Multiverse Theory is the science of guessing at the shape of the state space of all which exists, once existed, will exist, or exists without any temporal relation to our present. Multiverse theory attempts to model the unobservable, and it is very difficult.

Still, there's nothing that cannot be reasoned about, in some way (Tegmark's The Multiverse Heirarchy), given the right abstractions. The question many readers will ask, which is a question we ourselves˭ asked when we were first exposed to ideas like simulationism and parallel universes, is not whether we can, but whether we should, given that we have no means to causally affect any of it, and no reason to expect that it would causally affect us in a way that would be useful to predict