley value is a well-known example of a theoretically grounded measure of power and may serve as an inspiration. Also note that Assumption B contains an interpersonal comparison of utility. However, the potential harm of getting this one "wrong" is smaller than in the case of using the unweighted sum as a compromise. Depending on how you scale the different utility functions relative to each other, applying Assumption B may allocate the gains from trade differently, but it nonetheless ensures that everyone receives gains from trade at all. Further research is needed to identify the appropriate variant of Eq. (  3 ) or perhaps an alternative to it and subsequently the corresponding weight assignment. An example of a promising line of research in this direction is the work on variance voting, i. e. normalizing the variances, by  Cotton-Barratt (2013)  and MacAskill (2014, chapter 3). In particular, Cotton-Barratt shows that under certain assumptions, variance-normalized compromise is the only compromise that gives each player the same voting power. In addition to specific solutions, it would be useful to explore the necessary conditions for the existence of a weight assignment that satisfies Assumption B while producing positive gains from trade. For example, if you already know how much cake each player owns in the above Superrational cake cutting, there is no assignment of weights that reliably produces gains for everyone. No matter how the weights are assigned, there will always be one weighted utility function that strawberry cake is best invested into, one that vanilla cake is best invested into, and (at least) one that receives no cake at all. That is, unless two weighted utility functions generate the same amount of utility per unit of cake, in which case the compromise utility function is indifferent about who receives the cake. Besides the existence of gains from trade (see section 3.2.5), I suspect that the central assumption under which a weight assignment satisfying Assumption B exists is the continuity of the expectation E[u i (α 1 , . . . , α n ) | u * ] relative to the weights in u * .
 Updateless weights Seeing as the gains from compromise that Assumption B talks about depend on one's current state of knowledge, the weights to be assigned may do so, too. Consider the following example: Remote-controlled cake maker. Two agents are about to share cake again. Agent 1 prefers strawberry to vanilla cake at a ratio of 2:1. Agent 2 has the inverse preference ratio. On day one, neither of them owns any cake; however, they know that on day two, each will receive two control buttons for a distant machine, capable of producing and shipping only one type of cake. While it is, at this point, unknown which flavor of cake it will produce, they will know the type of cake maker once they receive the buttons. They will have the same amount of control over where the cake from the cake machine is sent: each agent can, by pressing one of the buttons, send some amount of cake to himself. By pressing the other button, they can send a 20% larger amount of cake to the other agent. Unfortunately, they can only press one button. The two agents' thought processes correlate perfectly when it comes to decisions regarding superrationality and they may already settle on a superrational compromise utility function on day one. On day two, they receive the control buttons and learn that it is a vanilla cake machine. They still cannot communicate, but use the same thought processes. Which button should each of the two press? 24 Let us first consider the situation on day one. Because their situations are fully symmetric, it seems reasonable to set u 1 (s 1 , v 1 ) = 2s 1 + v 1 , u 2 (s 2 , v 2 ) = s 1 + 2v 2 , u * (s 1 , v 1 , s 2 , v 2 ) = u 1 (s 1 , v 1 ) + u 2 (s 2 , v 2 ), where s 1 , v 1 , s 2 , v 2 are, again, the amounts of cake received by each player (which can be calculated from a set of actions). By any reasonable definition of "gains from compromise", this satisfies Assumption B. Accepting this compromise effectively means that agent 1 will receive all of the cake if the machine makes strawberry cakes, and agent 2 will receive all of the cake if the machine makes vanilla cakes. We now skip ahead to day two, when the agents are told that the machine makes vanilla cakes. In this new situation, u * (s 1 , v 1 , s 2 , v 2 ) = u 1 (s 1 , v 1 ) + u 2 (s 2 , v 2 ) is harder to justify, as it gives all the gains to agent 2 -agent 1 even loses utility relative to not compromising. Perhaps the more natural utility function to choose on day two is u * (s 1 , v 1 , s 2 , v 2 ) = 2u 1 (s 1 , v 1 )+u 2 (s 2 , v 2 ), which would be the compromise utility function under, e. g., variance normalization. From the perspective of day one, it is suboptimal if the two players change their minds on day two. Thus each player prefers precommitting to the initial compromise even though that implies a good chance of a net loss. Once again, we find that lack of knowledge is evidential power (see section 2.4) and that we should precommit to decision-theoretical updatelessness. In the context of MSR, I doubt that the weights of the compromise utility function would shift considerably once a few basic factors have been taken into account. For one, significantly updating one's prior about the expected gains from a compromise requires broad and reliable knowledge about the entire multiverse. Specifically, it requires knowledge about what decisions superrational collaborators will face in other parts of the multiverse, and how these decisions will affect different value systems. Even if you learn that some assignment of weights decreases your utility in this universe, the situation may differ in other universes. Many opportunities to have an impact may depend on as yet unidentified crucial considerations or unresolved issues in physics. Examples of issues of this kind which have already been identified include lab universes, artificial intelligence, artificial intelligence arms races, self-improvement races, suffering in fundamental physics, whole brain emulation scenarios (see section 3.4.4) and global catastrophic risks. That is to say: any kind of multiverse is so complicated that we should not expect to know much about it. If we think some pieces of information would significantly shift our weights in one direction or another, then this piece of information is potentially harmful. To the extent that it is possible, it would be important to convince superrationalists to become updateless before they encounter such information.
 Limitations The present analysis is limited in several ways. In general, we made many assumptions under the meta-assumption that the results generalize. For example, our arguments were often based on perfect correlation between the agents. Many aspects of our analysis were also semi-formal or informal. For instance, we did not formally justify the claim that settling on the same compromise utility function creates the largest gains from compromise. Further research is thus needed, including research into the largely unexplored area of superrational game theory.
 Heuristics It would certainly be nice to find a formal solution to the compromise problem (as described in section 2.8.2) at some point. However, such a solution is neither necessary nor sufficient for cooperating superrationally in practice. It is not necessary because cooperation based on intuitions about compromise may already get us quite far. Even without ever having heard a course on game theory, most people have intuitions about fairness that seem to suffice in most negotiations. We may expect that similar intuitions also suffice for reaping many of the benefits of superrational cooperation. It is not sufficient because we will not possess formal description of our collaborators' utility functions in the foreseeable future, anyway, given that we cannot even formally describe our own goals 25 With the description of their values being vague and qualitative, the compromise must, in the end, also be. Hence, we should also consider informal heuristic rules for making decisions. Below are some proposals. They have significant overlap and many of them also apply to causal cooperation; some are more moderate and intended to apply to people who do not fully accept MSR. Sorted in increasing order of the strength of their implications: • If some resource is mildly useful to you but very valuable to other (prominent) value systems, it is prudent to ensure that the resource is used for those other value systems. Similarly, avoid hurting other (prominent) value systems if it only gives you a comparatively small gain. • Utility functions that contribute a lot, e. g. because opportunities to increase them are rare, should perhaps receive disproportionate focus whenever such an opportunity arises. Otherwise, agents with such utility functions would have little incentive to compromise. • When the values of superrational cooperators diverge on some issue with a roughly equal number of supporters (or resources) on each side, these sides cancel each other out after compromise. That is, no superrational cooperator should act on a view on this issue. Toby Ord writes: "It is so inefficient that there are pro-and anti-gun control charities and pro-and anti-abortion charities. Charities on either side of the divide should be able to agree to 'cancel' off some of their funds and give it to a mutually agreed good cause (like developing world aid). This would do just as much for (or against) gun control as spending it on their zero-sum campaigning, as well as doing additional good for others." • Try to benefit many value systems at once, and deprioritize issues that are very specific to you or other agents (see section 4.1.1). • Metaphorically speaking, try to increase the size of the compromise pie, rather than to increase the size of your own piece. • In any situation, maximize for the (prominent) value systems that have the highest stakes in your decision. • For any policy decision, ask yourself whether superrationalists with other value systems would plausibly arrive at the same decision (to ensure that you are assigning weights impartially).
 Notes on superrational coordination Superrational compromise is easiest if it requires no coordination (see section 2.8.3). It can, however, also solve coordination problems -that is, problems in which the utility functions of the players do not decompose into local utility functions, and the utility of a strategy to some player thus depends in part on the moves of the other players. As before, we can also describe a variation of the problem with similarity instead of common rationality. And as usual, causal decision theory recommends to reply, a strategy that, if implemented by everyone (or more than 5 people), forgoes a golden opportunity. However, this scenario diverges from those we have previously discussed in that our impact on the other participants' utility depends on their actions. Nevertheless, we can use superrationality to our (and our superrational collaborators') advantage in Platonia five, although we have to apply it in a different way. The problem is that simply maximizing the compromise utility function does not really help us here. Given that all players are essentially in the same position, it seems reasonable to let the compromise utility function be the sum of the money gained by each player. That means it is either 5 billion if exactly 5 people send in the letter, or 0 if another number of people send in a letter. Maximizing the utility function only tells us that we should ensure that exactly 5 people should send a letter -something we already knew beforehand. The compromise utility function does not tell us who should send in the letter. Because it does not decompose into local utility functions, it does not tell each player what to do. This illustrates how, even with perfect correlation, the compromise utility function may not suffice for solving coordination problems. Hence, we go back to the more direct approach. We assume that, given the correlation between agents (or the ability to determine the rational choice), we should choose the strategy that would be best for us if it were adopted by everyone. Because the situation is entirely symmetrical, everyone is likely to go through equivalent lines of reasoning. Obviously, neither sending in the letter nor not sending in the letter are good strategies. We thus have to adopt a mixed strategy, i. e. one of choosing to send in the letter with some probability p, where players' samples from this distribution are independent. At the far ends, both p = 1 and p = 0 guarantee that we lose. However, if p is chosen from somewhere in between and everyone adopts the same mixed strategy, there is a non-zero probability that you, the individual participant, will win the billion. Thus, we now have to choose p so as to maximize our probabilities of success. (Alternatively, we can maximize the probability that the 5 billion are awarded at all. As we will see, the result is the same.) If you and everyone else each sends in their letter with a probability of p, the probability of your winning is p times the probability that exactly four of the other 19 players send in their letter. The overall probability of you winning a billion is thus p • 19 4 • p 4 • (1 − p) 15 , ( 4 ) where 19 4 is a binomial coefficient. We now choose p so as to maximize this term. Because 19 4 is a constant, we can maximize p 5 • (1 − p) 15 . (5) Incidentally, the p that maximizes this term also maximizes 20 5 • p 5 • (1 − p) 15 , ( 6 ) the probability that anyone wins at all. As it happens, Eq. (  6 ) is maximal for p = 1 4 , 27 which gives a probability of about 20% that the money is won, and thus a probability of about 20% • p = 5% that we win the money. Although a 20% probability of the money being won is better than 0%, it is still not quite satisfactory relative to the 100% that could be achieved with perfect coordination 28 . However, it seems as though there is no better way. We will revisit this question in section 2.8.9. While such coordination is qualitatively different from the other examples, it should still be seen as a form of cooperation (as opposed to some other applications of acausal decision theory like Newcomb's problem, or some coordination problems where all players have the same goal), because the game is positive-sum and (superrational) coordination improves everyone's outcome relative to CDT's recommendation. In Platonia five, the uncoordinated response involves everyone trying to get the money by sending in a letter. Many coordination problems suffer from the opposite problem, namely diffusion of responsibility. Consider the following example, versions of which were also discussed by, e. g.,  Leslie (1991, ch. 5 ) and Drescher (2006a, section 7.3.2): Superrational voting. You live in a country of superrationalists and today is election day. A strict secret ballot rule dictates that citizens are not allowed to tell each other which party they are going to vote for or whether they plan to vote at all. Unfortunately, going to vote costs a lot of time and you don't expect the potential impact of your vote to justify the opportunity costs. If you choose not to vote, then so will most of your fellow superrational citizens. That would be unfortunate. For one, the majority opinion of the people should be represented, if only because it is more likely to be your opinion. Besides, there is an uncorrelated minority that should not win, as all your superrational friends will attest! By what mechanism should you decide whether to vote or not? Again, the compromise utility function is not very informative. And again, a probabilistic (or mixed) strategy is optimal if the correlations are sufficiently strong overall and independent of the party one plans to vote for. To find out what exact probability should be chosen, one would need to come up with a term for the expected value under that probability, consisting of the cost of voting and the probability that some minority view wins, as well as the expected costs of the latter. Consider one last example, inspired by Pascal's button: Multiverse-reprogramming. Scientists inform you that the basic laws of the multiverse may be vastly more complicated than they originally thought. Specifically, they say there is a small probability that there exists some complicated and hard-to-find way of "reprogramming" parts of the multiverse. However, such reprogramming depletes some multiverse-wide resource pool. This means that the amount of reprogramming is independent of the number of agents who discover how such reprogramming can be done, provided that at least one agent discovers it and exploits it to full capacity. It would be unfortunate if no one in the multiverse seizes this opportunity or if everyone invests all their resources into finding it. As we have seen in the above thought experiments, we can use superrationality to solve this problem by determining some mixed strategy. Everyone lets some random process decide whether to invest significant resources into investigating the reprogramming mechanism, and then either pursues it fully or not at all. Once more, the compromise utility function does not tell us who should try to reprogram the multiverse; it does, however, tell us how each civilization should use the reprogramming mechanism. Note that this is another problem in which updateless weights (see section 2.8.6) are important, because once some civilization finds out how to reprogram the multiverse, it may be tempted to stop compromising.
 Schelling points We will now consider how we can get from a 20% probability of success in Platonia five to 100% under certain conditions. Consider the following variation of the dilemma: Platonia five with coordination help. S. N. Platonia is organizing another one of her eponymous dilemmata. However, this time she has compiled a numbered list of the participants beforehand. As a postscriptum to the standard content of the dilemma letter, Platonia writes: "Your number on the list of participants from 1 to 20 can be found on the back of this letter." Before looking at your number, is there any way the superrational participants can ensure that someone receives the money? In the original Platonia dilemma, the participants were all in the exact same situation. But now, different people have different numbers on the back of their letters. This can make a difference if, before looking at the back of the letter, the 20 participants agree on which numbers should respond to the letter. For example, all participants could precommit to respond only if their number is between 1 and 5, and only then turn the letter over and act according to their precommitment. In this way, they ensure that exactly five people send in a letter, thus maximizing the expected gains. (Also note that due to the symmetry of the situation, it also gives each player the same expected gains assuming that none of them are already suspicious about their position on the list.) In a way, the numbers on the back of the letter function as a coordination help that allows for coordination where it would otherwise be impossible. An even better coordination help would be one where each player receives a recommendation on whether to respond, along with a guarantee that only 5 of the 20 players will be prompted to respond. Alas, such direct coordination helps will usually be unavailable.  29  So how can people agree, without communicating, on which numbers should send in a letter? If the participants are guaranteed to be exact copies of one another, they can pick an arbitrary set of 5 numbers between 1 to 20 before checking the back of the letter, confident that the other 19 will choose the exact same set. In relevant applications, correlation will not be that strong. But since all agents have an incentive to settle on the same set of numbers, each could individually try to identify a set that is obvious or that stands out in some way. For example, the set of 1, 2, 3, 4 and 5 appears to be a candidate that others may choose as well  (as opposed to, say, 3, 7, 8, 11, 12) . Correlations play a role -if I choose numbers 1-5, then it is somewhat more likely that others do, too -but not a decisive one. Even if there are no correlations, abiding by such Schelling points (first introduced by Schelling (1960, chapter 3); see also  Friedman (1994, chapter I A) ) is beneficial to the individual player if she believes that (many of) the other players abide by that same Schelling point. In practice, many Schelling points are driven by minor yet obvious expected value arguments. For example, when someone mentions that they would like the window to be opened, the person sitting closest to it is often seen as the natural one to open it, because she does not have to walk as far as the others. This consideration is negligible, but it helps with coordination. Many Schelling points are also mere social conventions. For example, consider the issue with right-and left-hand traffic. Presumably, most people have no strong preferences between the two as long as drivers abide by the same standards when interacting with each other. Whenever two drivers drive towards each other on a road, they face the coordination game with a payoff matrix resembling that in Table  1  Countries have laws that tell citizens whether to drive on the right-hand or left-hand side of the road, solving this particular coordination problem. For multiverse-wide superrational coordination, such convention-based Schelling points are alas not available. The lack of a Schelling point could mean that it is impossible to reliably achieve optimal outcomes. Imagine meeting a member of an unknown society in a narrow alley. Should you pass them on their right-hand or left-hand side? Assuming there is no relevant established pedestrian traffic convention for that alley, there appears to be no way of deciding between the two.
 Coordination is relevant for everyone I suspect that most people who care about the multiverse have utility functions that "mostly" decompose additively, thus requiring little coordination. If you are in this majority, you may think the topic of superrational coordination is irrelevant for you. However, this view is mistaken, since the compromise utility function requires coordination if at least some superrationalists in the multiverse have utility functions that do not decompose into local ones. Of course, you could just ignore these value systems when constructing your compromise utility function, but this makes it more likely that other agents exclude you in other ways as well, as we will see in the following section.
 No reciprocity needed: whom to treat beneficially In this section, I will argue that the application of superrational cooperation requires no reciprocity. That is, none of the agents who benefit from our cooperation have to benefit us. Recall the basic argument for superrationality as based on non-causal decision theories: given that we are friendly, it is more probable that other agents facing similar choices will be friendly toward us and our values. Crucially, this argument does not require that the agents whose choices we acausally affect are the same as those who benefit from our own friendliness (2006a, section 7.2.1).
 Schemes of causal cooperation The classic cooperation scheme from causal cooperation is one of mutuality -"I scratch your back, you scratch mine", so to speak. This scheme is represented by the graph in Figure  6 . In mutual relations like this, it is possible to apply causal cooperation, although only if the interaction is repeated -i. e. if my choice causally influences the other agent's choice 30 , and then the other agent's choice can causally influence my choice, etc. 31 For introductions to causal cooperation, see, e. g.  Axelrod (2006) ;  Trivers (1971) ;  Fehr and Gächter (1999) ;  Dawkins (1976, chapter 12) ; Taylor (1987), and  Buss (2015, chapter 9) . Superrational cooperation also works in the above scheme, although repetition is not required. The prisoner's dilemma (with replicas or twins) is one example of this sort of problem.
 Circular cooperative structures and indirect causal reciprocity In principle, it is possible to establish causal cooperation even in cases where the two agents cannot directly benefit each other, provided there is a repeated causal link from my own decision to the decision of the agent who can benefit or hurt me, such that I can in some way reward cooperation and punish defection. As an example, consider the following variation of Hofstadter's donation game: Iterated donation circle. Like the circular donation game, only that the game is played many times (the exact number of times being unknown to the players). Donation circle. In every round, each participant is informed of their predecessor's past choices before deciding whether to send in 'C' or 'D'. Circular structures such as these can be represented by graphs such as the one in Figure  7 . Because each of the agents can causally (through the other agents) affect their predecessor, the iterated version of this problem could still, in principle, motivate causal cooperation. For example, one Nash equilibrium consists in everyone playing tit for tat. This Nash equilibrium is even stable, in the sense that one player diverging from tit for tat with a very small probability still leaves everyone else best off if they continue to use tit for tat. However, the same Nash equilibrium is also hard to achieve and unstable in a different sense, as it requires all 6 participants to use the same kind of strategy. Your response to your predecessor's cooperation is mediated by multiple other agents. If only one of them does not propagate your response correctly, the causal path from you to your predecessor is disrupted, leaving neither of you with a causal motivation to cooperate. For superrationality-based considerations, on the other hand, neither repetition nor the length of the causal path from one participant's cooperation to her predecessor are relevant. Instead, superrational cooperation only depends on the correlations between single pairs of agents. Hence, while the significance of causal cooperation in the Donation circle diminishes with every additional participant, the benefits from superrational cooperation remain constant regardless of how many players are involved.
 Hierarchies and acyclic graphs In an extreme case, there would be no causal path whatsoever from one participant's cooperation to that of his predecessor, making causal cooperation lose its entire appeal to the rational agent. Superrational cooperation, on the other hand, may still be applicable (cf.  Drescher (2006a, pp. 287-292) ; see section 6.1.1). Consider the following variant of the donation game: Donation ladder. Once more, Omega has a long list of participants, albeit a regular linear one this time. Omega sends all of them a letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. It explains that by sending in 'C', participants can increase their successors' payoffs by $5. The first person on the list cannot benefit from the cooperative behavior of others, and the last participant's choice has no effect on the others. Omega writes that each player can increase their own payoff by $2 if they defect. Participants do not know their position on the list, and are once again told that they all use similar decision algorithms. Every participant only cares about the balance of their own bank account, and not about Omega's or that of the other participants. Upon receiving the letter, should you cooperate or defect? Figure  8  illustrates the donation ladder. ... ... In such a cooperation scheme, causal cooperation cannot be established even if the problem is iterated, whereas the superrationality mechanism is just as reliable as in the other examples. Because the list is long, I probably have a predecessor; if I cooperate, then my predecessorwho is in a position similar to mine -will probably make the same choice. Cooperation thus informs me (or logically determines) that I am likely to gain $5, whereas defection only gives me $2. We can see this linear hierarchy of agents in practice among the different versions of an agent at various points in time. For example, I can causally affect the welfare of future versions of myself, but if I only (or primarily) care about my present experiences, they can never reward me in return. However, I could try to benefit future versions of myself to make it more likely that past versions of me have behaved nicely toward myself. More discussion with references to the literature is given by Drescher (  2006 ), section 7.3.4. Linear cooperation hierarchies come with a twist, however. Consider the following variant of the Linear hierarchical donation game: Donation ladder with known position. Identical to the linear hierarchical donation game, only that participants know their position in the list when they make their decision. A participant in the middle of the list may wonder how his situation differs from the regular donation ladder -after all, his predecessor on the list is in almost the same situation as he is. Assuming the conditions for superrationality are satisfied, their decisions should still correlate. Hence, if he cooperates, should we assume that his predecessor is likely to do the same? Not necessarily. The problem lies in the beginning of the list. The first person -let us call her No. 1 -will have no predecessor and thus no predecessor whose decision she could acausally influence, in effect giving her no reason to cooperate. Given this, No. 1 should defect (that is, unless she is already updateless; more on this below). Unfortunately, this puts No. 2 in a similar position. Realizing that No. 1 will defect, there is nobody left to benefit him. No. 3 will, in turn, reason that No. 2 expects No. 1 to defect, which means that No. 2 will also defect, leading No. 3 to defect as well. . . and so on, propagating down the entire list. You may notice that this propagating defection effect is analogous to the reason why standard game theory recommends to defect in the iterated prisoner's dilemma when the number of rounds is known 32 . Once more, we find that lack of knowledge is evidential power. For one, if the participants did not know their positions, they would all cooperate -and thus be more successful. If everyone could precommit to cooperation before learning about their position, they would do so. Again, cooperation can be maintained if all the agents are updateless in the first place (see section 2.4, cf.  Drescher (2006a)  In general, we can represent such hierarchical versions of the donation game using directed acyclic graphs like the one in Figure  9 . ... ... If participants knew their respective positions in the list, the considerations outlined for the Donation ladder with known position would apply analogously. In practice, such hierarchies may be hierarchies of power. Some agents are "lexically" more powerful than others, such that cooperation can only be beneficial in one direction -the less powerful have no way of helping the more powerful, while the powerful can help less powerful ones much more cheaply. As a perhaps paradigmatic example, consider a standard science-fiction scenario: Intergalactic relations. The universe contains many civilizations. Although they all followed similar evolutionary trajectories, each civilization developed at different times on different planets in different parts of the universe, and thus differ drastically in their levels of sophistication. Most civilizations eventually decided to conceal themselves to some extent, so no one knows which of the civilizations is the most powerful. You are the leader of a civilization, and one day, you encounter a comparably primitive civilization for the first time. According to your advisors, it appears that this other civilization has not even managed to harness the energy of their local star, they still suffer from diseases that your civilization's nano-devices could cure in an instant, and so forth. Your advisors, citing the other civilization's apparently laughable defense systems, recommend that you destroy them and use their resources to further your own goals. Should you follow your advisors' recommendation? Once again, causal reasoning may suggest that you should. By now, though, it should be clear that there are good reasons to ignore your advisor's recommendation if you believe there is a sufficiently strong correlation between your and the other civilizations. Note that one reason for civilizations to conceal themselves might be to induce a lack of knowledge about their relative positions within the hierarchy. If we remain hidden, other civilizations will be more likely to do the same, so neither we nor they would know who has the upper hand in a potential confrontation. On the other hand, if all civilizations loudly boasted their power, the most powerful civilization would realize its dominance and consequently have no reason to be friendly to the others -absent precommitment, the use of updateless decision theory, and the like. Another example of such power hierarchies is that of simulations. Simulators can causally influence the simulated in any way they want, but the simulated can do little to causally affect the simulators (e. g., by affecting the outcomes of the simulation or its computational demands). We will discuss this more in section 6.9. The following example may be typical of the hierarchies in multiverse-wide superrationality (MSR): Computable consequentialists. Meet Luca, who believes that consciousness cannot arise from classical computation alone.  33  He is also a consequentialist and primarily cares about conscious experiences. Through the writings of Tegmark, Luca has come to believe that many computable universes might exist in parallel to ours. However, since these computable universes do not contain anything that he would call a conscious experience, Luca does not care about what goes on inside them. He does, however, enjoy thinking about their inhabitants as an intellectual exercise, and this has led him to the conclusion that they can reason about Newcomb-like scenarios in a human-like way even though they are insentient. After all, neither calculating conditional probabilities nor operating on causal graphs requires sentience. Using the supercomputer in his basement, Luca has also come up with a number of predictions about the values held by consequentialists in the computable universes -let us call them the computable consequentialists (CCs) -a feat more difficult to achieve for incomputable worlds. He has even discovered a number of ways to benefit the CCs' values in our universe, all at a very low cost to his own values. While Luca himself does not care about computable universes, he sees no reason for the CCs not to care about worlds that are computationally more powerful than their own. Given that the CCs cannot do anything for Luca in their world, however, is it rational for Luca to be friendly to the CCs' values? Again, Luca does indeed have a reason to do so. If he benefits the CCs, other agentsincluding ones whom Luca cannot benefit -are more likely to realize Luca's goals in other parts of the multiverse. The ability to help can also come from knowing about the other agents. Consider the following example: Simple-world ignorance. Imagine a multiverse in which many different sets of laws of physics are realized. Some of the universes have very simple, parameterless, and easily understood basic laws, like Conway's Game of Life. Others have far more complicated rules. The inhabitants of the more complex universes may thus have more reason to believe in the multiverse than the inhabitants of the simple universes. In the complex universe, the multiverse hypothesis is attractive because it is simpler than the hypothesis that only their universe exists (cf. Schmidhuber, 1997). In the simple universe, on the other hand, the multiverse hypothesis may be more complex than the hypothesis that only their universe exists. Consequently, the inhabitants of the simple universes may adopt superrationality but only apply it toward other inhabitants of their universe. Let us assume that the values of the folks from the simple universes differ significantly from those of the inhabitants of the more complex universes. Should the inhabitants of the complex universes help the values of those from the simple universes? In this scenario, as with the previous ones in this section, I think that the superrationalists from the more complex universes have good reason to help the superrationalists from the simpler universes, as this makes it more probable that the former will receive help from other agents, including ones that they cannot help. For example, there may be many value systems that they (the inhabitants of the complex universes) do not know about (for reasons other than the Kolmogorov complexities of different multiverses). I think this particular scenario may well be relevant in our multiverse. More generally, some parts of the multiverse may contain different clues about the existence of other superrational agents. For example, some might live in parts of the universe from which it looks as though life is much rarer than it actually is, whereas others may discover that they are not alone as soon as they look through a telescope for the first time. In addition, while a superrational agent may be able to use some theory of physics to infer the existence of other agents, he or she may be unable to infer the existence of some particular value system.
 Only helping superrational cooperators helps you superrationally Cooperation usually excludes agents who are known to be unable to reciprocate. Yet as we learned from the Donation tree and Intergalactic relations, superrationality does allow for cooperation with non-reciprocating agents if helping them makes it more likely that other agents help us. There is, however, at least one limitation on the set of our beneficiaries that comes without negative side-effects. We can exclude from superrational cooperation all agents who do not cooperate superrationally at all. After all, every superrational cooperator knows that this exclusion will not affect her, and the exclusion appears to be symmetrical among all superrational agents. That is, it makes it more likely that other superrational cooperators make the same choice (rather than incurring some other limitation that excludes us). It seems risky to place any stronger limitation on the set of our beneficiaries, since this would give us reason to fear exclusion by other agents (cf. Drescher, 2006a, page 290), as we have seen in section 2.9.3. If we so much as try to look for rules of exclusivity that benefit us at the expense of other superrational agents, we have reason to believe that others will do so as well. Of course, superrationality and correlation between decisions are not binary properties, so neither is the limitation drawn above. For example, two artificial intelligences explicitly based on the same decision theory may correlate more than two (non-copied) humans, even if both have some incentive to cooperate. The stronger the correlation between us and some other agent, the more we will benefit superrationally from helping them (cf.  Drescher, 2006a, page 288f ). To illustrate this, consider a one-shot prisoner's dilemma-like situation (cf. figure  6 ) in which two very similar agents can simultaneously decide whether to give the other one some reward b other or to walk away with a smaller reward b u for themselves. Now, imagine the two agents are perfectly correlated, i. e. they always make the same decision. If this is the case, both agents should cooperate whenever b other > b u . ( 7 ) Now consider a situation in which the correlation between the two agents is weaker. Then, in EDT terms, they should cooperate if cooperation (C) is higher in expected value than defection (D). Using conditional probabilities, we can formulate this as Thus, the threshold for cooperation increases as the correlation between the two agents decreases. P (C | C) • b other > P (C | D) • (b other + b u ) + P (D | D) • b u = P (C | D) • b other + b u , If the cooperation graphs become more complicated, then so do calculations like those above. Further research is needed to find out whether the above result -that benefitting agents with stronger correlation is more important -holds true more generally. One interesting question is to what extent superrationalists would form clusters based on correlation strength. This is especially relevant if we believe the correlations to be especially strong among agents with the same value system.
 Cheating, signaling, and half-heartedness Causal and superrational cooperation differ in another important respect. In causal cooperation, the benefit of cooperative behavior comes from how other agents will react to one's own cooperative acts.  34  To facilitate cooperation, each agent may commit to reward cooperative and punish uncooperative behavior. In this way, they can motivate each other to cooperate. But seeing as behavior can only be rewarded or punished if it is observed at all, causal cooperation often ends up focusing heavily on signalling. If you can save costs by merely pretending (in a convincing way) to have cooperated, then that is the rational thing to do from a causal perspective. Conversely, if you can help someone without them knowing about it, you have no causal reason to do so. There are many practical examples of this, such as the tendency for governments to make a big deal out of international agreements or cooperative acts, even if the object-level gain is minor. Since the mechanism of superrational cooperation is different from that of regular causal cooperation, prioritization within it should be different, too. Specifically, superrational cooperation is beneficial not because others reciprocate one's cooperative acts, but because our (cooperative) decisions correlate with those of others. This means that we should sincerely attempt to maximize for benefits to other value systems, because this correlates with others doing the same, which in turn maximizes our own benefits. We are used to thinking about cooperation in causal terms, i. e. about how a certain cooperative act may in the end pay us back causally and in this universe. If we think about superrational cooperation in this mindset, we may be tempted to propose measures that are critically suboptimal from a superrational standpoint. For instance, one may adopt a "compartmentalized good will", talking at length about cooperation without actually trying to maximize for other agents' goal achievement, or spend time thinking about how the others might cheat us. However, all of these correlate with other superrational agents in the multiverse wasting effort on these exact same things. With superrational cooperation, only sincere attempts at improving other agents' value systems correlate with the same behavior in others, and thus with the optimal consequences. Hence, there is no way to "game the system" or to get benefits without honestly paying for them.
 Values We extensively covered the mechanism of (multiverse-wide) superrationality. However, in all thought experiments considered so far, we knew what impact our actions would have on the fulfillment of the other agents' preferences. For example, we know that the other participants in the donation game or Platonia five would prefer to have more money on their bank account. We also know that other civilizations would prefer not to be destroyed and would benefit from learning about our technologies in Intergalactic relations (section 2.9.3). Such knowledge has to be present or at least attainable in the future (cf. section 4.1), otherwise no side can benefit the others. This section gives an overview of how we can find out what other agents in the multiverse care about, as well as what aspects of their preferences we should focus on in the first place.
 Orthogonality of instrumental rationality and values One objection to superrational cooperation might be based on a possible convergence of terminal values, in which all agents with the correct decision theory will converge toward the same values. Moral realism claims that there are facts in morality as real and true as those in science. In addition, some moral realists believe that any rational agent investigating morality will ultimately arrive at these moral truths. Assuming that a large part of being rational involves using the right decision theory, maybe all agents with the right decision theory will independently come to adopt the "correct" moral system? If this is the case, no cooperation among these agents would be necessary (although some value systems may still require multiverse-wide coordination, see section 2.8.9). As a first counterargument, consider that knowledge of the correct decision theory is not necessary for superrational cooperation, seeing as a number of different decision theories (e. g., evidential, timeless and updateless decision theory) imply superrationality. Secondly, we do not seem to observe empirical evidence of such convergence. For example, Eliezer Yudkowsky and Brian Tomasik agree that non-causal considerations are important for decision theory, but Yudkowsky's values nevertheless differ significantly from Tomasik's. There are also principled reasons to be skeptical of value convergence among agents with the same decision theory. Decision theories are about instrumental rationality, i. e. about making decisions aimed at achieving goals, not at revising them  35  . That is at least the case for decision theories as they are discussed today. Consider the following variant of the donation game: Donation game for sadists. Omega has selected 20 pure sadists, who draw pleasure only from torturing others and nothing else. They all use similar decision making mechanisms when playing a donation game (against correlated agents). Instead of being paid in dollar sums, they are given individual hours to torture a slave as a reward. Assuming sufficient correlation between participants, the instrumentally rational decision for each sadist is to cooperate such that the total number of hours of torture increases relative to universal defection. The moral choice, on the other hand, would be to defect in order to reduce the number of hours in which anyone gets tortured. However, decision theories (as currently discussed in the literature) do not take moral considerations into account at all. They merely aim to fulfill the goals, whatever they may be, of the agent using that decision theory. Hence, when applied by a pure sadist, a given decision theory is meant to help her spend more time torturing others. 36 There could conceivably be some different kind of "decision theory" that does recommend taking morality into account (and not only cooperation, see section 6.7.1) even if the agent using it is amoral or immoral. One could, for instance, simply combine the correct decision theory with the "correct" moral view. Some people may consider such a decision theory objectively correct. However, for an agent with immoral goals (like pure sadism), it would be instrumentally irrational to adopt such a decision theory. In any case, the existence of such a "moral decision theory" does not contradict the existence of a decision theory in the classical, instrumentally rational sense, so an amoral or immoral agent would still be better off adopting a classical decision theory. Thus, it would seem that an agent's values and their use of acausal decision theories are orthogonal. This, in turn, suggests that agents with a variety of value systems will adopt a decision theory similar to our own, such that their decisions will correlate with ours. Similar views regarding the relationship between instrumental (and epistemic) rationality and ethical values have been defended under the term orthogonality thesis  (Bostrom, 2014b, ch. 7 , section "The relation between intelligence and motivation";  Bostrom, 2012; Armstrong, 2013) . Our claim that decision theory and values are orthogonal in principle does not imply that they never correlate in practice throughout the multiverse. Indeed, in section 3.4 and its companion papers, I will discuss various ways in which values and decision algorithms could be expected to correlate. However, it seems very unlikely to me that these correlations are so strong that they significantly dampen the relevance of superrationality.
 Necessary preconditions Before we start thinking about the values of agents in other parts of the multiverse, we need to consider what kind of agents can join multiverse-wide superrational cooperation (MSR) at all. In particular, what sorts of values do they need to have, independent of whether or how many such agents or value systems actually exist in the multiverse? We already know that only helping superrational or correlated agents benefits us (see section 2.9.4). However, the values of the superrationalists must also be open to the opportunity of gains from compromise. If an agent's values imply that she is better off without any trades, there is no point in helping her. In order to more closely examine this precondition, we can break it into five distinct criteria, all of which are necessary for a superrational collaborator to reap the gains from compromise. 1. Each collaborator must care to at least some extent about states of the world, as opposed to caring only about their own mental states or actions. 2. They must also care about consequences in areas of the multiverse where there may be other cooperators. 3. Other superrationalists must be able to infer and understand their values in sufficient detail. (To draw action-guiding conclusions from MSR, they themselves need to be able to infer the values of some other superrationalists or to influence future agents with this ability.) 4. Given this knowledge of their values, collaborators must have some power to behave nicely toward this value systems. (Again, if MSR is to be action-guiding to an agent, they in turn need to be able to benefit other values.) 5. Doing so produces gains from compromise. If everyone abides by an analogous cooperative strategy, everyone is better off than they would be without cooperation. If all these criteria are satisfied, superrational cooperation works. We will discuss them in turn in the following subsections. For some applications it may be fruitful to subdivide these criteria further. Furthermore, additional criteria, such as Bostrom's (  2014 ) "porosity", may determine the size of the gains from compromise. We could furthermore devise criteria to assess the extent to which superrational cooperation affects one's strategy. For instance, if all correlated agents have the same values anyway, superrational cooperation does not affect our policy except for cases of coordination (see section 2.8.9).
 Consequentialism Most people's ethical views are partly deontological (and sometimes virtue ethical). That is, they are not solely concerned about the state of the world and the consequences of actions, but als about "the actions themselves" (and, in case of virtue ethics, one's character). They usually try to follow some set of rules prescribing what actions are appropriate in which situations. For example, many people follow strict rules against killing (though these usually do not apply under all circumstances and the meaning of "killing" is rarely fully specified), even when breaking these rules would lead to fewer deaths. This type of ethical system forms a central part of many religious doctrines, with notable examples such as the Christian ten commandments, the Confucian filial piety, and the Islamic sharia. In addition, most national laws contain countless rules of this sort, many of which apply to more mundane domains like traffic or taxes. Isaac Asimov's three laws of robotics are yet another example of a deontological set of rules. The arguments for multiverse-wide superrational cooperation that I have given appeal to the consequentialist aspects of one's values -not because it requires us to push people off bridges (as in the Fat man version of the Trolley problem), but because its supporting argument is fundamentally based on the consequences of different actions. If we on Earth benefit other value systems, then this implies that others elsewhere in the multiverse also benefit our value system, which may produce better overall states of the multiverse overall via gains from trade. Hence, the value of superrational cooperation lies in its positive consequences on the world (or other worlds). The ethical duties of deontological ethical systems, on the other hand, usually concern the more immediate consequences of our actions. Thus, in a scenario like the Fat man version of the Trolley problem, most deontological would imply that the direct act of killing the fat man violates our duties towards him more than a failure to act violates our duty towards the five people on the track. In Bourget and Chalmers' (2014) survey of philosophers, 23.6% of respondents characterized their values as consequentialist while 44.1% identified as deontologists or virtue ethicistswith the remaining 32.3% choosing "other". However, most people probably espouse values that involve at least some consequentialist aspects (cf. Muehlhauser and Helm, 2012, section 5.3). I doubt that many modern consequentialists would be emotionally capable of murder or torture even under circumstances where they could be confident that doing so would yield the best consequences 37 . At the same time, I doubt that many defendants of rule-based ethics see no appeal in potentially reducing the amount of torture in the multiverse, even if only in an indirect way. In fact, many deontological rules are motivated or even defined by the consequences they produce. For example, murder is defined as any act that intentionally and directly results in the death of another person (although indirect ways of causing the same consequence (e. g., omissions) are not seen as murder). Rules against theft are often defended on the grounds that a society with such rules is preferable to one without, even if the rules might occasionally prevent a genuinely altruistic bank robbery. Some even interpret Kant's categorical imperative (especially its first "formulation") as a heuristic based on consequentially motivated decision-theoretical reasoning (cf.  Parfit, 2011, section 63; Hare, 1993) . As  Rawls (1971, ch. 6 ) writes, "deontological theories are [not defined] as views that characterize the rightness of institutions and acts independently from their consequences. All ethical doctrines worth our attention take consequences into account in judging rightness. One which did not would simply be irrational, crazy." Although most people refrain from the consequentialist choice in extreme situations, they do, in fact, often endorse it. For example, in  Bourget and Chalmers' survey (2014) , 68.2% of the respondents chose to pull the switch in the original trolley problem, and only 7.6% did not (with the remaining 24.2% choosing "other"). Pulling the switch is similarly popular among the general population. This suggests that people sometimes agree with consequentialist reasoning even if other, exclusively deontological or virtue ethical considerations can overrule it. Beyond consequences for things like the number of deaths, individual welfare, and fairness, people sometimes also care about the abidance by deontological rules in a consequentialist way. For example, most people not only avoid killing others themselves, but also care about preventing murders in general; many who personally avoid lying also strongly dislike it when others lie; and so forth. These kinds of consequentialism, which are rarely considered in the literature on moral philosophy, qualify for superrational consideration just as much as, say, utilitarianism. We will revisit this topic of caring about the deontologically ethical behavior of others in section 3.4.1, in which we review studies indicating that many people have values of this sort.
 Caring about the multiverse Presumably, some agents with significant consequentialist aspects to their values will almost exclusively care about their own part of the multiverse, if only based on egoism or absurdity heuristics 38 . It is thus very difficult or impossible to benefit them in other parts of the multiverse, in turn preventing cooperation. Although there is very little discussion about the moral relevance of other parts of the multiverse, the moral relevance of distance is frequently discussed in moral philosophy (see, e. g.,  Brock and Hassoun, 2013) . Note that while distance is usually understood to be spatial, other kinds of distance (e. g., temporal  (Beckstead, 2013)  or social) play similar roles in ethical judgment. While the debate in moral philosophy appears ambiguous, people's actions speak more clearly. Most people from high-income countries would save a child from drowning in a nearby pond, but donate only relatively small amounts to charity  (Singer, 1972) . Insofar as they do give to charity, they usually prefer local causes even though helping in low-income countries is more cost-effective. From this, we can safely infer that most people are altruistic to some extent, but seem to care more about near events than distant ones. One may suspect that an agent's ignorance about other parts of the multiverse would yield similar conclusions as a lack of interest. After all, if someone does not know about our part of the multiverse, they cannot help us. However, we must not forget that superrational cooperation need not be based on mutuality (see section 2.9). Even if someone cannot help us, we can still help them to make it more likely that we ourselves receive help from agents whom we cannot help.
 Knowable values In order to maximize for some given utility function, we or future superrationalists (see section 4.1) need a sufficiently detailed model of the utility function itself. In section 3.4, we will discuss how the evolutionary psychology of morality and related disciplines can be used to assess the values of superrational cooperators in the multiverse. There are at least some ways of making very educated guesses, although we cannot expect to arrive at a detailed and precise description of the values of all evolved civilizations and their descendants. However, perfect knowledge is not necessary for our purposes. Indeed, most people cannot even describe their own values in detail (see footnote 25). Yet despite this, humans are perfectly capable of helping one another achieve their goals. Thus, the question is neither whether we can gain relevant knowledge about the values of other agents in the multiverse at all, nor whether we can have a full map of extraterrestrial morality, but whether the information we can gather about other civilizations can be sufficiently accurate to yield a usable model.
 Fragility of value Yudkowsky (2015, ch. 279) argues that human values are not just complex (cf. section 3.4.1); they are also fragile, in the sense that even minor errors in a non-human agent's picture of them can completely derail that agent's efforts to optimize for them. According to Yudkowsky, "Any Future not shaped by a goal system with detailed reliable inheritance from human morals and metamorals, will contain almost nothing of worth." Perhaps more generally, we could say that any resource expenditure will generate next to no value for an intelligent evolved being X unless that resource expenditure is shaped by a detailed inheritance of X's morals and metamorals. Yudkowsky gives boredom as an example of a small but indispensable part of human values: "Consider the incredibly important human value of 'boredom' -our desire not to do 'the same thing' over and over and over again. You can imagine a mind that contained almost the whole specification of human value, almost all the morals and metamorals, but left out just this one thing and so it spent until the end of time, and until the farthest reaches of its light cone, replaying a single highly optimized experience, over and over and over again." Presumably, many other seemingly insignificant aspects of human values are of similar importance as boredom. One would need to get all of these aspects just right in order to benefit human values. This suggests that it will be difficult to benefit many evolved value systems, due to the large amount of detailed knowledge it would require and the difficulty of gathering that knowledge. There are various points to discuss in this context. For one, the fragility thesis is rather vague; it does not say how fragile our values are, or how accurate and reliable the inheritance must be. This is not to say that the fragility thesis makes no testable claim at all. Yudkowsky formulated it with the value loading problem of artificial intelligence in mind. Since AIs can be programmed to pursue any goal (cf. section 3.1), the space of possible values with which an AI could end up is vast, and the target goal systems occupy only a small fraction of this space. The fragility hypothesis can be interpreted as one elaboration on just how small this part of value space is, and how catastrophic it would be (from the perspective of that value system) to miss it by even a small margin. In other words: even if we take care to represent all of the most central aspects of our values (e. g., "increase the welfare of sentient beings" or "reduce inequality") in the goal system of an AI, the outcome may still be as bad as an entirely random one if we omit seemingly peripheral values such as boredom. Although I agree with the fragility thesis as a descriptive (rather than normative) statement about human values, I do not think human values are quite as fragile as Yudkowsky writes. Specifically, I think the outcomes brought about by AIs with two different goal systems can differ enormously in their overall worth even if both miss important aspects of human values. For example, Yudkowsky's hypothetical world full of repetitive happiness may be boring, but it is still much better than a world full of suffering, unethical behavior, etc. and nothing of worth to compensate. But perhaps this judgment is influenced by my own values (which are mostly about ensuring the welfare of sentient beings with a strong priority for preventing their suffering), to the point where it would not generalize to how other humans, or other evolved agents in general, would view the situation. Transferred to our variant of the fragility thesis, this nevertheless suggests that even if we miss significant parts of the values of other superrational cooperators, taking their values into account may still make a big difference to them. More importantly, AI value loading differs significantly from our attempt to benefit agents in other parts of the multiverse. The main problem of AI value loading is getting the AI to care intrinsically about human values. MSR, on the other hand, already gives us the sincere (instrumental) goal of helping other agents, which the AI lacks. If anything, we lack knowledge of the others' values, whereas AIs may still not care about them even with perfect knowledge of their values. Another crucial difference between these two contexts is that in AI value loading, we usually want the AI to hold the values of one particular species or group of people. In contrast, when cooperating superrationally, it is sufficient to know that we benefit many other superrational agents. We do not need to know whether we benefit some particular species. The extent to which this makes our job easier depends on how evolved value systems are distributed over value space. Perhaps they form a few (or many) very small clusters, as depicted in Figure  10 . (Needless to say, Figure  10  is not meant to be an accurate map of value space. The placements on the map have no factual basis.)
 Utilitarianism Human values Figure  10 : A map of a part of value space under the assumption of there being distinct clusters with a lot of empty space in between. Every blue point on the map is some value system held by a significant number of agents. The white areas of the map contain value systems that do not have a significant following, such as paperclip maximization. If our map really did represent value space and each individual value system is fragile, then it is difficult to benefit other value systems, because if we miss the targets only by a bit, we end up with a value set that nobody cares about. However, it could also be that the values of different evolved agents occupy some compact part of value space, as depicted in Figure  11 . In this map, darker areas represent value systems with many agents and lighter areas indicate value systems with fewer agents. If value space looks more like this map than our previous one, then it is easier to make "guesses into value space" to help superrational collaborators. As long as one is roughly aiming at the right part of value space, small errors just mean that one benefits slightly different superrationalists than intended. Only a few maps of humanity's value space have been created, the best-known of which is probably the Inglehart-Welzel cultural map of the world. I would nonetheless wager some guesses as to how more fine-grained maps of values would look like: on any individual planet, there are clusters formed by major religions, nations, political camps, and other cultural groups. For example, there are many people who hold many of the moral views of the Quran and many who hold many of the moral views of the Bible, but presumably much fewer who defend a mix of the two. Nonetheless, the space between the clusters is not completely "uninhabited". Furthermore, the existence of these clusters seems to be partly arbitrary, a
 Human values Utilitarianism Figure  11 : A map of a part of value space under the assumption that extant values occupy a relatively compact part of value space. mere result of the way that different ideas were packaged together historically. If things had gone slightly differently, as they doubtlessly do in other parts of the multiverse, the authors of the Bible may have written that it is mandatory to fast during the month of Ramadan, thus filling a spot in value space with life that is only sparsely inhabited on Earth. If the multiverse is large enough, all these possible variations of values are realized somewhere and probably no less common than the two religion clusters on Earth. One last difference between the way we extract values from other superrational cooperators and the way AIs might receive their values from humans is, of course, that the former involves no direct contact. Section 3.4 will address ways of circumventing this problem in order to identify the values of agents elsewhere in the multiverse.
 The ability to help others In some cases, it will not be in our power to help other value systems at all. Since any will to cooperate with these agents cannot possibly be action-guiding, we do not have to help them. Other agents in the universe may have other resources available to them and thus choose to behave in a friendly way toward these values. If, on the other hand, agents know that nobody else can help them to achieve their goals, multiverse-wide superrational cooperation (in particular, any version of it in which they just give resources away) becomes less attractive to them. One example of a value system that we cannot help is the following version of speciesism (that may or may not be a straw man): The Namuh-centrists. One day, scientists inform you about a highly intelligent species of extraterrestrials known as "Namuhs". Like us, the Namuhs have built a flourishing civilization with art, trade, science, language, humor, philosophy (including advanced decision theory research), and so on. However, the Namuhs do not live in our universe, but in a distant part of the multiverse, completely inaccessible to us. In fact, they could not even exist in our part of the multiverse, as their bodies require slightly different laws of physics to function. Knowing about superrational cooperation, you hasten to ask whether they have thought about problems analogous to Newcomb's problem and the donation games between similar agents. A trustworthy scientist explains that their minds are indeed prone to thinking about such topics -much more so than those of humans, in fact! Understandably thrilled, you ask what values the Namuhs have, and specifically what values are held by those who have thought about acausal cooperation. The scientist then informs you that all Namuhs are very narrowly focused on their own species. They are Namuh-centrists who do not care one bit about anything that does not involve fellow Namuhs. For example, they shrug at the thought of non-Namuh suffering, the flourishing of non-Namuh civilizations, or non-Namuh well-being. In fact, they are so strict that they do not even care about simulated Namuhs or other approximations. Learning about their values, you may be disappointed. There is nothing that you can do to help them and it is therefore irrelevant whether they use a decision theory similar to yours or not. I should point out that the speciesism endorsed by the imaginary Namuhs is very rigid and more narrow than most other views that we would usually classify as speciesist. Far from caring only about their own species, most people seem to care about the welfare of non-human animals to at least some degree, usually privileging some species (like cats and dogs) over others (like pigs and cows). Such views classify as speciesist, but nevertheless allow for superrational cooperation. Other views do not value humans over other animals for their species membership per se, but instead privilege other characteristics that (allegedly) only humans (and sometimes a few other species) possess. A common variant of this holds 39 that only members of very few species are conscious. Humans are one of them, but, according to such views, they otherwise do not deserve any special moral status. Given the implications of this view, proponents are sometimes (and often incorrectly) branded as speciesist. If the Namuhs were to hold such a view, and humans (or other earthly species) meet their criteria for consciousness, then our decisions can be beneficial or detrimental to the Namuhs' preference fulfillment. A similar reasoning applies to the possession of language, free will, the ability to pass the mirror test or other (potentially) strict but non-speciesist restrictions to one's set of morally relevant agents. There are other reasons why we might be (practically) unable to help other agents. For example, helping an agent could require some set of specialized abilities that they themselves developed based on their value systems. Consider the following example: The Advanced math maximizers. One day, you learn that out there in the multiverse, there are civilizations made up entirely of mathematicians whose primary concern is maximizing mathematical knowledge. They don't care about the number of established truths or proofs per se, but rather value pieces of knowledge based on their novelty or interestingness, possibly resembling the way earthly mathematicians often prioritize their research. For instance, the mathematicians place a very high value on a proof or disproof of the Riemann hypothesis, whereas mundane factoids like the three-billionth digit of π have very little value in comparison. Moreover, once a fact becomes known to at least one of the mathematicians, reproducing that same piece of information elsewhere in the multiverse creates no additional value for them. (We assume that the universe is finite -otherwise every piece of knowledge may be known to some Boltzmann brain.) While they are not particularly skilled at anything else, their strong intrinsic motivation and dedication has made them into truly excellent mathematicians, unrivalled by anyone across the multiverse. It is not easy to benefit the advanced math maximizers. We do not know what knowledge they already possess, and given their level of skill, we should assume that they will come up with most interesting pieces of mathematical knowledge that we could devise on our own. The math maximizers are thus so capable of maximizing their own utility function that there is little we could do to assist them (cf. section 3.2.5).
 Zero-sum and "below-zero-sum" tradeoffs on resources Not all interactions between agents allow for cooperation. Specifically, there is no way or reason to cooperate in zero-sum games, i. e. ones in which the overall payoff is always the same. Consider the following example: The Maximizer Monarchs. Imagine a multiverse consisting of two universes. One is ruled by a queen whose only drive it is to create as many paperclips as possible. The other universe is ruled by a king who only cares about producing as many staples as possible. Each stationery-maximizing monarch knows that the other exists and that they both use the same decision algorithms. They each have one hundred tons of steel at their disposal. What should they do with it? Assuming that staples (specifically the kind of staples that the queen cares about) cannot be built out of paperclips or vice versa, this interaction is zero-sum. Every bit of material that one of them uses for the benefit of the other is an equivalent loss to themselves 40 . Thus, no form of cooperation between the two is beneficial. As the reader may suspect, zero-sum interactions are rare. We should expect that any given resource is better suited to achieving one goal than another and so trade can arise from allocating resources based on what value systems benefit most from them. Analogously, value systems care more about certain situations than others. Furthermore, whereas it may not be possible to combine a paperclip and a staple, many goals are compatible with each other. For example, a society's citizens can at the same time be happy and virtuous.
 Gains through specialization and comparative advantages At times, trying to achieve multiple goals at once is not just pointless -it can actually be worse than having each agent focus on one, typically their own, goal. To see how, let us revisit The Maximizer Monarchs of the previous section: The Ever-improving Maximizer Monarchs. Like The Maximizer Monarchs, but this time, the efficiency at which each agent can produce paperclips or staples grows monotonically with the produced quantity. Again, each monarch wields one hundred tons of steel. Without delving into mathematical details, it is best (in terms of overall number of paperclips/staples produced) if each of the two specializes in one kind of stationery. In particular, there are no gains from compromise over each monarch maximizing only for their own goals. There may also be comparative advantages from the outset. Based on their respective motivation and prior experience, the queen may already excel at producing paperclips, while the king may be better at producing staples. Another important source of comparative advantages is unequal knowledge about different value systems. For example, if the queen does not know exactly what the king cares about, then she will be worse at benefitting him. Similarly, our knowledge of what other humans care about is much more precise than our knowledge of what agents elsewhere in the multiverse care about. The fact that specialization and division of labor play such a crucial role in the economy suggests that superrationalists will also tend to focus on a single goal rather than maximizing for multiple things at once. However, I think that this will not be the case, at least in our present situation. The primary reason is that the instrumental goals of agents with different moral values are often the same. For example, no matter the direction into which we would like to drive society, we will try to acquire money and political influence. These resources are often generic, such that when they are acquired with one goal in mind, they can also be employed in pursuit of another. As an example, consider how Donald Trump maximized his personal wealth for a long time, yet his resulting fame and money nevertheless enabled him to become president of the US, which in turn allows him to achieve all kinds of goals. The fact that instrumental goals tend to converge suggests that superrationalists in the multiverse rarely have a strong comparative advantage at achieving their own goals. If comparative advantages are not strongly aligned with goals, specialization can produce gains as well. For example, imagine a number of superrational agents, each of whom would like to maximize many different things separately, e. g., knowledge, fun, happiness and technology. Here, a no-compromise outcome -i. e. one wherein each agent only maximizes their utility function in their own universe -might be worse than a potential division of labor with one agent focusing on generating knowledge, another one focusing on fun, and so forth.
 What values? To help other agents, one at some point needs to have some workable model of their preferences. In general, it is difficult to extract preferences from a given agent if the agent is not von Neumann-Morgenstern (vNM) rational and cannot state her goal explicitly. Humans surely are not vNM-rational. Additionally, moral judgments are usually seen as being inaccessible to us in their complete form (see footnote 25) and as emerging from the whole brain rather than exclusively from, say, the anterior cingulate cortex. This makes sense from an evolutionary point of view. Preferences are tools for increasing the fitness of an organism, and there is no reason to assume that such tools would be any more open to scrutiny by the organism than, say, the detailed inner workings of the digestive system. In addition, while most organisms have rudimentary mechanisms for avoiding harm and seeking food and reproduction, holding grudges -i. e. a preference for retaliation -is only adaptive in non-solitary organisms with sufficiently good memory and recognition to correctly identify transgressors. In the evolutionary process, different values thus evolve separately and are unlikely to form a coherent whole (cf.  Dennett, 1991; Kurzban, 2012) . Thus, even if we had a complete model of our superrational collaborators, it would nevertheless be difficult to extract clear-cut values from them. In the absence of such exact models, it makes little sense to for us to discuss the technical details of relevant preference extraction algorithms 41 . We will, however, still need to think about informal ways of inferring preferences from a model of a superrational collaborator.
 Idealization One dimension along which preference extraction algorithms vary is the extent to which they idealize values. Consider the following example of preference idealization (adapted from a recent blog post of mine): Steve holds a glass of transparent liquid in his hand. A woman walks by, says that she is very thirsty and that she would like to drink from Steve's glass. What she does not know, however, is that the water in the glass is (for some unspecified reason) poisoned. Should Steve allow her to drink? Most people would say he should not. While she does want to drink from the glass, her desire would probably disappear upon learning of its content. Therefore, one might say that her object-level or stated preference is to drink from the glass, while her idealized preference would be not to drink from it. Similar questions apply to ethical preferences. For example, most people find meat consumption acceptable on the object-level, but are simply unaware of information about the world that could change their minds, e. g., knowledge about the similarities between human and animal minds or the conditions in factory farms and slaughterhouses. Perhaps these people's idealized preferences favor vegetarianism? If we reduce meat consumption, should we count it as beneficial to people who approve of eating meat, but who could be convinced otherwise? Should we, in other words, idealize our collaborators' values when taking them into account in this universe? Besides gaining more information about the world, people's preferences may also change upon engaging with moral arguments (e. g., the original position or the drowning child argument). Even though such arguments do not provide new facts, they may invoke trains of thought that lead people to change their moral position. Should we also idealize preferences based on such moral arguments? At least idealization based on moral argument can cause trouble. For one, some moral arguments can be viewed as potentially illegitimate "tricks" for persuading people to adopt undesired positions 42 . An extreme example of this could be some moral or religious scripture that hypnotizes and brainwashes the reader. Surely, nobody would want other superrational collaborators to apply such a treacherous "idealization procedure". 41 Examples are described in Hansson and Grüne-Yanoff (2012),  Varian (2006) ,  Neumann and Morgenstern (1953) ,  Ng and Russel (2000) , and  Oesterheld (2016) . Also consider Brian Tomasik's How to Interpret a Physical System as a Mind. 42 One class of such tricks is described in my blog post Cheating at thought experiments. Order effects constitute another problem in using moral arguments to idealize preferences. Depending on the order in which we present someone with moral arguments, they may lock into a position and resist further arguments. If someone's moral views allow for more than one such lock-in they may not be uniquely idealizable. A recent study by  Schwitzgebel and Cushman (2012)  shows that even philosophers exhibit order effects when considering thought experiments. In general, we may view agents as having (meta-)preferences regarding idealization. These determine how exactly they would like to have their values idealized. We should then abide by respective agent's preferences, since we can then expect others to idealize our values in the way that we want them to be idealized. Unfortunately, this solves the problem only theoretically. In practice, finding out what idealization procedures other superrationalists would approve seems very difficult. 43 For more thoughts on preference idealization, the reader may consult any of the following:  Yudkowsky (2004) ;  Grill (2015) ;  Muehlhauser and Helm (2012) , chapter 6; the Negative Utilitarianism FAQ, especially section 2.1; section 15 of Brian Tomasik's Hedonistic vs. Preference Utilitarianism; and my blog post entitled Is it a bias or just a preference? An interesting issue in preference idealization, in which I discuss the specific issue of removing cognitive biases from preferences. 44
 Beware motivated idealization One potential pitfall of idealizing another agent's values is that it might bias the result toward one's own moral views if one is not careful. After all, you will be more familiar with the arguments and thought processes that favor your own position, and they will seem more convincing to you than the arguments you know in favor of other positions (if you knew of similarly strong arguments in favor of other positions, there is a good chance you would have adopted them already). Such a process of legitimizing what we already want to do via superrationality-based reasoning could be nicknamed "superrationalizing". For instance, I might be tempted to think that supporters of deep ecology and (non-anthropocentric) environmentalism would, if they were rational, update their views significantly upon learning about Darwinian evolution and wild animal suffering. I may even presume that deep ecologists would support intervention in nature or even habitat destruction under idealization! While I do indeed think that many people's judgment of nature and preservation would change significantly upon understanding the above topics 45 , I am worried about what such an aggressive stance on idealization tells me about the way other agents might go about idealizing values. For instance, when idealizing my values, environmentalists might reason that I just never thought enough about the beauty of nature. "If only this Caspar guy had taken the time to really contemplate the natural world in all its magnificent complexity, he would not think of nature as a tragedy, no matter how 'red in tooth and claw' it may be." Consequently, they might conclude that it is in my idealized interest if they lobby for leaving nature untouched or even spread it to other planets. I would not want others to idealize my values in such a way. While it may be true that a sufficient amount of time spent enjoying beautiful landscapes could convince me that nature is beautiful, I might not view that as a legitimate idealization procedure, as it merely reinforces conservationist arguments rather than offering new arguments or some form of balanced view. An example of a more obviously flawed extrapolation process is that of a mother reasoning that everyone's idealized values would be to prefer her son over all other children. After all, if they only spent enough time with him (just as she did), they would surely prioritize his well-being over that of other children! Once again, the respective idealization process seems unduly biased towards a certain position and will thus be rejected by most agents' meta-preferences.
 Values and distance People care about things differently depending on whether they happen nearby or far away in space and time. For example, while many liberals and quite a few conservatives politically favor legalizing cannabis, I expect that many of them would nevertheless feel mildly annoyed or uncomfortable if their best friend, spouse, or daughter were to start smoking it on a regular basis. For brevity, I will use the term near values for the part of our values that are about near things and far values for the part that is concerned with distant things. Both in the ancestral environment and today, most people operate primarily on their near values (with one notable exception being politics). In the context of superrationality, however, we are only interested in far values. Most other superrationalists are so far away from us that our values pertaining to their worlds fall under our far values. Hence, we want ETs to consider only our far values, which in turn means we should only consider the ETs' far values as well. That is, we do not need to know how they want their friends to treat each other, how they feel about drug use in their own social circles, and so forth. (Some think that the discrepancy between near and far values should disappear under idealization; we will discuss this below.) According to construal level theory, the difference between near and far values mainly results from the difference between two kinds of thinking or construal: concrete (or low) and abstract (or high) levels of construal. Which level of construal is applied mainly depends on the psychological distance to an event, i. e. the combined temporal, spatial, social and "hypothetical" (near = likely, far = unlikely) distance. People tend to construe psychologically near events concretely and psychologically far events abstractly. A recent summary of construal level theory is given by  Trope and Liberman (2010a) . The mapping between levels of construal and psychological distance is imperfect. We sometimes think about psychologically distant things concretely, such as when watching a science-fiction movie, and about psychologically near things abstractly. Nevertheless, the mapping is useful. While there is little theoretical and empirical research on how people (and other evolved creatures of human-level intelligence) think and care about alien civilizations, there is some research on how people generally care about other psychologically distant and abstractly construed things. According to construal level theory, the abstract mode of thinking is similar regardless of the kind of psychological distance that is involved. Thus, we can use general research about abstract construal values to at least inform our first tentative guesses about values in the particular case of caring about distant civilizations. We have some reasons to expect construal level theory to generalize to other evolved beings. According to Trope and Liberman (2010a, section III, subsection "Discussion"), High-level construals and low-level construals serve different cognitive functions. High-level construals have evolved to represent distal objects because, with distance, one needs to conserve the essential, invariant properties of the referent object. In contrast, low-level construals preserve the object in minute detail for immediate use. The fact that abstract and concrete construals solve different problems suggests that they evolved separately. Indeed, low-level construals probably evolved earlier. Whereas processing one's immediate surroundings and short-term goals is necessary for any animal to survive, many can get by without processing psychologically distant things. Some of the feats achieved by civilization-forming species, on the other hand, require abstract thinking. In the conclusion of their paper, Trope and Liberman (2010a) write: The turning points of human evolution include developing tools, which required planning for the future; making function-specific tools, which required considering hypothetical alternatives; developing consciousness, which enabled the recognition of distance and perspective taking; developing language, which enabled forming larger and more complex social groups and relations; and domestication of animals and plants, which required an extended temporal perspective  (Flinn, Geary, and Ward, 2005) . Human history is associated with expanding horizons: traversing greater spatial distances (e. g., discovering new continents, space travel), forming larger social groups (families vs. cities vs. states vs. global institutions), planning and investing in the more distant future, and reaching farther back into the past. In sum, I see some good reasons to expect that construal level theory applies to many other evolved species of human-level intelligence.  46  It thus matters whether we optimize for others' near or far values. Interestingly, we may also see the difference between different construals and thus near and far values as a cognitive bias that would disappear upon reflection, and that we should correct for in preference idealization. This may well be the case, but it is unclear which of the two views is more "correct" about ethics. One may argue that only thinking about concrete events can yield actual moral judgments, while abstract thinking may result in imagining a situation inaccurately or not at all and thus being unable to assess it correctly. Moreover, we tend to have weaker attitudes in general toward distant things than towards close things, 47 and this also seems to apply to moral weight assignment. 48 46 The presented argument resembles the general argument for modularity in evolutionary psychology (see, e. g.,  Cosmides and Tooby, 1994) .  47  For example, people prefer to receive money immediately rather than in the far future. They are risk averse and, of course, care more about socially close individuals. 48 For example, thinking about a concrete, identifiable goal or benefactee seems to be associated with feeling happier from donating money  (Rudd, Aaker, and Norton, 2014) . People are more motivated by (concrete) identifiable victims than by (abstract) large numbers of victims, although a recent meta-study by S.  Lee and Feeley (2016)  shows the effect to be small. People are also more relativist when judging the acts of extraterrestrials and people from other cultures  (Sarkissian et al., 2011) . Some arguments in moral philosophy evoke concrete construals (e. g., the fat man trolley problem or the drowning child argument) and some evoke abstract construals (e. g., the original position or many of the examples from my blog post Cheating at thought experiments)  49  . Both classes contain arguments that I find useful and legitimate. This suggests that neither of the two is morally superior across the board. Trope and Liberman (2010a, section VI) describe several experiments wherein high-level construals seem to capture the participants' values, whereas low construals led people to give more weight to "local" circumstances (such as social pressure and lack of self-control) (cf. Trope and Liberman, 2010a, section VII, subsection "Affect"). In high levels of construal, people tend to judge consequences more by their desirability than their feasibility, and thus assign more weight to moral views. More recent studies like those of  Torelli and Kaikati (2009)  and  Agerström and Björklund (2013)  have corroborated this result. However, it could also be interpreted as an indication that abstract thinking makes people more hypocritical.  Yang, Preston, and Hernandez (2013)  summarize further evidence in favor of giving more weight to high-construal judgments: High-level construal is associated with [...] an analytical, critical-thinking mindset  (Torelli and Kaikati, 2009) . For example, people at a high level of construal are [...] more comfortable with messages that convey mixed emotions  (Hong and A. Y. Lee, 2010) , suggesting greater cognitive flexibility. Indeed, previous literature showed that when an object is distanced from the self, individuals are less likely to be "trapped" in their own preconception or knee-jerk reactions  (Kross and Grossmann, 2012) . Moreover, high levels of construal may enhance perspective taking toward others whose interests conflict with one's own. That said, abstract thinking is not without its systematic failure modes. It is, for instance, associated with overconfidence and the illusion of explanatory depth  (Alter, Oppenheimer, and Zemla, 2010) . Further thoughts on the topic are given by Samuel Hammond in How to Conceptualize Morality: Near vs Far. In any case, we should keep in mind that idealizing away the difference between near and far values may be inconsistent with many agents' meta-preferences.
 Different kinds of preferences People often report that preferences in different domains feel qualitatively different from one another. For instance, it is common to distinguish moral preferences from other preferences. My preference for world peace over war is a moral one, for instance, but my preference for bananas over carrots is not. Of course, this line between moral and non-moral values is often blurry. For example, it is unclear whether wanting revenge or a cancer victim's desire to focus altruistic efforts on cancer research are moral preferences. I think a distinction between moral and non-moral preferences can also be drawn among far values. For example, my preferences for beings in other parts of the multiverse to be happy rather than to suffer is a moral one, but I would not view my preference for these civilizations to be fascinating, fun, or otherwise beautiful to my eyes (in the way that advanced civilizations in science fiction movies are) as a moral preference. Others might disagree, but that dispute is not worth exploring in this paper (indeed, I suspect it may be a largely verbal one). Potential criteria for this distinction between moral and other preferences may be that moral preferences are those we want others to share or that are somehow universal. Another distinction could be one based on a dual-process theory of morality (see Greene 2013, part II for an overview and references to the literature). Or consider  Sarma and Hay (2016) , who propose that "what we call human values can be decomposed into 1) mammalian values, 2) human cognition, and 3) several millennia of human social and cultural evolution." I do not think such distinctions are necessary when cooperating superrationally. Instead, we should focus on all preferences that are action-guiding to the respective agent (if this is not included in the term "preference" anyway 50 ), irrespective of whether they are "moral" or "mammalian". By definition, if I have to decide between two courses of action and one of them better suits the preferences that guide my actions, I will choose that one. In the case of superrationality, only accounting for other agents' action-guiding preferences correlates with others also taking only my action-guiding preferences into account. Therefore, taking all action-guiding preferences into account is best according to my action-guiding preferences. Hence, we should only take steps to fulfill the action-guiding preferences of other superrational collaborators, ignoring any other preferences they might hold. Given the above, I shall in this piece not differentiate between moral and other far values. Instead, both terms will be used to signify our action-guiding far values.
 The values of our superrational collaborators in the multiverse Having outlined what kinds of values we would like to know about for multiverse-wide superrational cooperation (MSR), we can finally proceed to discuss these values. Whereas it is not strictly necessary for us to know about our cooperators' values right away in order to benefit them (see section 4.1), such knowledge is surely useful and has to be attained at some point. In fact, one objection to MSR that many people have brought up in private conversation is that given our uncertainty about other value systems in the multiverse we should focus solely on our own values (also see section 6.11). As readers may suspect, a comprehensive discussion of this topic is beyond the scope of the present paper. However, we will give an overview of how we (or future superrationalists) can gain knowledge about the values of our collaborators elsewhere in the multiverse. Besides guiding future research, this overview will also demonstrate that we can learn anything about their values in the first place. 50 Many definitions of preferences are based on choice (see footnote 41). Some examples where preferences may not be what our choices reveal include: • akrasia and lack of willpower, as it manifests itself in procrastination and inability to adhere to exercise routines and healthy diets; • preferences about fiction, as people often care deeply about how a story ends but usually without trying to lobby or coerce the authors to satisfy that desire  (Radford and Weston, 1975; Schneider, n.d.) ; and • preferences for states of affairs that are mathematically inconsistent or physically impossible (Oesterherld, 2017b). It seems as though there are two main ways of assessing the values of other agents in the multiverse. The first involves empirical research into the values of superrational cooperators on Earth. Because the sample size is so small, we may also look at humans in general, under the assumption that the values of superrationalists resemble the values of their native civilization. It may be that the values of superrationalists differ from those of other agents in systematic and predictable ways. General human values may thus yield some useful insights about the values of superrationalists. That said, it may be that only a small fraction of superrationalists in the multiverse are human-like. For example, it could be that most other superrationalists are artificial intelligences and whole-brain emulations. It could also be that many other evolved agents are very different from us. The other approach involves understanding the processes that generate and select the values of agents in the multiverse, such as biological and cultural evolution, the transition to superintelligent AIs, etc., and extrapolating them into workable predictions about the preferences of agents on other planets. In principle, this approach is sufficient for gathering a good map of the values of civilizations throughout the multiverse. In practice, however, it is probably very difficult to accurately predict how these processes play out. A combination of both approaches might be easier to work with. We can begin with human values as a baseline and inspiration for what kinds of moral attitudes may exist, and then review whether the processes of biological and cultural evolution systematically favor these attitudes. This would enable us to find out whether they are coincidental and hence rare in the multiverse, or necessary and thus common. At the same time, we will of course need to avoid being biased toward human values, making sure not to drift off into telling just-so stories about why some human practices and values might be universal among evolved agents of human intelligence  (Buss, 2015 , chapter 2, section "Methods for Testing Evolutionary Hypotheses"). Theoretically, we or future superrationalists need to find some way of coming up with new moral values, i. e. ones that we do not observe on Earth. Based on a model of the values of evolved agents we can then think about the values of these agents' descendants (whole brain emulations, superintelligent AIs). Assessing the action-guiding, consequentialist far values of agents in the multiverse could be a scientific (sub-)discipline in its own right. That being said, I do not expect there to be a "Journal on Extraterrestrial Value Systems" to materialize anytime soon. Untestable speculation about ETs does not inspire academic respectability. In researching this paper, I did not find much prior work on any aspect of the values of evolved agents in the multiverse, which in turn makes me less than hopeful that the more specific issues pertaining to multiversewide superrational compromise will be picked up by other researchers out of curiosity. Hence, superrationalists will probably need to think about ET values themselves.
 On the far values of humans and human superrational cooperators We will now explore what superrational humans might care about in distant civilizations. Unfortunately, our sample of these people is small, and path dependencies may imply that current earthly superrationalists may not be very representative of those elsewhere in the multiverse. We will, therefore, also look at general human values and far values in particular.
 Organizing human values Although most people have reliable intuitions for what other people care about, these intuitions are hard to pin down, owing to the inherent "messiness" of human moral intuitions (cf.  Stewart-Williams (2015) , section "Morality Is a Mess";  Muehlhauser and Helm, 2012, chapters 3-5.3) . This "messiness" makes evolutionary sense  (Cosmides and Tooby, 1994 ) and should therefore be expected from other civilizations in the multiverse as well.   2012 )), as well as those of  Shweder et al. (1997)  (also see Pinker (2011, chapter 9.4) for a short, accessible summary). There is also Peter Levine's Alternative to Moral Foundations Theory, which is not formally published. There are also some characterizations of the cultural and moral differences among humans. For example, Inglehart and Welzel divide moral values into just two factors: traditional versus secular-rational values, and survival versus self-expression values (2010, note 10). Hofstede recognizes six cultural dimensions, and Trompenaars' model of national culture differences has seven dimensions of varying moral relevance.
 Human far values We have seen that far values are the parts of our preferences that are relevant to MSR (see section 3.3.2). There are almost no studies on how humans care about alien civilizations. However, construal level theory suggests that we think and thus care similarly about different psychologically distant things. This brings us to the question, how do people usually care about psychologically distant or abstractly construed things? In contrast to their concrete counterpart, values at abstract construal levels tend to focus more on the central (as opposed to peripheral) features of a given situation (see  Trope and Liberman (2010b) , esp. section V). Values in abstract construal levels are therefore less fragile (see section 3.2.3), which is good news for us, as this inherent stability makes them easier to account for in our superrational cooperation. But what are those central features? A few studies have been conducted to find out, most notably one by  Bain, Hornsey, Bongiorno, Kashima, et al. (2013) . The authors summarize the results in a blog post: In our research, we asked people to think about the effects that changes in society today would have on society in the future (the Year 2050). For instance, we asked people to consider what society would be like 50 years in the future if climate change was mitigated, marijuana was legalized, abortion laws were relaxed, or the proportion of atheists or Muslims in society increased substantially. Participants considered changes in society relating to people's characteristics (how caring, moral, and competent people would be in 2050), whether people's values would change (e. g., becoming more concerned with security or achievement), whether there would be more societal problems (like crime and poverty), or greater societal development (economically, technologically, and socially). The different contexts produced diverse and nuanced images of what future society would be like. For example, participants saw a more atheist future society as making people less friendly but more competent than today, but saw a future society where marijuana was legalized as both less friendly and less competent. Overall, people's images of future society weren't all good or all bad, suggesting they had realistic rather than fantastical projections about what society would be like in the future. What may be most surprising, however, is that only one dimension emerged as a reliable motivator of people's actions in the present. People supported changes in policies today (e. g., legalizing marijuana, acting on climate change) if they believed it would lead to a future society where people were more caring and moral. Other dimensions -people's values, their competence, or levels of societal problems and societal development -emerged less strongly, only in a few contexts, or were irrelevant to people's willingness to act. Similar findings were made by  Bain, Hornsey, Bongiorno, and Jeffries (2012) ,  Park, Bain, and Kusumi (2015) ,  Judge and Wilson (2015)  and  Bain, Milfont, et al. (2015)  in other policy areas. These results are quite surprising -I know of no explicit discussion of "virtue consequentialism" in moral philosophy, for instance. Unless we think that superrationalists consistently hold different values, that humans are atypical or that these findings are somehow invalid, the findings suggest that the application of MSR implies significant policy changes for people espousing more commonly discussed consequentialist value systems like utilitarianism. Unfortunately, the above studies have some limitations. For example,  Bain et al. (2013)  do not ask for a utilitarian evaluation -i. e. one based on overall (average or total) welfare (or preference fulfillment) -of the future societies. Perhaps participants only put much weight on future citizens being caring and moral because these are proxies for other moral issues (such as welfare)? Besides methodological issues with the study itself, the results may not transfer to MSR without complications. In any case, social psychology studies often fail to replicate or generalize as expected. Construal level theory notwithstanding, it could be that people's views on alien civilizations differ from those on "collective futures". These results should thus be seen as tentative and preliminary until further replications come in; for now, we can regard them as serving an illustrative, rather than action-guiding, purpose. Moreover, benevolence -the term used by Bain et al. to encompass the characteristics caring, moral, and competent in their 2013 study -is still a rather fuzzy concept that probably depends on people's general moral views. It seems likely, for instance, that the definition of benevolence in a given situation varies considerably between, say, a devout Jain and a devout Salafist Muslim. In future research we should therefore look more into what kind of benevolence or moral behavior people value. For example, Napier and Luguri found that abstract mind-sets decrease preferences for loyalty, authority, and purity, all of which lie on the conservative and tribe-specific end of the moral spectrum (cf.  Luguri and Napier, 2013) .
 The values of human superrational cooperators We should also investigate how the values of today's superrational cooperators differ from those of other humans. Unfortunately, while I suspect that the results would be both interesting and informative, the number of people who actively reason superrationally today is too small to yield a statistically representative sample. We will therefore focus on who, for various reasons, are likely to embrace most (if not all) of the arguments underlying superrational cooperation. Of course, all of this again only gives us very weak evidence about the content of the compromise utility function. For one, it does not tell us much about civilizations that are very different from humanity. Moreover, the values of earthly superrationalists may in great part be the result of path dependencies. Thus, they may differ even from the values of superrationalists in civilizations that are very similar to humanity. Despite these considerations, I think that this most direct empirical approach to ascertaining the content of the compromise utility function is worth investigating.
 Philosophers Given that the central theme of this paper rests to a large degree upon philosophical considerations that are unlikely to be well-known outside of analytic philosophy, it seems reasonable to begin our review with analytical philosophers. While many philosophers seem to accept causal decision theory (see section 2.2), they are nevertheless far more likely to be aware of such ideas at all. 52 Furthermore, we can use  Bourget and Chalmers' (2014)  survey of philosophers to look at correlates of making the non-causal choice in Newcomb's problem. Most decision theorists see Newcomb's problem as analogous to the question of whether to cooperate superrationally in the prisoner's dilemma with a strongly correlated opponent  (Lewis, 1979) . The correlations, taken from the survey website, are inconclusive. Apparently, one-boxing in Newcomb's problem correlates very weakly with non-physicalist views in philosophy of mind (0.139), and only slightly stronger with viewing one's own work as Wittgensteinian (0.15). Two-boxing, meanwhile, has similarly weak correlations with endorsing the B-theory of time (0.141), embracing classical rather than non-classical logic (0.136), not being a communitarian (0.128), atheism (0.125), scientific realism (0.121), seeing one's work as , and with externalism in moral motivation (0.102).  53  Correlations between choices in Newcomb's and the trolley problem were too weak to warrant 52 That said, philosophers often do not act on their self-reported views  (Schwitzgebel and Rust, 2011) . For example, while philosophers (and ethicists in particular) are much more likely to rate eating meat as morally reprehensible, differences in behavior (i. e., actual meat consumption) are, at best, meager. 53 Interestingly, two-boxing is not only mainstream among philosophers in general (see section 2.2), but also slightly more common among philosophers with whom I (and most acausal decision theorists I know) would otherwise agree more. For more discussion of this phenomenon from the perspective of a one-boxer, see Carl Shulman's Why do theists, undergrads, and Less Wrongers favor one-boxing on Newcomb? and its comments. any mention 54 . These results do not appear to offer much insight into what value systems should be taken into account for superrational compromise. So, if anything, we could look into the values of philosophers in general.
 Effective altruists Let us turn to another community, in which taking action based on philosophical arguments is common: the effective altruist and rationalist spheres. Specifically, we will look at the effective altruist, LessWrong, and Slate Star Codex communities. A multitude of surveys of these demographics are available.  55  Within the LessWrong community, one-boxing in Newcomb's problem is about ten times more common than two-boxing, as evidenced by their 2012 and 2013 member surveys.  56  The 2009 survey also revealed that most LessWrong users would cooperate in one-shot prisoner's dilemmas against one another. Acausal reasoning thus appears quite common in this community. In fact, updateless and timeless decision theory (see 2.2) arose from discussions on LessWrong. The surveys also show that many members of the community identify as consequentialists (see below). Indeed, effective altruism is itself built upon a foundation of consequentialist arguments, although it is consistent with additional deontological restrictions. The community's general world view is entangled with both their consequentialist and decision-theoretical views, 57 as well as a general curiosity for discussing ethics and decision theory in the first place 58 . Hence, we may regard their views as indicative (if only weakly) of those of other superrational consequentialists in the multiverse. Even the existing surveys reveal some interesting facts about the values held by community members. For instance, they are overwhelmingly liberal, with only a few percent selfidentifying as conservative. Furthermore, they show a significantly greater concern for animals than the average person in Western industrialized countries.
 Considering larger and smaller groups 54 Unfortunately, at the time of writing, the site that is supposed to show all (as opposed to only the strongest) correlations between Newcomb's problem and other questions appears to be broken. 55 General surveys on LessWrong were made in  2009, 2011, 2012, 2013, 2014 and 2016.  There is a Slate Star Codex Survey survey from 2014, which only asked non-LW users to participate. Surveys of the EA community were done in 2014 and 2015.  56  The results (as of December 2016) of another LessWrong poll confirm that most community members strongly favor one-boxing. 57 For example, they view rationality and consequently decision theory and other sciences as being, in the end, about winning, in line of the instrumental and epistemic conceptions about rationality, rather than about acting or thinking in accordance with some reasons and requirements. Another example of a connection is that Eliezer Yudkowsky, the founder of LessWrong, has dedicated his life to making sure that artificial intelligence has a positive impact and convinced many in the community that this is a worthy goal. It also seems to me that the context of (superintelligent) machines can function as an intuition pump for consequentialism. 58 Decision theory and a goal system are two important ingredients to solve that problem of AI alignment (see the preceding footnote) (Soares and Fallenstein, 2015; Bostrom, 2014b, chapter 13, section "Component list"). Furthermore, effective altruism, i. e. systematically trying to do as much good as possible, requires that one knows what is good at least in some detail. For example, metrics like the quality-adjusted life year or the disability-adjusted life year may be used to evaluate intervention against poverty. (See GiveWell's articles on the topic.) Effective altruism presumably also inspires learning about rationality. We could also try to survey the values of much smaller sets of people, like those who have argued against causal decision theory (e. g., in academic papers) or indicate that they take the implications of non-causal decision theories seriously. Conversely, we can also study the values of much broader sets of people to make use of the academic literature. For example, we can reasonably assume that in order to discover superrationality, one would need a general philosophical mindset (rather than, say, a merely pragmatic one) and a willingness to engage in thought experiments that have no immediate practical relevance. We could then try to identify groups of people who meet these criteria, and to discover what values their members have in common. While we should also help superrationalists who do not believe they live in a multiverse (see section 2.9), we should nevertheless expect superrationality to be more widely accepted among people who do believe in a multiverse. After all, superrationality is probably far less action-guiding on its own than in combination with the multiverse hypothesis (see section 6.6), so it is comparatively unlikely to spread by itself. Thus, we could also survey the values of people who believe in the multiverse hypothesis. Similarly, we could study people who accept similarity to and correlation with others (as opposed to thinking that they are unique in the entire multiverse). Interestingly, such people may be likely to be conservative  (Stern, West, and Schmitt, 2014) . On the other hand, it may be that our currently available sample of superrationalists are atypical simply because the topic of MSR is still in its infancy here on Earth. If superrationality eventually becomes more popular on Earth and elsewhere in the multiverse, we may find that only the relatively few early adopters of the idea differ significantly from the human mainstream. Presumably, this is common in many areas of progress (cf. Rogers, 2010, chapter 7). For example, the average computer user in 1970 was very different from the general population at the time, since operating a computer back then required a particular set of technical skills that most people did neither possess nor have the time to learn. But once these early adopters improved the technology and convinced others to buy computers, they were soon outnumbered by people who would never have worked with the older computers, eventually culminating in today's ubiquitous use of computers. Thus, the average of the computer users of the past 50 years would probably resemble an average young person in a developed country. Analogously, early superrationalists may need to be more willing to study obscure thought experiments and look deliberately for crucial considerations. Soon, however, these early adopters may find themselves outnumbered by less explorative people who would have never thought about donation games between correlated agents on their own. While it is very unlikely that MSR will spread as widely as computers, the average superrationalist may nevertheless end up looking more similar to the average person than today's sample suggests.
 Biological evolution According to conventional views of the multiverse and its physical laws, almost all 59 of its inhabitants are evolved agents or descendants of evolved agents. This means we can use our knowledge of evolution and its workings to predict what values these other agents have. Since much has been written about evolution and the more relevant fields of evolutionary psychology and (descriptive) evolutionary ethics, we shall not discuss them in detail here. Readers may consult the works of Pinker (1999),  Stewart-Williams (2015) ,  Greene (2013) ,  Axelrod (2006) , and  Buss (2015)  for introductions.
 Cultural evolution A process similar to evolution takes place on the cultural level. Whereas biological evolution operates on genes, this cultural evolution determines the development of pieces of culture or memes such as "tunes, ideas, catch-phrases, clothes fashions, ways of making pots or of building arches"  (Dawkins, 1976, chapter 11) . 60 Again, this is not the place to review the literature on this topic. For an introduction to cultural evolution consider, e. g.,  Henrich (2015) .
 Which moral views correlate with superrationality? We can turn to the study of cultural evolution to learn about the prevalence of various consequentialist value systems. But whereas superrationalists probably resemble other intelligent agents biologically, they may well differ from them culturally. Thus, in addition to considering the civilizational baseline, we may also look into what values often go hand in hand with superrationality. Below are some preliminary examples of lines of reasoning that might be relevant in this context, some of which resemble the more empirically-minded comments in section 3.4.1: • Cooperation in general is more relevant for people with value systems that differ strongly from the mainstream in their civilization. • Some value systems benefit more from cooperation (and are harmed more by its breakdown) than others. Agents with these value systems are more interested in cooperation than others. • Superrationality is a "weird" philosophical idea. Therefore, it is more accessible to people who care about knowledge, are open-minded, philosophically rather than pragmatically inclined, and so forth. • Superrationality on its own is probably insignificant to most people's lives (see section 6.6). Hence, we should expect many superrationalists to only care about the idea because it comes packaged with multiverse theories. While this does not necessarily have implications for the other superrationalists' values, it does underline the point about a "philosophical" rather than "pragmatic" mindset. After all, thinking about all these other universes usually does not matter for our actions. • The significance of MSR is more apparent to people who think of goals as utility functions or the like, since this view makes it easier to to see that we can have preferences about distant parts of the multiverse. Once someone notices that many agents have preferences about each other's universes, she can see room for trade. If thinking about utility functions or similar formalisms indeed paves the way for MSR, we may also expect artificial intelligence researchers, game theorists, and some ethicists to be prominently represented among superrationalists in the multiverse. • The significance of MSR is more apparent if one realizes that it may imply radical compromise wherein everyone effectively changes their utility function. This, in turn, may be most apparent to people who are familiar with arguments like Rawls' original position  (Freeman, 2016)  or (preference) utilitarian reasoning along the lines of "it would be best if everybody. . . ". • MSR may come more naturally to people whose values require coordination (see sections 2.8.3 and 2.8.9). Most of these considerations apply mainly to civilizations resembling our own. Of course, we can similarly think about correlates of superrationality in more advanced (or, in principle, more primitive) civilizations. Such thoughts are even more speculative, especially if we do not know what future civilizations might look like. In the next section (or rather, its companion papers) we will also consider cultural (and biological) evolution in specific models of more advanced civilizations.
 Other considerations Biological and cultural evolution are not the only processes that affect the distribution of moral views throughout the multiverse. In particular, I would like to draw attention to three other candidates. Given that the underlying considerations in these areas are advanced, speculative, and not strongly related to superrationality itself, I will not go into detail; rather, I will refer to complementary notes for further tentative ideas. • Some civilizations may inadvertently self-destruct before they can shape their part of the universe. Others, meanwhile, may voluntarily refrain from colonizing space. The Fermi paradox suggests that either of these are likely. The values of such civilizations should not receive the same weight as one would have believed before considering this argument. For more information see the complementary note Civilizational filters and distribution of values in the multiverse. • An important step in the development of humanity and potentially other advanced civilizations could be whole brain emulation, i. e. scanning a biological brain, uploading it into a computer, and then simulating its behavior to a level of detail that preserves the brain's functionality. Since, by assumption, they are functionally equivalent to human brains, whole brain emulations (ems) can do most of the things that humans can. However, they can also do many things that humans cannot. Because ems are software, they can be copied, their information processing can be sped up (by moving them to a faster computer or giving them more CPU time on their current one), and they can use the internet to travel much faster and cheaper than humans. These advantages may be sufficient to allow ems to become more numerous and more powerful than humans. They also imply predictable cultural changes, including an increased willingness to adopt non-causal decision theories. See the complementary note Values and acausal reasoning of whole brain emulations for more details. • Because evolved minds (whether uploaded or not) are not made to be maintained or improved, I expect that many long-lasting civilizations will eventually create artificial superintelligence. Because programming an AI to pursue one's goals might be difficult, the values of such an AI may differ from those of humans. For more information, see the complementary note Values and non-causal reasoning of superintelligent AIs.
 Interventions In this section, I propose a few interventions that multiverse-wide superrationalists should pursue. Many of these are tentative ideas to consider more in the future rather than confident suggestions for what we should do today.
 Cooperation in the face of uncertainty about values We begin with a general challenge: given that we currently know so little about the values of other agents in the multiverse, how can we cooperate with them? With our current state of knowledge, it appears impossible to conclude what position MSR recommends on particular issues. For example, it seems impractical to decide whether we should vote and lobby in favor or against mass surveillance, abortion, marijuana legalization or the death penalty. Perhaps MSR, while interesting in theory, is practically impossible to apply because of our ignorance of the values in the multiverse? (Also see section 6.11.) While our uncertainty about the values of our collaborators is no doubt a major obstacle to the application of MSR, I will nonetheless argue that there are relevant policy changes that we can implement even today. The first class of such interventions requires no knowledge about other value systems at all, as long as we are confident that future agents will be able to attain such knowledge. Meta-activities are examples of this: no matter what the aggregated utility function of all superrationalists in the multiverse turns out to be, we could still benefit it indirectly by learning what it is or by spreading MSR itself (see section 4.5). One way of doing so is to ensure that artificial intelligences cooperate superrationally (see section 4.6). In the second class of feasible interventions, we try to draw conclusions from what little we do know about the distribution of values in the multiverse. We can, for instance, be sure that extraterrestrials will care less than humans about the Bible or the United States of America (though some will care about them a lot and many may care about preserving local traditions in general). On the other hand, we can be reasonably confident that many extraterrestrials care about satisfying the preferences of some other agents (e. g., "innocent" agents capable of reciprocating) (see, e. g.,  Axelrod, 2006; Trivers, 1971; Fehr and Gächter, 1999; Dawkins, 1976; Taylor, 1987; Buss, 2015, chapter 9) . Hence, we should perhaps embrace such "universal" moral values more than human superrationalists would otherwise do. (We explore this further in section 4.1.1.) Consider another example: the far values of at least some humans probably resemble those of many evolved extraterrestrial superrationalists, which means that we can benefit our superrationalist collaborators by increasing the capabilities of these humans to fulfill these preferences (see section 4.4). As a last example of how we can use a small piece of knowledge, consider how we can sometimes know that someone's values are at an extreme end of some scale or otherwise far away from the multiverse-wide superrationalist average. In this case, MSR suggests that we shift these extreme values towards the middle of their scale. For example, utilitarians are extreme in that they only care about welfare, whereas most superrationalists presumably care about a lot of other things as well. Thus, it would be good to convince the utilitarian to take other considerations into account (although it is not clear what these ought to be and how much they should be taken into account). In both of these classes, we overcome the obstacle posed by our lack of knowledge by benefitting a wide variety of value systems, rather than picking out any particular subset of extraterrestrials.
 Universalism I think satisfying universalist values, i. e. ones that are shared by a large fraction of superrationalists, may become somewhat more important for all superrationalists, although the case is not entirely clear. Imagine a group of people with a few shared concerns, such as justice, welfare and freedom, and a large number of non-shared concerns, such as each person's egoism, tribal loyalties, etc. 61 Given this, they can produce gains from trade by moving resources from the nonshared concerns to the shared concerns. In terms of the compromise utility function (see section 2.8), the idiosyncratic concerns do not receive lower collective weight than prior to cooperation. However, since each individual idiosyncratic value receives much smaller weight in the compromise utility function and interventions usually cannot satisfy many of them at the same time, interventions targeted at the universal concerns will usually increase the compromise utility function more efficiently. Although this argument is quite persuasive, it is not as strong as it initially seems. For example, it assumes that each individual's values are a simple weighted sum of universal and idiosyncratic concerns. But preferences can also have different shapes. In fact, each agent may explicitly protect its idiosyncratic values against losing its weight in such a preference aggregation mechanism. One example could be that the idiosyncratic values are much stronger than other preferences, but face diminishing returns. For instance, most people probably care almost exclusively about their own well-being until their level of well-being reaches some threshold. There may also be agents who exclusively care about their idiosyncratic preferences. For agents with these values, a compromise in which resources shift to universal concerns is negative. Another reason to disregard idiosyncratic preferences is that they are often not more common than their opposites. For example, Marxism, the US or Islam are liked by many, but also disliked by many others. Therefore, it is not even clear whether the compromise utility function evaluates either one of them positively. It should be noted that some universalist values may refer to others' tribal values. For example, many humans care about preserving cultural heritage. That said, this preference is usually weak and usually abandoned if it conflicts with other values. For instance, few would argue that human sacrifices should be continued to preserve tradition. Although most people do not care enough about animals to become vegetarians, my impression is that most people in Western countries would favor the abolition of bullfighting.
 Moral advocacy Advocating one's moral views can be an effective intervention if they differ significantly from those of most other people. In light of superrational cooperation, we should perhaps change the values we advocate.
 Universalist values As I argued in section 4.1.1, superrational compromise may imply that more resources should be used to satisfy universal as opposed to idiosyncratic concerns. This suggest that spreading universalism is good from an MSR perspective.
 Expanding the moral circle Most people care much more about themselves, their kin, and their associates than about others. From their point of view, they, their kin, and their friends are all special. From the outside view, however, most people are not more important than others. It is thus in the benefit of altruistic outsiders (e. g., other humans) to reduce the difference between how much people care about themselves, their family, friends, etc. versus other humans. In Singer's terminology, an outsider who cares about all humans equally would similarly want people's "circle of empathy" to expand outwards to include other humans  (Singer, 2011) . In this way, we can align their decisions with the goals of the outside party. The perspective of superrational collaborators elsewhere in the multiverse is similar, in that many things that are morally special to us are not special to them. Take nationalism and patriotism: many people assign particular moral value to the country they grew up in or to its citizens, with little support through impartial reasons 62 . Needless to say, most superrational collaborators elsewhere in the multiverse will adopt a different perspective. If they care more about Japan than about the United States (or vice versa), it would be for specific impartial reasons. Making people care intrinsically less about particular nations thus aligns their values more with those of superrational collaborators elsewhere in the multiverse. Similarly, intrinsic preferences for members of one's race, species, or substrate are inconsistent with an outside view of someone from a completely different species with a different substrate. 62 Surely, there are some impartial reasons to like one country more than another. For instance, Sweden is more tolerant of homosexuals than Iran, which is a reason to favor Sweden if one cares about the welfare of homosexuals. Nationalists often provide impartial reasons for favoring their country. For example, US nationalism is often about how the US is the country with the most freedom in the world. But if people really cared about such impartial reasons, the "best country in the world" would often not be their own country. Furthermore, nationalism often exaggerates the difference between countries in a way that seems inconsistent with an impartial point of view: sure, the US has a lot of freedom, but so do many other Western countries. If the US is better than everyone else along such dimensions at all, then surely not by a big margin. In any case, I am only talking about the kind of nationalism that is not based on impartial arguments.
 Which moral foundations? Given the criterion of universalism, what aspects of morality are worth spreading? As an illustrative classification of moral intuitions, we use Haidt's moral foundations theory, which divides morality up into five foundations: care/harm, fairness/cheating, loyalty/betrayal, authority/subversion and sanctity/degradation (see section 3.4.1). Liberals tend to care primarily about the first two aspects, whereas conservatives care about all five. Liberal values are universalist, while the exclusively conservative values are not. As J. Greene (2013, chapter 11, section "Why I'm a liberal, and what it would take to change my mind") writes (references added from the endnotes): According to Haidt, American social conservatives place greater value on respect for authority, and that's true in a sense. Social conservatives feel less comfortable slapping their fathers, even as a joke, and so on. But social conservatives do not respect authority in a general way. Rather, they have great respect for the authorities recognized by their tribe (from the Christian God to various religious and political leaders to parents). American social conservatives are not especially respectful of Barack Hussein Obama, whose status as a native-born American, and thus a legitimate president, they have persistently challenged. [...] Likewise, Republicans, as compared with Democrats and independents, have little respect for the authority of the United Nations, and a majority of Republicans say that a Muslim American with a position of authority in the U.S. government should not be trusted (Arab American Institute, 2014). In other words, social conservatives' respect for authority is deeply tribal, as is their concern for sanctity. (If the Prophet Muhammad is sacred to you, you shouldn't be in power.) Finally, and most transparently, American social conservatives' concern for loyalty is also tribal. They don't think that everyone should be loyal to their respective countries. If Iranians, for example, want to protest against their government, that is to be encouraged. In other words: authority, loyalty, and sanctity are all non-universalist values. While many people have values that structurally fit into these categories, the content (e. g., the referent) of these values differ. Applied to multiverse-wide superrational cooperation, this means that we cannot benefit the authority, loyalty, and sanctity values of other superrationalists unless we are in a society with the "right" authorities and sanctity rules. In fact, if we push for these three values in our tribe (or civilizations), it may actually be bad from the perspective of people with conservative values from other tribes. American social conservatives tend to dislike Islam and loyalty to its authorities, even more than American liberals do. Overall, this suggests that when it comes to multiverse-wide compromise, spreading values in the domains of authority, loyalty, and sanctity is not very fruitful. Instead, we should try to make people care more about the universalist liberal foundations. Having said this, there may be a few exceptions to the rule (cf. the last paragraph section 4.1.1). For example, Christian social conservatives may like parental authority even if one's parents are Muslims or extraterrestrials. In the sanctity domain, a preference for leaving nature untouched may extend beyond an agent's planet, although many extraterrestrial habitats are probably "slimy" and full of scary animals. Presumably, such reasoning is also applicable to other moral values. For instance, some people care about the traditions of other tribes, including their art, social institutions, laws, religions and other non-universal aspects. It should also be noted that aspects of the liberal value of fairness also vary strongly between different people. For example, a progressive may see wealth inequalities as unfair, while a libertarian finds wealth redistribution unfair. Thus, supporting one conception of fairness can hurt another. That said, there are many sorts of unfairness that almost everyone recognizes as bad. Another reason to focus on the liberal aspects of morality is that potential superrationalists on Earth are rarely conservative (see section 3.4.1). That said, future societal transitions might make people more conservative (see the companion paper Values and acausal reasoning of whole brain emulations).
 Concern for benevolence We have seen provisional research indicating that, when it comes to distant societies, humans mainly care about the benevolence, warmth, and moral behavior of its inhabitants (see section 3.4.1). If these tentative findings turn out to be correct and other evolved species resemble ours in this regard, we should try to align people's near values more with these (typically far) goals. However, given the tentativeness of said research, I do not think this should significantly affect our actions at present.
 Consequentialism Even though superrationalists elsewhere in the multiverse may care most about whether we behave in a non-consequentialist but broadly ethical way, they do so in a consequentialist way (see section 3.2.1). For example, they might care about the numbers of crimes and selfless acts, or total amounts of happiness and suffering in a given population. This stands in contrast to the preferences revealed by most people's charitable efforts: most money is donated to charities that are comparably ineffective, i. e. ones that do not achieve the best possible consequences. By making people more consequentialist, we can improve their resource use from the perspective of consequentialist third parties. This suggests that we should spread consequentialist ideologies like effective altruism, potentially independently of any particular optimization target (such as injustice, suffering, happiness, or knowledge).
 Pluralism Whereas the compromise utility function incorporates a plethora of concerns, most individuals' values are much more narrow. This is especially true among people who give morality some thought. For example, some people adopt utilitarianism, while others become proponents of Kant's categorical imperative.  63  As I am primarily a utilitarian, I sympathize with adopting a single ethical view (and utilitarianism in particular). From an MSR perspective, on the other hand, this misses out on gains from compromise between these opposing value systems and it would be better if everyone adopted a mix of different values instead. Thus, we may want to promote moral pluralism. One version of this view is MacAskill's (2014) moral uncertainty. Operating under the assumption of moral realism (which I reject), he argues that and how we should be uncertain about which ethical system is correct. Another related view is the normative reading of  Yudkowsky's complexity of value (cf. Stewart-Williams (2015) , section "Morality Is a Mess";  Muehlhauser and Helm, 2012, chapters 3-5.3 ), according to which what humans care about cannot be captured by a simple moral system and instead incorporates a large number of different values.
 Promoting moral reflection Probably wanting more idealized and reflected upon values to be implemented is much more common in the multiverse than wanting less idealized values to be implemented. 64 This is especially the case for agents who have not yet settled on a moral view. For example, I am genuinely uncertain about what I would or should count as morally relevant suffering when it comes to small minds (such as those of insects) and the like, just as I am not sure how to deal with infinities in ethics. I could thus benefit a lot if someone were to make more people think about these problems. Interestingly, the appeal of promoting moral reflection decreases upon idealization. Most people probably endorse moral discourse, the importance of reflection and argument, etc., in part because they think their moral view will result from that process -if they did not believe they had the arguments on their side, they might not hold their moral position in the first place. However, not everyone can be right about this at the same time. If someone only cares about preference idealization because she thinks that her value system will win, then preference idealization may remove that meta-preference. Beyond the question of whether evolved agents in the multiverse care about moral discourse, we must ask an empirical question about our own universe: will moral discourse bring people's object-level positions closer to those of our multiverse-wide superrational compromise utility function? For example, does moral discourse make people care more about, say, benevolence, assuming this really turn out to characterize much of evolved agents' far values (see section 3.4.1)? Perhaps moral reflection can also have negative consequences as well, such as attitude polarization  (Lord, Ross, and Lepper, 1979; Taber and Lodge, 2006) . These questions appear suitable for further research. that utilitarianism cannot make sense of  (Nathanson, n.d., section 3.b.i) . For example, they argue that utilitarianism is not (always) consistent with moral intuitions about equality  (Pogge, 1995; Gosepath, 2011) , the wrongness of killing  (Henson, 1971), and justice (Smart and B. Williams, 1973, part 1, chapter 10) .  64  The main data point is that humans think about morality and engage with others' moral views. The evolutionary psychology and cultural evolution perspectives, on the other hand, are non-obvious. Some moral arguments may be favored by cultural group selection, others may offer intelligent individuals to get their way more often. On the other hand, individuals who change their moral views may be perceived as unreliable or illoyal. Besides promoting societal discourse on ethical questions, one intervention in this domain is the use of preference idealization in artificial intelligence value loading (see section 4.6).
 Multiverse-wide preference utilitarianism In addition to spreading MSR itself, one could also spread value systems that in some way mimic its implications. Specifically, the proposed neutral aggregated utility compromise is essentially a form of preference utilitarianism or multiverse-wide preference utilitarianism. Multiverse-wide preference utilitarianism might therefore be a promising moral view to advocate on the basis of multiverse-wide superrational compromise. Of course, spreading a proxy for MSR has some general disadvantages. Most importantly, it is not very robust. If multiverse-wide preference utilitarians come to prioritize very differently than multiverse-wide superrationalists, then spreading the preference utilitarianism would not yield much in our favor. The question nonetheless deserves some thought. After all, if there is a significant chance that multiverse-wide preference utilitarianism approximates the conclusions of MSR, then we should at least be on the lookout for very cheap ways of promoting it. One main difference between preference utilitarianism and superrational cooperationwhether in the form of aggregated utility compromise or otherwise -is that the latter only takes the values of other superrationalists in the multiverse into account (see section 2.9.4). Preference utilitarianism, on the other hand, accounts for the preferences of a much broader set of agents, such as all sentient beings, all agents that have preferences of any sort, or all agents who satisfy some other criteria for personhood. This may mean that preference utilitarians arrive at very different conclusions than MSR proponents. For example, if they take small minds into account, these may well dominate preference aggregation. If, on the other hand, they only take members of human-like species into account, then the difference between these and superrationalist preferences may be much smaller. Another difference could be the way interpersonal comparison of utility is handled (cf. section 2.8.5). In the context of compromise, an individual's interests are usually given weight in proportion to the individual's power. So, for example, the interests of a superrational billionaire receive orders of magnitude more weight than the interests of a superrational beggar. However, most would view this approach as unethical and most preference utilitarians would disagree with it. Thus, multiverse-wide preference utilitarianism gives more weight to the moral views of the poor than MSR suggests. Yet another problem could be that preference utilitarians would not arrive at the more meta-level MSR interventions. Even if MSR and multiverse-wide preference utilitarianism had the same object-level implications, the justification for MSR is different from (non-MSR) justifications for preference utilitarianism. Thus, preference utilitarians would not support or even come up with interventions that are about spreading the MSR-based justifications for MSR's and preference utilitarianism's joint conclusions. For example, a preference utilitarian (who does not agree with MSR) would not spread the MSR idea itself, nor try to ensure that future people (and AIs, see section 4.6.3) reason correctly about decision theory. Because these are plausibly among the most promising interventions, this consideration suggests some significant divergence in priorities. In sum, it is unclear to what extent multiverse-wide preference utilitarianism could approximate a superrational compromise utility function. At this point, however, spreading multiverse-wide preference utilitarianism is unlikely to be a top priority.
 No multiverse-wide tug-of-war over values Value systems can be viewed as having several dimensions, like relative importance of welfare, population size, art, knowledge, justice, compassion and freedom, tradeoffs between suffering and happiness, tradeoffs between extreme happiness/suffering and mild happiness/suffering, and severity of punishments, to name but a few. Different groups in the multiverse invest resources into pulling the relative values of these dimensions into different directions. Some may want people to care more about suffering, while others want them to care more about nature or happiness instead. Now, imagine you care more about suffering than most others and that you live in a civilization with a merely average concern for suffering. Presumably, you would want to pull the "concern for suffering rope" into your direction, potentially at the cost of other values. But knowing about superrationality, this would make it more likely that those who care less than average about suffering will also pull the rope into their direction elsewhere in the multiverse, thus offsetting your impact. Therefore, MSR would recommend against shifting concern away from other superrationalists' values, e. g., nature or happiness, to suffering. It should be noted that the above does not (necessarily) apply if the values of your civilizations strongly diverge from those of the superrationalist average far values. In such cases, it may be somewhat beneficial if all superrationalists pull the values of their civilization toward the average.
 Promoting causal cooperation Imagine two value systems, each of them common throughout the multiverse, engaged in conflicts with one another on Earth. Let us also assume that most people with these value systems find ideas like acausal decision theory and the multiverse highly speculative, such that we cannot convince them of cooperating on a MSR basis. In this case, we can still cooperate superrationally with others in the multiverse by promoting causal cooperation between the two sides (provided this does not end up hurting some third superrational party of agents 65 ).  65  As a non-obvious example, consider global catastrophic risks. Presumably, most people would not want humanity to experience a global catastrophe. Promoting peace and cooperation between nuclear powers is thus positive for all nuclear powers involved. In the plausible event that humanity would survive a nuclear winter and quickly recover, however, post-apocalyptic human society may come to hold different moral views that conflict with the views of current nuclear powers. For instance, it may be that in the first months after a global catastrophe, there would be frequent violence and chaos among survivors. They may also be forced to exert violence themselves to survive. Thus, the survivors may be desensitized to violence. Even after civil order is reestablished, citizens may still be relatively unconcerned about violence towards animals, criminals, the weak and poor, etc. (Note that I am not claiming that this would necessarily be the case; indeed, personal hardships can also make people more compassionate. I am merely using it as a somewhat plausible scenario to illustrate the present point.) All of this would imply that mitigating global catastrophic risks on Earth ends up hurting agents in the multiverse who would like societies to be organized according to post-apocalyptic survivor values. If agents with such values are sufficiently common in the multiverse, For example, let us assume that the payoff matrix of their interaction is that of a prisoner's dilemma given in table 2. Let us assume that both players' utility functions are equally common in the multiverse. We also assume that other value systems have no interest in the outcome of the interaction. From the perspective of a third party who accepts MSR, the effective payoff matrix for this interaction may look like the one given in table 3. That is, when such a third party can influence the outcome of the interaction between player 1 and player 2, she acts as though she maximizes the utilities given in that table, even if she intrinsically cares about something entirely different. When such an agent is able to influence at least one of the players, she will lobby him to choose C, 66 because to her, the payoffs are proportional to the number of C 's that are chosen. 67 A disinterested non-superrational third party, on the other hand, -i. e. one who does not care about the payoffs of each of the two agents intrinsically -would assign no value to either of the four outcomes, nor would they invest any resources in bringing about a particular outcome.  Next, let us assume that, rather than some third party, player 1 himself learns about and adopts multiverse-wide superrational cooperation, while player 2 stays ignorant of the idea. The new effective payoff matrix may then look like table 4. Player 2's payoffs are the same as in the original prisoner's dilemma, but player 1's effective payoffs have changed. He now then causal cooperation between nuclear powers should actually be sabotaged! That said, I do not find this conclusion all that plausible. It seems to be based on more and less likely assumptions than other action-guiding arguments and so it is much more fragile. One specific problem is that I would expect humans (and most other evolved beings) to become more tribal in response to a global catastrophe  (Henrich, 2015, chapter 11 , section "War, External Threats, and Norm Adherence"), which may make these values less important (see section 4.2.1). 66 For ideas on promoting cooperation from the outside, see Tomasik's Possible Ways to Promote Compromise, as well as  Axelrod (2006, chapter 7) . 67 Note that in some prisoner's dilemma-like problems, mutual defection is overall better than unreciprocated cooperation, in which case the superrationalist's job is more difficult. If she convinces one player of cooperation but fails to convince the other one, she will have done more harm than good. maximizes the sum of the two value systems' payoffs, because player 1's and player 2's utility functions are equally common in the multiverse. This puts player 1 in a peculiar situation: whereas defection is the dominant strategy in the original prisoner's dilemma (and therefore still the dominant strategy for player 2), cooperation dominates in this new version. Player 1 would thus cooperate in a one-shot version of the problem. On Earth, however, most interactions are repeated, like an iterated prisoner's dilemma. At first glance, one may suspect that player 1 would still cooperate in every round given that, no matter what the opponent on Earth does, he will want to make it more likely that agents elsewhere in the multiverse behave in a similarly cooperative way. However, such a strategy of unconditional cooperation makes defection player 2's best strategy. This is suboptimal for player 1, given that he prefers mutual cooperation (C,C) over unilateral cooperation  (C,D) . In an iterated version of the game, player 1 might therefore punish defection to some extent, similar to how successful strategies punish defection in the iterated prisoner's dilemma. Nevertheless, the dynamics of this new problem are different than those of the prisoner's dilemma. Based on the ordering of the outcomes for the different players, the game is identified as g 261 or g 266 in the periodic table for 2x2 games by  Robinson and Goforth (2005) , who also provide a few examples of games in this category. A few additional examples of this type of game exist, but overall, the game has not been studied extensively in the literature. Further research is thus needed to identify the right strategy for iterative versions of the game.
 Increasing capabilities Broadly speaking, agents have two reasons to increase other agents' capabilities: a) they may care about it intrinsically, or b) they may share the goals of the people whose capabilities they increase (and thus care about increasing them instrumentally). For example, someone who mostly cares about other people's freedom to pursue their goals has a type a) reason to raise the capabilities of poor people, and someone who agrees more with the people than with the dictator has a type b) reason to increase democracy. But if you hold less common values, such as reducing animal suffering, giving people more power is of unclear value. MSR broadens type b) motives to increase others' capabilities: even if we do not share someone else's goal, we have reason to increase his capabilities if we believe that significant parts of his goals are shared by superrational agents elsewhere in the multiverse. There is some relevant literature on increasing an agent's goal-achievement capabilities. In economics, the capability approach is an alternative to welfare economics and primarily studies how to measure an individual's capabilities. Some of its metrics include health, freedom of thought and expression, education, political participation, and property rights. In his dissertation on Ethics Under Moral Neutrality, Evan Gregg  Williams (2011)  discusses a topic closely related to acting under MSR: he assumes that we do not know what the "correct" moral theory is 68 , and that while we all have some access to moral truth, this access is unreliable. He then discusses, among other things, what policies we should take given such uncertainty. In many ways, this scenario is analogous to MSR 69 , where the necessity to maximize for multiple moral views comes from uncertainty about the utility functions of other agents in the multiverse as well as their diversity rather than conflicting intuitions about the "moral truth". Many of Williams' conclusions resemble those of the present paper. For instance, he identifies the appeal of preference utilitarianism in chapter 3.1 of the dissertation (compare sections 2.8 and 4.2.6 of the present paper). Many of his intervention ideas are about improving the capabilities of others who may plausibly have access to the moral truth. First and foremost, he defends democracy (chapter 3.3) and liberty (chapter 3.4). Of course, MSR does not have the same implications as the above approaches. For one, when we raise others' capabilities as superrationalists, we favor people whose values we suspect to be typical of what superrationalists in the multiverse care about. For example, from an MSR perspective it is much more important to support consequentialists. Moreover, some of the proposed measures merely move resources or power from one group to another (e. g., from a dictator to the people) without adding optimization power aimed at the goals of superrational agents in the multiverse. I doubt that raising capabilities will often be a top intervention. Nonetheless, it might be an option when good and inexpensive opportunities, such as sharing knowledge, arise.
 Meta-activities Relative to any goal, meta-activities are either about a) amassing more resources, or b) improving the efficiency of one's object-level resource expenditure. To achieve the goals that superrationality prescribes, we may thus also engage in such meta-activities. In the following, I will describe two meta-activities, one of each kind.
 Research The present paper lays out the foundations for research on multiverse-wide superrational cooperation. Further research is needed in all three areas discussed in this paper, i. e. how our new criterion for choosing policies is to be constructed (see chapter 2), what values our superrational collaborators have (see chapter 3), and which interventions are most promising (chapter 4). 68 I side with moral anti-realism (R.  Joyce, 2016)  and non-cognitivism in particular (R. Joyce, 2016, section 3). That is, I do not think that moral theories can have (objective) truth values. 69 In fact, I learned about variance voting, which I take to be the most promising approach to constructing the compromise utility function (see section 2.8.5), via the literature on moral uncertainty, in particular via MacAskill  (2014, chapter 3) . Note that some research, e. g. investigations of whether a compromise is beneficial for you, can (in theory) be harmful if one has not properly precommitted as illustrated in the Remote-controlled cake maker thought experiment (see section 2.8.6). A similar danger lies in finding out whether other agents cooperate (see section 2.1).
 Promoting multiverse-wide superrationality Since multiverse-wide superrational cooperation produces gains from compromise (under certain assumptions about the collaborators, discussed in section 3.2), having more multiversewide superrational cooperation produces more gains from compromise. Hence, a common interest of all collaborators is to increase the number of people who adopt (multiverse-wide) superrational cooperation. Indeed, it is plausible that small groups of superrationalists should focus on promoting the idea rather than attempting to help other superrationalists directly. After all, if one of them can convince only two others to cooperate superrationally, she already doubles her impact relative to cooperating on her own. Of course, the two others could also convince others in turn. Needless to say, spreading the idea saturates at some point. At least when all humans are convinced of superrational cooperation, the idea cannot be spread further. More realistically, we will run out of people who are willing to think about such seemingly speculative topics.
 Artificial intelligence One particularly important way of shaping the future is artificial intelligence  (Bostrom, 2014b) . Given our newfound knowledge, we can differentiate between AI safety measures that are inspired by superrational cooperation and AI safety measures that are not.
 AI safety not based on superrationality-related considerations The goal of current AI safety research is to make AIs behave in ways that are more compatible with some human value system. 70 From a multiverse-wide cooperation perspective, this is positive to the extent that human values correlate with the values of other evolved agents in the multiverse. A human-controlled, non-superrational outcome may nonetheless be suboptimal from an MSR perspective. Imagine a distant civilization of billions of happy, law-abiding, art-producing, yet, from a human perspective, ugly-looking extraterrestrials. Each year, they enslave or kill trillions of other, less intelligent extraterrestrials, such that the number of miserable lives and involuntary deaths caused by the civilization is orders of magnitude higher than the number of positive lives it supports. Most people on Earth may not care about this civilization at all because it contains no humans. Some may only care about the smart extraterrestrials and thus evaluate the society very positively  (Kagan, 2016) . However, I suspect that many of those who care at all about distant ugly aliens also care about less intelligent aliens. These people would evaluate the civilization as far less positive. Similarly, many superrationalists in the multiverse may not evaluate our civilization positively if it were to continue its current mistreatment of animals. Another concern is that a civilization might prioritize near-view values when value loading an AI. This suggests that even if our values resembled those of other civilizations, the goals we give to an AI might differ significantly from what extraterrestrials care about in our civilization. FRI has previously investigated ways of making AI alignment failures less harmful by focusing on avoiding very bad AI outcomes rather than attempting more fine-grained control  (Gloor, 2016) . One motivation to do so is this approach's cooperativeness: different value systems may disagree on what future should be created. For example, some want the universe to be filled with concentrated pleasure, whereas others envision human civilizations of varying social, economic and political systems, often rid of poverty, diseases, involuntary death, and so forth. However, different value systems often agree on a large set of futures that should not be created. Things like premature death, suffering, war, and extinction are almost universally seen as bad. Avoiding dystopian scenarios can thus benefit a wider range of value systems. Another MSR-based reason to focus on very bad outcomes is that, because our civilization will be destroyed in all of them, avoiding them evokes abstract construals. These probably do a better job than concrete construals at approximating what extraterrestrials care about in our civilization (cf. section 3.3.2). However, making AI more fail-safe from a MSR perspective would be less focused on preventing outcomes with a lot of suffering than FRI's previous work. Also, its level of priority depends on its feasibility. Whereas heuristic arguments suggest that merely avoiding bad outcomes might be more feasible than working toward fully human-aligned AI, it has so far proven difficult to do any concrete work in the area. Overall, I think it is an approach worth investigating further in the context of superrational compromise, but not likely to be a top intervention.
 Multiverse-wide superrationality-inspired value-loading In section 2.8.2, we viewed compromising as a one-time process, in which all agents adopt a new utility function u * to maximize in their part of the multiverse. If they indeed acted as though they now only care about maximizing u * , the natural consequence would be to push for AI values that are closer to u * . One way to do this is to directly implement the value systems that one would also spread to other humans (discussed in section 4.2). For example, one could try to make future AIs hold a wider variety of values (see section 4.2.4) or perhaps prioritize universal concerns a bit more (see section 4.2.1). More robustly, one could directly implement a pointer to the aggregated consequentialist far values of superrationalists in the multiverse. Indeed, extracting u * from the multiverse appears to be roughly as difficult to specify as extracting goals of humans. Just as one could identify humans in the world model, extract their goals and aggregate them, so one could identify superrational cooperators, extract their goals and aggregate them. 71 (A somewhat similar proposal was made by  Bostrom (2014a, page 14) ; see section 6.1.2.) Of course, it is unlikely that superrationalists could convince the majority of people of such goal systems. Nonetheless, at this early stage of the field of AI safety, it seems useful to also explore unrealistic proposals like this one. Additionally, less attractive goal functions may still be relevant as backups (see  Oesterheld 2016) . Another disadvantage of this approach is that it breaks if the analysis underlying our specification of u * is incorrect. For instance, if MSR does not work at all, then making AI care about ET values directly is much worse than simply implementing our own values.
 Making an AI come up with superrational cooperation on its own Instead of directly implementing our compromise utility function, we could also make the AI come up with such a compromise on its own. This has several advantages. Most importantly, it protects against some possible mistakes on our side. If, say, we were unable to find the correct superrational compromise, we could let the AI find it on its own. Also, the AI may at some point discover that there are no other agents in the multiverse after all, at which point it could choose to stop wasting further resources into compromising with these nonexistent agents. The primary way of getting an AI to compromise superrationally is to ensure that it reasons in accordance with the right decision theory.  72, 73  This in turn involves advancing the field of decision theory and investigating possible ways of implementing decision theories in AI systems. Given how both of these areas seem neglected and gains from trade may be quite significant, I could very well imagine that interventions in this area are among the most effective of those hitherto considered by effective altruists.
 Value loading is still necessary If all acausal collaborators settle on maximizing some utility function, perhaps value loading is unnecessary for AIs with the right decision theories anyway? After all, once such an AI joins the MSR compromise, it will update its utility function accordingly -regardless of whether it originally wants to maximize paperclips or to reduce suffering. But this reasoning seems unsound. While all AIs may settle on the same compromise utility function, the original value system of the AI still affects what that compromise utility function ends up being. Without superrationality, value loading affects the dominant values of one AI. If there are m superrationalist civilizations, then each can affect the dominating values normalization) is more or less difficult to implement than the aggregation procedures one would implement for humans. 72 Reasoning in accordance with some decision theory is not meant to imply that the decision theory is hard-coded into the AI. Instead, the decision theory that an AI uses may be the result of particular choices of architecture. To ensure that the AI reasons in accordance with the right decision theory, we would then have to find out what the decision-theoretical implications of different AI design choices are and ensure that these receive due consideration in the construction of intelligent machines. 73 There are other ways to make it more likely that the AI applies MSR. For example, one could ensure that its epistemology enables it to infer the existence of other universes that cannot be observed directly. We could also think of an AI that would accept MSR, but somehow never has the idea of MSR. Much more plausibly, some AIs will simply not care about distant universes in a consequentialist way. However, all of these parameters seem more difficult to influence than the AI's decision theory. in m AIs by 1 m (assuming that all civilizations are equally powerful, etc.). So, proper value loading is actually just as effective as before, if not more because of gains from trade. Even if we manage to reliably make the AI join a superrational compromise, we will still want to make it value the right things. I am uncertain about whether some version of the above argument against value loading may work after all. Even if all AIs have "paperclipper values", perhaps they would still recognize that other value systems originally had all the power, causing the AIs to give them higher compromise weights? Similarly, one may have some intuitions that value loading superrational AIs should not be necessary, given that it just moves power between superrational cooperators. However, at this point, these are merely intuitions and not arguments. Except from potentially guiding future research, I do not think they should affect our priorities.
 Compromise-friendly backup utility functions Even though value loading is still necessary, we can nonetheless benefit our superrational collaborators (and thereby ourselves) in cases where value-loading fails. Even if an AI has values that differ from those of humans, it may still trade with other civilizations. Hence, we should attempt to load it with values that especially lend themselves to compromise, such that the other value systems benefit as much as possible (cf.  Bostrom, 2014a) . Because one would usually attempt to load an AI with one's own values, such a compromise-friendly ("porous", in Bostrom's terminology) utility function would usually only be a backup (see  Oesterheld 2016) .
 Acknowledgements I came up with superrational compromise after a conversation with Lukas Gloor about decision theory and the multiverse. Prior to writing this paper, I extensively discussed the topic with him, Carl Shulman, and Brian Tomasik. I also thank Max Daniel, Tobias Baumann, Carl Shulman, David Althaus, Lukas Gloor, Kaj Sotala, Jonas Vollmer, Johannes Treutlein, Lucius Caviola, Joshua Fox, Jens Jaeger, Ruairí Donnelly, Brian Tomasik, Owen Cotton-Barratt, Magnus Vinding and Dominik Peters for valuable discussions and comments on this paper. Last but not least, I am indebted to Adrian Rorheim for careful copy editing and Alfredo Parra for typesetting.
 Appendix The appendix contains discussion of additional, more tangential topics.
 Related work
 Gary Drescher on superrationality Superrationality, i. e. cooperation based on correlation, is a well-known idea in decision theory  (Kuhn, 2017, section 7; Horgan, 1981, section X; Hofstadter, 1983; Campbell and Sowden, 1985; Ahmed, 2014, section 4.6 and references therein) . However, most authors do not discuss much beyond the basic idea. Chapter 7.2 of Gary  Drescher's Good and Real (2006)  is the most extensive analysis of the concept of which I am aware. Among other things, Drescher notes that superrationality -or, as he calls it, subjunctive reciprocity -can be applied broadly as a justification for "altruistic" behavior, which I discuss in section 6.7. He also points out that superrationality removes the need for reciprocity (see section 2.9). Although Drescher discusses the Everett interpretation of quantum physics in his book, he does not connect it with superrationality. His considerations thus focus on superrationality among agents on Earth, which I would argue to be quite weak (see section 6.6). Nonetheless, his account of superrationality is more thorough than any other I have seen, and strongly influenced chapter 2 of this paper.
 Acausal trade Acausal trade is another (mostly informally discussed) form of cooperation based on noncausal decision theories and has often been combined with the multiverse concept. However, the mechanism usually discussed under the term acausal trade differs from superrationality. Instead of assuming the similarity between two agents, acausal trade merely requires them them to have models of each other. For example, the two agents may know each other's source code.  74  The main technical difficulty here is to avoid the infinite loop associated with this mutual modeling. The basic idea is that both agents adopt the policy of cooperating if and only if the other agent cooperates. 75 This is intended to incentivize cooperation in a way reminiscent of causal cooperation via tit for tat. One can also view this policy of mirroring the other agent's strategy as a way to create correlations between the decisions of the two agents. However, if both agents use this policy, they run into an infinite loop: To make a decision, the first agent has to find out (probabilistically) what the second agent does. But to do so, it has to find out what the first agent does, which in turn means finding out what the second agent does, etc. As illustrated by  Barasz et al. (2014) , this problem can sometimes be solved, thus making it rational for two programs with knowledge of one another's source code to cooperate with each other (cf.  LaVictoire et al., 2014; Critch, 2016) . Superrationality may be seen as a special case of acausal trade in which the agents' knowledge implies the correlation directly, thus avoiding the need for explicit mutual modeling and the complications associated with it. This makes superrationality much more easy to apply than acausal trade. Consequently, whereas I propose that humans should reason superrationally, acausal trade is usually discussed only in the context of superintelligent AIs (e. g.,  Bostrom, 2014a) . 74 Alternatively, one of the two agents can observe the others' behavior. In this case, only the other agent needs a model.  75  Of course, it would be even better if one could defect against that cooperate unconditionally.
 Various mentions of multiverse-wide superrationality While I am not aware of any substantive discussion of MSR, some have mentioned it as a side remark, or proposed specific applications: • Bostrom writes: "We might [...] hope that some of the other civilizations building AIs would [also implement their AI in a way that enables trade (see sections 4.6.3 and 4.6.3)], and perhaps the probability that they would do so would be increased if we decided to take such a cooperative path."  (Bostrom, 2014a , page 4) On page 14, he also argues that one should perhaps diversify the values of an AI for a similar reason. • Almond discusses a few examples of how we can utilize the correlation with other civilizations  (Almond, 2010c, ch. 4) . One of them is discussed in section 6.9.
 Many agents One essential ingredient of multiverse-wide superrationality is the number of intelligent agents that exist. We have, to some people's surprise, not (yet) found extraterrestrial life in the observable universe. However, the universe, or multiverse, probably extends far beyond the region we can observe. More likely than not, it contains so many agents that the number of humans on Earth pales in comparison. Unfortunately, physics and cosmology are not the most accessible of fields. Introductions tend to either involve advanced mathematical notation or fuzzy explanations with terms like "space-time distortions", "waves", space being referred to as "flat", dimensions as "curled up", etc. that seem hard to understand without looking at their technical meaning. For an overview of the latter kind, consider Tegmark's Parallel Universes  (2003) , which also discusses the number of intelligent agents specifically. Another, even broader popular science overview is given by  Greene (2011) . In this section, we focus on the easiest to understand aspects. As mentioned in chapter 1, we will use the term "multiverse" to also refer to, say, a spatially infinite universe. It is important to note that most talk about multiverses is not something physicists make up out of thin air as an intellectual exercise. Instead, certain well-tested theories in physics and cosmology seem to imply the existence of a large universe or multiverse. One of the easier to understand examples is the Everett or many-worlds interpretation (MWI) of quantum mechanics. For an introduction, consider Yudkowsky's introduction (2015, ch. S), which makes a strong case for MWI and goes through some of the issues typically discussed, like falsifiability/testability and the law of parsimony  (Tegmark and Wheeler, 2001; Tegmark, 2007; Vaidman, 2016) . For a more critical account, see, e. g.,  Kent (1997) . Tentative polls of physicists' opinions on MWI indicate that between 10% and 50% agree with MWI (Raub 1991, unpublished as cited in, e. g., Tipler, 1994, section 5, "Nonrelativistic Quantum Mechanics is Deterministic"; Tegmark, 1997;  Nielsen, 2004; Emerson and Laflamme, 2006) . But the many-worlds interpretation of quantum physics is not the only case that can be made for a universe with a very large or infinite number of agents. In fact other arguments are probably more widely accepted. Maybe the least "extraordinary" hypothesis implying the existence of many agents is one which says that this universe is spatially infinite. According to Tegmark, "this spatially infinite cosmological model is in fact the simplest and most popular one on the market today" (2003). Even if the universe is spatially finite and small, it may still contain a lot of civilizations that cannot interact with each other if it is temporally infinite. For example, on a cyclic model the universe goes through an indefinite number of oscillations of expansion and collapse. If sufficiently many of these oscillations give rise to different civilizations, then these civilizations can cooperate with each other superrationally. Another more complicated yet popular cosmological theory is eternal inflation as described in ch. II of Tegmark's Parallel Universes. Eternal inflation postulates the existence of multiple universes which not only differ in initial conditions but also in their number of dimensions, their sets of fundamental particles, and their physical constants. On the more speculative (but also more accessible) side, there are various forms of modal realism (sometimes also called mathematical monism), the view that every "possible world" exists in the same way in which our world exists. While modal realism is controversial and rarely discussed by physicists, some view it as an elegant solution to some philosophical problems. Modal realist theories are also very simple, although to make predictions with them, they require supplementation with indexical information about which agent in which possible world we are  (Hutter, 2010, ch. 3) . For different starting points for thinking about modal realism, see any of the following:  Lewis (1986 ), Tegmark (1998 2008; Schmidhuber (1997) . Acting under the assumption of modal realism is associated with some complications, however. In particular, because literally everything can happen, everything will happen in some possible world, no matter what we do. Thus no action seems to be better than another  (Oesterherld, 2017a)  Besides the arguments in favor of assigning a high probability to living in a universe with many agents, there also exists a prudential reason to act as though one lives in a large universe. Even if we only assign, for example, a 50% probability to the existence of other civilizations, our decisions matter much more if there are more other agents with whom we are correlated. Thus, we should optimize our decisions more for the large universe. This line of reasoning does not work for all value systems, however. For example, in terms of multiverse-wide average welfare, our influence may be much bigger if the universe was very small. An average utilitarian may thus follow the opposite prudential argument and act as though the universe was small.
 Testability of superrationality Eliezer Yudkowsky (2010b, ch. 13) writes: If a dispute boils down to a testable hypothesis about the consequences of actions, surely resolving the dispute should be easy! We need only test alternative actions, observe consequences, and see which probability assignment best matches reality. Unfortunately, evidential decision theory and causal decision theory are eternally unfalsifiable-and so is [timeless decision theory (TDT)]. The dispute centers on the consequences of logically impossible actions, counterfactual worlds where a deterministic computation returns an output it does not actually return. In evidential decision theory, causal decision theory, and TDT, the observed consequences of the action actually performed will confirm the prediction made for the performed action. The dispute is over the consequences of decisions not made. This also means that superrationality itself -not only its application to agents in faraway parts of the multiverse -is untestable. If I win money by cooperating in a prisoner's dilemma against an exact copy of mine, causal decision theorists will point out that my copy would have cooperated either way and so defecting would have been better. Based on this anecdotal evidence, people do not consider superrationally in this real-world donation game, although they sometimes make the superrational choice for other reasons.
 Do people reason superrationally? In general, there are many hypotheses about why people sometimes cooperate that do not involve any sort of acausal reasoning. Presumably, many are either unaware of the causal line of reasoning or do not properly set up the proposed experiment in their mind. For instance,  Yudkowsky (2015, chatper 275)  argues that people cannot pretend to be selfish and therefore take the reward to the other player into account.  Kanazawa and Fontaine (2013)  demonstrate that "the subject's behavioral choice (cooperation vs. defection) varied significantly as a function of subconscious perception of cues to possible reputational effect (in the form of a video image of another subject in the experiment)." Cultural norms are also often invoked to explain cooperation. 76 This short list of example explanations is by no means an exhaustive review of the literature on why people cooperate in one-shot games like the prisoner's dilemma and public goods games. Drescher (2006a, page 288f) defends the opposite view. He argues that although people do not act according to some systematic acausal decision theory, they nevertheless implicitly account for acausal reasoning into account implicitly. Similarly, Leslie writes, "perhaps the germs of [evidentialist reasoning] are already present in thoughts influential in getting people into polling booths, thoughts on the lines of 'What if everybody in my party stayed in bed?"'  (Leslie, 1991, ch. 7) . Perhaps this "lack of a correct explicit decision theory leaves the solution somewhat vulnerable to seemingly sound counterarguments, and thus leaves the solution's influence somewhat tentative"  (Drescher, p. 289) . This could explain why many people who have considered the problem in great detail do not go with the recommendation of acausal arguments despite potentially having an innate intuition for them. Recently, Fischer (2009) has proposed that people do engage in superrationality-like reasoning. In a study, he showed that participants' cooperation in a one-shot prisoner's dilemma correlated with reported probabilities of the opponent making the same choice as oneself (cf.  Krueger, DiDonato, and Freestone, 2012) . One further piece of evidence in favor of this hypothesis is that cooperation decreases when people learn about the other person's choice before they make their own choice.  Pothos et al. (2011)  write:  Shafir and Tversky (1992; Busemeyer, Matthew, and Wang, 2006; Croson, 1999; Li and Taplin, 2002; Tversky and Shafir, 1992 ) created a well-known modification to the Prisoner's Dilemma game: in some trials, participants were told what the other player was doing. Unsurprisingly, when participants were told that the other person decided to D, then their probability to D was 97%; and when they were told that the other person decided to C, then their probability of D was 84%. However, in trials (within participants design) when participants were not told what the other person did, the probability to D dropped to 63%. While inconsistent with mere causal reasoning, this can be explained with acausal reasoning. Given knowledge of the other person's decision, the evidential impact of cooperation diminishes (cf. section 2.1). Moreover, this behavior cannot be explained by reputational issues or altruistic preferences, which would, if anything, suggest that one would return the favor upon learning that the other person cooperated. However, the standard explanation attributes this behavior to people's irrationality. Overall, I lean towards the view that people do not have strong acausal intuitions in day-today scenarios, which means that people who do take such considerations seriously do not correlate strongly with the average person.
 The evolution of superrationality Even though superrationality is not testable in any given situation, it does produce actual benefits. This much is clear even to a causal decision theorist, who would thus self-modify to take some, though not all, acausal considerations into account (see section 2.3). For the same reasons, a causal decision theorist would also program an AI to take these considerations into account. Similarly, evolution favors agents that take some superrational considerations into account. For example, imagine a planet on which near copies of agents are created on a regular basis. They then interact with each other in cooperation and coordination games like the donation game. To facilitate evolution, copies are created in proportion to the payoffs in the cooperative games. On this planet, superrational agents -i. e. those who cooperate with close copies and other correlated agents, while defecting against uncorrelated agents -have an evolutionary advantage over CDT-based agents who always defect. They will, on average, receive higher payoffs and thus reproduce more successfully. Evolution can, therefore, in principle favor genes (and memes) that promote superrational reasoning. In some sense, the described planet resembles ours. On Earth, "near copies" of humans are created via reproduction and upbringing. Moreover, many have pointed out that scenarios paralleling the prisoner's dilemma and public goods games were common in our ancestral environment. In principle, such considerations also apply to the application of superrationality to cooperation with agents in other parts of the multiverse. That is, multiverse-wide evolution favors creatures who increase the genetic fitness of agents with similar decision algorithms elsewhere in the multiverse. In practice, however, I suspect that almost all creatures with at most human capabilities are unable to benefit any genomes other than those extant in their environments.
 Superrational cooperation on Earth Some, e. g.  Leslie (1991, ch. 8)  and Nate Soares, have argued that superrationality and acausal decision theory are relevant even in daily interactions between humans on Earth without considering the multiverse.  Drescher (2006a, ch. 7 ) even contends that it is an argument for egoists to behave altruistically. Others, like  Almond (2010b, ch. 4.6; 2010c, ch. 1)  or  Ahmed (2014, ch. 4) , maintain the opposite position, i. e. that acausal reasoning is rarely relevant. I will argue for the latter claim. Indeed, my belief that acausal cooperation is usually inapplicable is the reason why this paper discusses its application to the multiverse rather than more "down to Earth" scenarios.
 Fewer agents Superrationality becomes relevant in the multiverse because it contains so many disconnected agents. Thus, even if the correlation with every individual agent's decision is small, the overall acausal impact of our decisions dominates (see section 2.7). The smaller the number of agents, the higher the relative importance of the causal implications of our actions. Since the number of agents on Earth is comparably small, causal considerations may well dominate. 6.6.2 Argument from evolution: Superrationality did not evolve (strongly) We argued that superrational compromise can, under certain conditions, evolve by natural means and that many of the respective conditions are even met on Earth (see section 6.5). Hence, the mere observation that most people do not reason superrationally (see section 6.4) makes a case against its importance.
 Causal cooperation seems more important Humans rarely face one-shot prisoner's dilemmas against agents whom they know sufficiently well to be strongly correlated with them. Instead, their interactions are usually iterated and open to mutual causal influence. As a result, causal cooperation mechanisms apply, at least in principle (see section 2.9 for references to introductions on causal cooperation). Surveying the vast literature on causal cooperation and how it compares to superrational cooperation is beyond the scope of this paper, but two key points are worth highlighting. First, rational agents establish causal cooperation in a surprisingly wide range of situations. Second, successful strategies like tit-for-tat or Gradual  (Beaufils, Delahaye, and Mathieu, 1997)  tend to start the game by cooperating and never defect unless the other side starts defecting. Together, this suggests that sufficiently smart people -which, I assume, includes most agents who might apply superrationality -are capable of strong cooperation with one another without ever having to invoke superrationality.
 Hard-wired alternatives Superrationality is not the only solution to the adaptive challenge of having to cooperate with similar agents (e. g., members of the same tribe and relatives). One alternative is to hard-wire creatures to cooperate with very similar agents and defect against everyone else. This approach to ensuring cooperation has received some attention in the literature, although it is not nearly as widely known as the mechanisms of causal cooperation (see, e. g.  McAfee, 1984; Howard, 1988; or Tennenholtz, 2004) .
 Superrationality and morality Cooperation is often invoked as an argument why altruistic behavior and following moral rules is rational (e. g.,  Dawkins, 1976, ch. 12; J. Greene, 2013) . In many ways, the application of superrational cooperation resembles altruistic behavior even more closely. For example, superrationality implies that we should help a value system even if we know for certain that no agent with this value system will or can reciprocate (see section 2.9). Additionally, in suggesting that we treat others the way they would like to be treated (in order to make it more likely that others treat us the way we would like to be treated), superrationality resembles Kant's categorical imperative and the Golden Rule. Once someone is updateless, she has additional reasons to be nice to others: even if she learns that they do not or will not cooperate, she would potentially still behave nicely toward them (see section 2.4). Similarly, if she were ever to find herself in a situation resembling the Remote-controlled cake maker thought experiment (see section 2.8.6), where she knows that cooperation hurts goals, she might still make that sacrifice. Some implications of superrationality thus bear a close resemblance to altruistic or moral behavior.  Drescher (2006a, ch. 7.2 .1) makes similar points regarding the similarity between superrational cooperation and altruism. However, he goes further by arguing that superrational cooperation is the basis for morality -a way of "deriving ought from is". I will discuss two questions that might arise from this argument: is altruistic action derived from self-interest really the essence of morality or altruism? And: is superrationality sufficient for arriving at the desired altruistic conclusions? 6.7.1 Real altruism  Yudkowsky (2015, ch. 259)  writes: Consider the following, and ask which of these two philosophers is really the altruist, and which is really selfish? "You should be selfish, because when people set out to improve society, they meddle in their neighbors' affairs and pass laws and seize control and make everyone unhappy. Take whichever job that pays the most money: the reason the job pays more is that the efficient market thinks it produces more value than its alternatives. Take a job that pays less, and you're second-guessing what the market thinks will benefit society most." "You should be altruistic, because the world is an iterated Prisoner's Dilemma, and the strategy that fares best is Tit for Tat with initial cooperation. People don't like jerks. Nice guys really do finish first. Studies show that people who contribute to society and have a sense of meaning in their lives, are happier than people who don't; being selfish will only make you unhappy in the long run." Blank out the recommendations of these two philosophers, and you can see that the first philosopher is using strictly prosocial criteria to justify his recommendations; to him, what validates an argument for selfishness is showing that selfishness benefits everyone. The second philosopher appeals to strictly individual and hedonic criteria; to him, what validates an argument for altruism is showing that altruism benefits him as an individual: higher social status or more intense feelings of pleasure. So which of these two is the actual altruist? Yudkowsky elaborates in the rest of the chapter. The point he is making is that "actual altruism" is usually understood to mean caring about others, rather than merely behaving altruistically based on egoistic reasoning. Verbal disputes about the meaning of "true altruism" aside, there is a difference between having the welfare of others as part of one's goal on the one hand, and benefitting others for egoistic (or other non-altruistic or amoral) reasons on the other. I am an altruist of the former kind, but cooperation (whether superrational or not) only supports altruism of the latter kind. I would think that most other people are also altruists of the former kind (in addition to sometimes being altruists of the latter kind). 77 Altruism of the latter kind also does not "derive ought from is" 78 , as Drescher promises in chapter 7 of Good and Real. Instead, it derives (potentially unexpected) action recommendations from an already existing ought, i. e. egoism or whatever values an agent already has. Specifically, (multiverse-wide) superrational compromise can be viewed as agents switching to a new utility function, but only because it benefits their current utility function. There are many other examples of agents effectively adopting a new goal. Consider an egoist living in 16th-century Spain. Her environment punishes people who are not aligned with Catholicism. To further her goals, the egoist should therefore behave as though she was a Catholic with pure Catholic goals. She thus derives a new "morality" from purely egoistic goals, but I suspect that meta-ethicists' excitement about this is limited.
 How much altruistic behavior does superrationality entail? The second issue is that superrationality does not suffice for reproducing all of our moral intuitions. For one, I am not sure to what extent superrationality has a bearing on interactions with other people on Earth at all (see section 6.6). Furthermore, we saw that superrationality only warrants helping other superrational agents (see section 2.9.4). But our moral intuitions also regard other agents as morally relevant. As an example, consider Alice, a purely causal decision theorist who even defects in a prisoner's dilemma against her copy. Does this mean that Alice is morally irrelevant, no matter her degree of consciousness, capacity to suffer, etc.? Alice is not just a thought experiment -many philosophers would two-box in Newcomb's problem (see section 2.2). Since Newcomb's problem is roughly equivalent to the prisoner's dilemma against an identical copy (  Lewis, 1979) , this shows that most philosophers reject superrationality. Nevertheless, I and presumably most others care intrinsically about the welfare of these moral philosophers; the same is true for young children and non-human animals, most or all of which do not reason superrationally. Superrationality and what we would usually call "morality" thus disagree strongly on who is morally relevant  (Drescher, 2006a , sections 7.2.2 and 7.2.3).
 Multiverse-wide superrationality for causal decision theorists Throughout this paper, I have assumed that some acausal decision theory is correct, albeit without narrowing it down to any particular theory. To me, this is no limitation of MSR, because I hold that causal decision theories fail in examples like the donation game with similarity. However, many professional philosophers are causal decision theorists (see 2.2). Are the arguments presented in this paper entirely irrelevant to them? 79 Remember, from section 2.3, that CDT actually recognizes its flaw. Specifically, CDT self-modifies to cooperate acausally with copies that are created in the future. After all, these copies can be causally influenced to cooperate acausally to each other's benefit. Other humans and extraterrestrials in far away parts of the multiverse do not fall into that category, of course -so causal decision theorists would not precommit to engage in full multiverse-wide superrational cooperation. However, one multiverse theory is the Everett interpretation of quantum physics, according to which our universe constantly "splits" into different branches. Thus, under the Everett interpretation, near-copies of oneself are created all the time and in large quantities. Moreover, it pays in causal terms to cooperate across time, i. e. to commit me tomorrow and me in-30-years to cooperate. A causal decision theorist would therefore cooperate with a large number of agents created after CDT's precommitment. It thus seems as though a weaker version of the considerations from this paper apply to causal decision theorists after all. 79 One obvious way in which the implications are relevant to causal decision theorists is decision-theoretical uncertainty  (MacAskill, 2016) . Perhaps, even ardent defenders of CDT have probability on CDT being the wrong way to make decisions. I, at least, do not have a probability of 100% on a single decision theory being the right one. If you have some weight on some of the alternatives to causal decision theory, then you would also give MSR considerations some weight. In fact,  argues that if we live in a sufficiently large universe, then EDT and other non-causal decision theories immediately dominate expected value calculations that take decision-theoretical uncertainty into account.
 Simulations Paul  Almond (2010c, ch. 2;  has argued that correlations across the multiverse have implications for whether and how we should simulate other civilizations. The idea has also been proposed by others. It is mainly relevant for agents and civilizations who primarily care about copies of themselves, which it is not discussed in the main text.
 If being in a simulation is bad, avoid creating one Almond (2010c, section 4.2) writes: If you take the simulation argument seriously, then evidential decision theory would seem to allow you to assert some control over the other civilizations that might be building these simulated realities. One way in which evidential decision theory would be relevant is in the way it allows you to control the probability that you are in a simulation in the first place. If your civilization decides to develop the capability to run simulated realities, then you are meta-causing [i. e. influencing acausally] civilizations in general to do likewise (including civilizations on which our own might be modeled), and making it less likely that almost all civilizations end before they are capable of producing simulated realities, in turn making it more likely that you are in a simulated reality. If, however, your civilization decides not to acquire this capability then you are meta-causing civilizations in general to do likewise, making it less likely that you are in a simulated reality. Once your civilization has the capability to produce simulated realities, if your civilization decides to do it, this would make it more likely that other civilizations also do it, again making it more likely that you are in a simulated reality. On the other hand, if your civilization decides not to produce simulated realities, this makes it less likely that other civilizations would choose to do so, and therefore less likely that you are in a simulated reality yourself. If you assume the view of anthropic decision theory  (Armstrong, 2011 ) instead of classical anthropics (i. e., the self-sampling or self-indication assumption), then your decision can affect the fraction of copies of you that are in a given simulation. Note that under certain assumptions about the efficiency of simulations, one's effect on the probability of being in a simulation may be negligible. If any civilization could run orders of magnitudes more simulations of civilizations than there are civilizations in the basement, then most copies will be in simulations no matter what you decide. Regardless of your choice, you will probably be in a simulation.
 Happy simulations Almond (2010c, section 4.2) proposes to simulate civilizations in a nice way to increase the probability of being in such a simulation oneself. While evidential decision theory might be applied to try to reduce your "risk" of being in a simulated reality, some people, and some civilizations, might not see it that way: They might think that being in a simulated reality could have benefits if the entity that constructed the simulation is kind; for example, the inhabitants of the simulation might be protected from existential risks to their civilization, or they might be provided with an afterlife. Evidential decision theory suggests the possible tactic of making large numbers of simulated realities in which the inhabitants are treated kindly as a way of trying to meta-cause civilizations in general to do the same thing. This would be going further than what I said previously about treating the inhabitants of your own simulations kindly: This would be done so as to make it more likely that you are in a simulation, and that it is one in which you will be treated kindly. We might imagine a civilization doing this as a way of trying to use evidential decision theory to pluck an afterlife out of nowhere for itself, if it has recently acquired the computing power to simulate many civilizations, and provide them with an afterlife, but does not yet have technology such as mind uploading which it might use to obtain an afterlife more directly. A civilization might attempt this even if it does not yet have the computing power to construct simulated realities: It might set up some kind of legal or corporate framework to ensure that large numbers of ancestor simulations, complete with an afterlife, are constructed in the future, the idea being to strengthen the case that it is itself in such a simulation, made by a civilization with a past that is strongly correlated with its own present. Someone might even set up some organization for this purpose as a result of reading this article!
 Infinite ethics In all our calculations (sections 2.7 and 2.8) we assume finite numbers of agents each with a finite causal influence on their world. However, the multiverse -or even a single universe -may well be infinite. These infinities entail severe complications for the application of multiverse-wide consequentialist moral views like those required for multiverse-wide superrational cooperation  (Bostrom, 2011; Arntzenius, 2014) . Superrationality is a form of what  Bostrom (2011, ch 4.6)  calls "class action": through our actions, we can acausally affect an infinite amount of value, even if each physical instantiation of ourselves only has a finite causal impact. It seems unclear whether this makes infinite ethics even more challenging, or whether it can be viewed as a step toward a solution (cf.  Almond, 2010c, ch. 3.2 ). One's preferred approach to the problem of infinite ethics may well be consequential for a variety of issues (including MSR), which is why FRI lists infinite ethics as a promising area for future research. Nonetheless, I expect a solution to preserve most of the conclusions drawn from traditional (i. e. finite) ethics.
 Objection based on uncertainty about the values of superrationalists in the multiverse Thoughts on the value systems of extraterrestrials are necessarily speculative and uncertain. At what level of certainty about some other value system should we invest resources into maximizing it? Indeed, one possible criticism of MSR is that we will never be sufficiently certain of just how common some other value system is. Thus, the argument goes, we should in practice never take any specific value systems other than our own into consideration. First note that superrationality is still relevant even if you do not know the other value systems. There are some interventions that benefit other superrationalists without requiring knowledge of their values (see section 4.1), such as making future superintelligent AIs cooperate superrationally (under the assumption that they will come to understand the values of other agents in the multiverse much better than we do). But even if the argument acknowledges this, it is still invalid, primarily because it ignores the fact that we do not know how common our own value system is, either. In section 2.8 we argued that if we consider the correlations between our actions and the behavior of agents elsewhere in the multiverse, then maximizing a neutral compromise utility function in our local universe maximizes our original utility function in the multiverse at large. This argument also applies if we are uncertain about the other agents' utility functions and thus the compromise utility function itself. Thus, it must be possible to state the criticism in terms of the compromise utility function. For example, the criticism may translate to the following statement: the only terms in the compromise utility function that we can be certain about represent our own values. We are so uncertain about all other value systems that they do not contribute much to estimates of compromise utility. This criticism could, in theory, be true. Imagine you grew up on a planet where everyone had the same value system as yours; even if you believed that the universe also has other value systems, you would be justified not to assign much weight to any other specific value system. On Earth, however, we already observe quite some variety in what people care about. Thus, no matter what value system you hold, there are probably other value systems that are similarly common on Earth. Of course, we still do not know whether these value systems are also common elsewhere in the universe, but your own value system is a priori not in a privileged position that would justify assuming it to be more common than others. Solely maximizing our own utility function in this universe thus seems to be a bad approach towards maximizing the compromise utility function, in turn making it suboptimal in terms of our multiverse-wide utility. Figure 1 : 1 Figure 1: A causal graph representing the Donation game with copies and precommitment.
 Figure 2 : 2 Figure 2: A graph representing the causal relationship in the CGTA thought experiment.
 Figure 3 :Figure 4 : 34 Figure 3: Generic causal graphs representing the two types of Newcomb-like decision problems. Medical Newcomb problems are illustrated on the left. Newcomb problems based on similarity between decision algorithms are illustrated on the right.
 Figure 6 : 6 Figure 6: A graph representing a situation of mutual cooperation. An arrow from A to B indicates that A can benefit B.
 Figure 7 : 7 Figure 7: A circular cooperation graph representing cooperation schemes of the sort used in the Donation circle. Again, an arrow from A to B indicates that A can benefit B.
 Figure 8 : 8 Figure 8: A linear cooperation graph (graph theoretically speaking, a 1-ary tree) representing schemes of cooperation like that in the donation ladder. An arrow from A to B indicates that A can benefit B. Again, the nodes represent participants and an arrow from A to B indicates that A can bring causal benefits to B.
 Figure 9 : 9 Figure 9: A directed acyclic graph representing the schemes of cooperation like that of the Hierarchical donation game.
 where, for example, P (C | C) is the probability that the other side cooperates conditional on my cooperation. Solving for b other yields b other > b u P (C | C) − P (C | D) , (8) where P (C | C) − P (C | D) can be interpreted as quantifying how much more likely my cooperation makes the other's cooperation. Because there is at least some correlation, the term is always greater than 0. If the correlation is perfect, then P (C | C) = 1 and P (C | D) = 0, such that we get Eq. (7) as a special case of Eq. (8). If the correlation is less than perfect, then b a > b s may not be enough. For example, if P (C | C) = 0.8 = P (D | D) (such that whatever one agent does, the other agent is 80% likely to do the same), then it must hold that b a > b s P (C | C) − P (C | D) = b s 0.8 − 0.2 = 5 3 b s .
 Omega decides to play a game of heads or tails with you. You are told that if the coin comes up tails, Omega will ask you to give it $100. If it comes up heads, Omega will predict whether you would have given $100 if the coin had come up tails. If Omega predicts that you would have given it the money, it gives you $10,000; otherwise, you receive nothing. Omega then flips the coin. It comes up tails, and you are asked to pay $100. Do you pay? 2.2):Counterfactual mugging.If you can precommit to giving the money before you learn about your poor luck, you should do so. After all, this would render it near-certain that Omega would give us $10,000 if the coin comes up heads, at the mere cost of $100 if it comes up tails. By precommitting to pay Omega, we thus gain 0.5 • $10,000 − 0.5 • $100 = $4,950 in expectation.
 . Meanwhile, of people who do not chew gum, only 10% die of throat abscesses before the age of 50. The researchers, to explain their results, wonder if saliva sliding down the throat wears away cellular defenses against bacteria. Having read this study, would you choose to chew gum? But now a second study comes out, which shows that most gum-chewers have a certain gene, CGTA, and the researchers produce a table showing the following mortality rates: CGTA present CGTA absent Chew gum 89% die 8% die Don't chew 99% die 11% die
 First, we have to consider what negative correlation means. Let's say you currently think that roughly 0.1% of evolved agents in the multiverse who have thought about MSR decide to cooperate. Now, you learn of one randomly chosen agent that she cooperates. The intuitive response is to increase the 0.1% estimate, if only slightly (depending how confident you were in your initial estimate). If this agent were negatively correlated with the others, then upon learning that this one agent cooperated, you would adjust your estimate of how many agents cooperate downward.
 One fine day, out of the blue, you get a letter from S. N. Platonia, a renowned Oklahoma oil trillionaire. The letter states that 20 leading rational thinkers have been selected to participate in a little game, and you are among the lucky players. "Each of you has a chance at winning one billion dollars, put up by the Platonia Institute for the Study of Human Irrationality", it explains. "Here's how: if you wish, you may send a telegram with just your name on it to the Platonia Institute. If exactly 5 people reply within 48 hours, they each receive one billion dollars, otherwise no prizes are awarded to anyone. You are not allowed to communicate with each other or share the prize afterward." What do you do? 26  For example, consider the following variation of the Platonia dilemma, adapted from Hofstadter (1983) :Platonia five.
 Table 1 : 1 . Payoff matrix for two people driving in opposite directions. player 2 right-hand left-hand player 1 right-hand 0 -10 left-hand −10 0
 Omega has a list of 6 participants. The list is circular, meaning that every participant has a successor. Omega sends each participant a letter, asking them to respond with single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. It explains that by sending in 'C', participants can increase their successor's payoff by $5. By sending in 'D', they can increase their own payoff by $2. As usual, the participants are told that they are all rational or that they use similar decision mechanisms. Every participant only cares about the balance of her own bank account, and not about Omega's or that of the other 6 participants. Upon receiving the letter, should you cooperate or defect?
 Secondly, thinking about the other agents' decisions can be dangerous. No. 42 defects solely because he thinks about what the preceeding 41 participants decide. Knowing what the other agents think is thus harmful for some not-yet-updateless decision theories. Hence, similar to how it is wise to remain ignorant about your position in the list, many decision theories would recommend not thinking about what the other agents will do. If the players are human, then No. 1 may not be able to refrain from realizing that he wins by defecting. Perhaps No. 2 cannot refrain from realizing that No. 1's situation is different and his decision therefore independent of hers. However, participants with two-figure positions may be able to refrain and go with the reasoning originally presented: whatever I choose, my predecessor will probably choose the same, as his situation is similar to mine. If I just go ahead without thinking about the "chain of defection" initiated by No. 1, then people with similar numbers are probably going to do the same. Donation tree. Omega has a long list of participants again. It sends all of them a letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. Omega explains that by sending in 'C', participants can increase the payoff of at least 3 participants down the list by $2 each. For example, if the 4th participant chooses to cooperate, this benefits a subset of the participants in positions 5, 6, etc. but not the previous 3 participants. The cooperation of the last few participants has little to no effect. By sending in 'D' participants can increase their own payoff by $5. Participants do not know their position on the list or whom they could benefit. As usual, they are told that they all use similar decision mechanisms. Every participant only cares about the balance of their own bank account, and not about Omega's or the other participants'. Upon receiving the letter, should a participant cooperate or defect? The linear structure can be generalized to non-linear hierarchical cooperation schemes. Consider the following variant of the donation game: , chapter 7.2.2). If all of this is not the case, nothing can change the fact that at least No. 1 "wins by defecting once she knows her position on the list.
 To talk about human values, it is at least helpful (if not necessary) to develop some systematic terminology and overview of what kind of things people care about. Luckily, we can get help from moral psychologists and others who have attempted to develop just this sort of overview.One example is Jonathan Haidt's and Craig Joseph's moral foundations theory. It divides morality up into five foundations -care, fairness, loyalty, authority and sanctity -although the authors do acknowledge that some other values (such as liberty) may deserve foundation status as well. Haidt and his colleagues have also shown that while social conservatives tend to embrace all five moral foundations, liberals/progressives seem to focus primarily on the first two, i. e. care and fairness.51  We can thus also use the terms "liberal" and "conservative" to describe values, even though it is, of course, uncertain whether this distinction carries the same weight in other civilizations.Other theories outlining what humans value include Schwartz' Theory of Basic Human Values (updated and extended bySchwartz et al. (
 Table 2 : 2 The payoff matrix of a prisoner's dilemma. player 2 C D player 1 C 4 3 D 3 2
 Table 3 : 3 The effective payoffs of a prisoner's dilemma to a third party that cooperates superrationally.
 Table 4 : 4 The effective payoffs of a prisoner's dilemma, in which player 1 cooperates superrationally (with extraterrestrial agents who hold player 2's values), but player 2 does not.
 Do people already apply superrational reasoning when interacting with each other on Earth? Certainly, many disagree with CDT's choice in contrived examples like Newcomb's problem or the prisoner's dilemma against a copy, but does it ever influence their real-world decisions? When conducting a donation game for his Scientific American article, Hofstadter (1983)  asked the participants to explain their reasoning: I would like to quote to you some of the feelings expressed by my friends caught in this deliciously tricky situation. [...] Martin Gardner (yes, I asked Martin to participate) vividly expressed the emotional turmoil he and many others went through.Many people flirted with the idea that everybody would think "about the same", but did not take it seriously enough. Scott Buresh confided to me: "It was not an easy choice. I found myself in an oscillation mode: back and forth. I made an assumption: that everybody went through the same mental processes I went through. Now I personally found myself wanting to cooperate roughly one third of the time. Based on that figure and the assumption that I was typical, I figured about one third of the people would cooperate. So I computed how much I stood to make in a field where six or seven people cooperate. It came out that if I were a D, I'd get about three times as much as if I were a C. So I'd have to defect. Water seeks out its own level, and I sank to the lower right-hand corner of the matrix." At this point, I told Scott that so far, a substantial majority had defected. He reacted swiftly: "Those rats -how can they all defect? It makes me so mad! I'm really disappointed in your friends, Doug." So was I, when the final results were in: Fourteen people had defected and six had cooperated [...]. bought the Brooklyn Bridge than the person who sold it. Similarly, I'd feel better spending $3 gained by cooperating than $10 gained by defecting." Charles Brenner, who I'd figured to be a sure-fire D, took me by surprise and C'd. When I asked him why, he candidly replied, "Because I don't want to go on record in an international journal as a defector." Very well. Know, World, that Charles Brenner is a cooperator! Sidney Nagel was very displeased with his conclusion. He expressed great regret: "I actually couldn't sleep last night because I was thinking about it. I wanted to be a cooperator, but I couldn't find any way of justifying it. The way I figured it, what I do isn't going to affect what anybody else does. I might as well consider that everything else is already fixed, in which case the best I can do for myself is to play a D." [...] 'C' is the answer I was hoping to receive from everyone. I was not so optimistic as to believe that literally everyone would arrive at this conclusion, but I expected a majority would -thus my dismay when the early returns strongly favored defecting. As more phone calls came in, I did receive some C's, but for the wrong reasons. Dan Dennett cooperated, saying, "I would rather be the person who "Horrible dilemma", he said. "I really don't know what to do about it. If I wanted to maximize my money, I would choose D and expect that others would also; to maximize my satisfactions, I'd choose C, and hope other people would do the same (by the Kantian imperative). I don't know, though, how one should behave rationally. You get into endless regresses: 'If they all do X, then I should do Y, but then they'll anticipate that and do Z, and so . . .' You get trapped in an endless whirlpool. It's like Newcomb's paradox." So saying, Martin defected, with a sigh of regret.In a way echoing Martin's feelings of confusion, Chris Morgan said, "More by intuition than by anything else, I'm coming to the conclusion that there's no way to deal with the paradoxes inherent in this situation. So I've decided to flip a coin, because I can't anticipate what the others are going to do. I think -but can't know -that they're all going to negate each other." So, while on the phone, Chris flipped a coin and "chose" to cooperate.
			 This is consistent with the terminology by Tegmark (2003) but otherwise uncommon.
			 Quantifying utility in a way that allows for comparison among different agents is difficult. For now, we will assume that it is possible. The question is revisited in section 2.8.
			 Speaking about correlations between decisions only makes sense under the Bayesian interpretation of probability. If we see an agent cooperate, then this makes us assign a higher credence to a similar agent cooperating as well. However, if we were to observe two similar agents make the same decision over and over again, then their decisions would be uncorrelated in the resulting empirical distribution.I should also note that, in principle, I could also talk about dependences rather than correlations. Our decision and the outcome of some other causally disconnected event could be dependent in all kinds of ways, including being dependent but uncorrelated. Throughout this paper I will assume that the dependences can be viewed as simple linear relationships (as measured by the Pearson correlation coefficient) and that it always holds that the more I cooperate, the more others cooperate. I briefly discuss the possibility of negative correlations in section 2.6.2.
			 Note that the term "non-causal decision theory" is not meant to imply that these theories do not rely on the concept of causality at all.5 Some have argued that evidentialist intuitions are even stronger in problems of cooperation like versions of the prisoner's dilemma with correlated decision making. Egan (2007)  presents yet another decision problem as a decisive counterexample.6 If you have anthropic uncertainty over whether you are currently in a simulation used to decide how to fill the boxes with money, CDT may also recommend one-boxing if the simulated version would still care
			 In some versions of this problem, Omega has already flipped the coin when it approaches you. In those cases, you would still win by precommitting long after the coin has already landed, provided you are still uncertain about the result of the coin flip.9 Similar lines of reasoning about precommitment apply to thought experiments like the Newcomb's problem with transparent boxes(Drescher, 2006a, chapter 6.2), retribution(Drescher, 2006a, chapter 7.3.1) and Parfit's hitchhiker(Parfit, 1984, chapter 1.3).
			 In fact, most multiverse theories contain infinitely many agents. This leads to some additional complications, discussed in section 6.10.13 Decision theorists have picked up on the point that large numbers of agents can bring out the differences between CDT and EDT in realistic cases. In particular, large elections are often mentioned as such a case (see, e. g.Ahmed, 2014, chapter 4.6.3).14 Note that this is usually not an instance of Pascal's mugging, although the underlying mathematical mechanism (multiplying very small numbers with very large numbers) is similar. Whereas in Pascal's mugging, a big reward outweighs the low probability assigned to it, multiverse-wide superrationality (MSR) involves a low probability being outweighed by the large number of near-independent instances of that probability. The positive result occurs with a high probability as long as the other agents' decisions of whether to cooperate are mostly independent of one another. For comparison, imagine drawing balls out of a box containing 1,000,000 balls. You are told that the probability of drawing a blue ball is only 1/1,000 and that the probabilities of different draws are independent. Given this information, you can tell with a high degree of certainty that there are quite a few blue balls in the box. Multiverse-wide correlations between agents thus becomes much more important to consider than the correlations in smaller scale problems like the donation game, unless we are skeptical of some of the underlying assumptions.
			 This differs somewhat from more standard game-theoretical definitions of coordination. For a discussion of the relationship, see (Oesterheld, 2017) .
			 This notation -viewing the lotteries as probability distributions over action vectors -is a bit unnatural, and stems from the lack of an intermediate step of world states or histories between action vectors and utilities in our notation. If we extended our notation with such an intermediate step, then the lotteries would be over states of the world rather than action vectors. Although the proofs also work with action vectors, it may help to think of the lotteries as being over histories.18 Interestingly, the proof of the aggregation theorem given by Harsanyi (1955)  contains an error. However, since then a few alternative, correct proofs have been published(Fishburn, 1984; Border, 1985;  Hammond,  1992).
			 Note that none of the previous arguments were based on interpersonal comparisons of utility.20  There is a technical problem with utility functions that do not assume a highest/lowest value at all. If they are nonetheless bounded, the infimum and supremum must be set to 0 and 1. If the utility functions assume arbitrarily high values, range normalization is not possible. That is, for an unbounded utility function u there is no bounded utility function u' that is equivalent to u.21 For ethical comparisons, the lowest and highest values usually depend on an agent's moral relevance, or some measure of the intensity of preference (un)fulfillment she can experience. Alternatively, the utility function may be weighted by such values at some other steps of the interpersonal comparison of utility.22 As I will argue below, there are some pathological cases in which every possible compromise utility function leaves someone worse off. However, both of the following cases can, if they avoid these pathologies,
			 Another approach, which I have brought up in previous work(Oesterheld, 2016a, section 3.2), is to use any utility function extraction procedure that is not explicitly biased in any way and hope that such "fair[or,  perhaps, equal]  treatment in determining all individuals' utility functions induces moral permissibility," even if the utility functions are not normalized afterward. This is especially promising if you do not yet know which agents will be favored by the procedure.
			 In If you don't know the name of the game, just tell me what I mean to you, Stuart Armstrong uses a similar game to make a somewhat similar point.
			 For instance, Peter Levin writes:The reasons that people give for their judgments are post-hoc rationalizations(Haidt, 2012,  pp. 27-51; Swidler, 2013, pp. 147-8; Thiele, 2006). "Individuals are often unable to access the causes of their moral judgments"(Graham et al., 2011, p. 368).
			 Also seeMuehlhauser and Helm (2012, ch. 5).26 Again, see the technical note Oesterheld (2017)  on how this compares to more standard game theoretical definitions of coordination.
			 You may have noticed that p=1/4=5/20, i. e. the number of players who would need to win divided by the number of players. This result generalizes.28 Specifically, if the 20 participants could let some some uniform random process determine the set of the 5 people who are allowed to send a letter, everyone could commit to going with that proposal. Consider the concept of correlated equilibria.
			 In the game-theoretical concept of correlated equilibria, the agents receive a similar form of coordination help. SeeLeyton-Brown and Shoan (2008, chapter 3.5) andOsborne and Rubinstein (1994, chapter 3.3) for introductions.
			 Note that in causal cooperation, cooperative or uncooperative behavior may also causally affect bystanders and thus increase the probability that I can establish cooperation with them in the future.31 Throughout this treatment, the graphs do not represent time and repetition. This could be done by taking the given static graphs and "unfolding through time", similar to how it is done when applying backpropagation to recurrent neural networks. The resulting graph may then resemble a UML interaction diagram.
			 Even in the iterated prisoner's dilemma, this answer -supported by backward induction -is often seen as unsatisfactory. Other examples of paradoxes caused by backward induction are the chainstore paradox, the traveler's dilemma, the unexpected hanging paradox, the Bottle Imp paradox, the centipede game, the interesting number paradox, the guess 2/3 of the average game. A good introduction is given byBasu (2007). For further references, see Basu (1994) .
			 Two classes of hypotheses in this space are substance dualism and the quantum mind. Both have a few prominent proponents but are nonetheless fringe positions in philosophy of mind. I concur with the majority and am skeptical of both hypotheses.
			 For references to the literature, see section 2.9.1.
			 Apparently, some authors differentiate between instrumental and "value rationality". I would probably disagree with the assumptions underlying the use of the term "value rationality" (see footnote 68). Nevertheless, I agree with the differentiation itself.
			 In most human sadists, sadism is probably not the only goal or cause of happiness. Many sadists probably recognize their urges as morally wrong, yet are unable to control them to varying degrees. To these sadists, a decision theory may provide a nudge towards seeking professional help (at least if they cannot satisfy their sadistic preferences in morally nonproblematic ways).
			 In my personal experience, self-identified consequentialists actually tend to be more virtue ethical in their behavior than the average person.
			 One may argue that absurdity heuristics are a part of someone's epistemology. That is, the "absurdity" of the Everett interpretation is used as a reason to give it low probability as a theory of physics. However, it is not clear whether there is a clear-cut, operational difference between belief and preference if the belief does not make a testable prediction.
			 Note that some authors are skeptical to there being any fact of the matter in questioning whether some being is conscious or not. Instead, they view terms like "consciousness" and "sentience" as definitional categories or expressions of particular values. See, e. g., Dennett (1991)  and Brian Tomasik's Dissolving Confusion about Consciousness.
			 If we normalize their utility function, both assign the same utility to a situation in which all the multiverse's metal is transformed into their favorite office supply. This also means that they assign the same utility to any other other fixed amount of metal being transformed into paperclips.
			 In Divergent preferences and meta-preferences, Stuart Armstrong makes a few points that are closely related to the preceding three paragraphs.44 Habermas' discourse ethics is also worth mentioning. Alas, the best discussion of its main ideas that I am aware of -ch. 5 of Norbert Hoerster's Wie lässt sich Moral begründen? -is currently only available in German.45 On the other hand, many (if not most) biologists seem to care about conservation -popular biology textbooks like Campbell Biology (Urry et al., 2016)  and Life: The Science of Biology (Sadava et al., 2012)  cover and seem to endorse conservation biology. There are various counter-considerations, though. For example, a prior concern for the environment may be a strong motivator for many to study biology in the first place. Perhaps many also did not think about the moral value of nature all that systematically. From what I can tell, neither Campbell Biology nor Life cover wild animal suffering at all.
			 Many arguments also present a conflict between abstract and concrete thinking. For example, the repugnant conclusion can be seen as a clash of the evaluation by the concrete welfare of the identifiable victim or representative moment and the abstract evaluation by the aggregate welfare.
			 Many other characterizations of the difference between liberals and conservatives have been proposed. For example, Robin Hanson compares the differences between liberals and conservatives to the differences between foragers and farmers. Other distinctions have been proposed by Sinn and Hayes (2016)  and Lakoff (1997) .
			 The most notable exceptions are probably Boltzmann brains, which do not have a significant impact on the universe.
			 There is some debate as to whether the the term "evolution" fits this process, i. e. about the validity and usefulness the analogy between cultural evolution on memes and biological evolution on genes (Edmonds, 2005; Kuper, 2000; Gil-White, 2005; Wimsatt, 1999; Claidière and André, 2012; Atran, 2001;  Pinker, 1999,  chapter 3, section "What now?"). Anyway, my impression is that nowadays the study of cultural evolution does not heavily rely on the analogy, even when the term "cultural evolution" is used.
			 Note that the distinction between universal and idiosyncratic concerns is not binary. For example, I would guess that valuing eternal flames is much more common in the multiverse than most religions and tribal loyalties but less common than concern for justice, welfare and freedom.
			 That said, advocates of simple ethical views like utilitarianism often argue that the implications resemble other ethical notions. For example, because receiving an additional unit of resources has a greater impact on a poor than a rich person's happiness, utilitarianism tends to prefer an even distribution of resources(Studebaker, 2012). Similarly, it has been argued that utilitarianism is (often) consistent with the wrongness of killing, justice (Mill, 1863)  and other moral rules(Smart and B. Williams, 1973, part 1, chapter 7). This decreases the value of making utilitarians more pluralistic. It should be noted, however, that many (especially critics of utilitarianism) have argued for the opposite, i. e. that there are some moral intuitions
			 For example, the Machine Intelligence Research Insitute's "Research" page is titled "Aligning advanced AI with human interests". Another AI safety organization even mentions it in their name: the Center for Human-Compatible AI. Also consider the Asilomar AI principles and the discussion of value loading byBostrom (2014b, chapters 12, 13).
			 Of course, identifying superrational cooperators in a world model may be more or less difficult than identifying humans in the world model. My tentative guess would be that it is easier, because I think the category of superrationalists can be described more succinctly than the category of humans, but of course I am not very confident in this claim. Similarly, it may be that MSR-type aggregation (e. g., variance
			 Data from other games with similarly dissatisfying Nash equilibria can be used as further tests of such models of human reasoning. For example,Basu (2007)  reviews research on people's choices in the traveler's dilemma. He also hypothesizes that many people do not go with the Nash equilibrium because of hardwired altruism.
			 Note that while humans evolved to spread their genes as much as possible, they are neither pure fitness maximizers nor pure egoists (in the sense of not caring about others' welfare). Our altruistic intentions evolved for reasons of fitness, but that does not mean they are not genuine altruistic intentions(Yudkowsky,  2015, section 138; Cosmides and  Tooby, 1995, page 54f. Wright, 1995, page 225f.).78 This is no surprise, as deriving ought from is cannot -at least in my view -be done.

Abstract:
Some decision theorists argue that when playing a prisoner's dilemma-type game against a sufficiently similar opponent, we should cooperate to make it more likely that our opponent also cooperates. This idea, which Hofstadter calls superrationality, has strong implications when combined with the insight from modern physics that we probably live in a large universe or multiverse of some sort. If we care about what happens in civilizations located elsewhere in the multiverse, we can superrationally cooperate with some of their inhabitants. That is, if we take their values into account, this makes it more likely that they do the same for us. In this paper, I attempt to assess the practical implications of this idea. I argue that to reap the full gains from trade, everyone should maximize the same impartially weighted sum of the utility functions of all collaborators. I also argue that we can obtain at least weak evidence about the content of these utility functions. In practice, the application of superrationality implies that we should promote causal cooperation, moral pluralism, moral reflection, and ensure that our descendants, who will be smarter and thus better at finding out how to benefit other superrationalists in the universe, engage in superrational cooperation.
 Introduction -the basic idea This paper makes an extraordinary claim: that a few interesting but by themselves inconsequential ideas from decision theory and physics together give rise to a crucial consideration with strong implications for how to do the most good. In this first section, I will outline the main idea and forward-reference sections with the full arguments and detailed elaborations. Afterward, I give an overview of the entire paper, section by section (section 1.1). Consider the following thought experiment, adapted from Hofstadter's (1983) Dilemmas for Superrational Thinkers, Leading Up to a Luring Lottery: Donation game with superrationality. Hofstadter sends 20 participants the same letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with the other participants. Hofstadter
 Superrationality Despite what the name might suggest, superrationality does not have anything to do with extraordinary levels of rationality. "Super" refers to inclusivity, as in superorganism, and "rationality" specifically denotes instrumental rationality. The term was introduced by Hofstadter (1983), although the basic argument had been discussed before  (Davis, 1977; Horgan, 1981 , section X). In the following we give an abbreviated and simplified account of the prisoner's dilemma or public goods game-like experiment Hofstadter ran with some of his friends and colleagues as participants. It is the same thought experiment we discussed in the introduction, although we now distinguish two slightly different versions. The argumentation for superrationality will be relatively brief. For more detailed accounts, see Hofstadter's original article or some of the references in section 2.2. Donation game with common rationality. (This is more similar to the version Hofstadter uses in his article.) Hofstadter sends 20 participants the same letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. Hofstadter explains that by sending in 'C', a participant can increase everyone else's payoff by $2. By sending in 'D', participants can increase their own payoff by $5. The letter ends by informing the participants that they were all chosen for their high levels of rationality and correct decision making in weird scenarios like this. Note that every participant only cares about the balance of her own bank account and not about Hofstadter's or the other 19 participants'. Should you, as a participant, respond with 'C' or 'D'? Donation game with similarity. The same as the donation game with common rationality. However, instead of informing the participants that they are all rational, the game master informs them that they think in similar ways about weird decision problems like this one. The basic setup of this thought experiment is equivalent to those found in, e. g., the prisoner's dilemma with copies (sometimes also referred to as the prisoner's dilemma with replicas or twins). All of these games share an important feature: they are not iterated. Participants respond only once, then find out what the others chose -and the game is over.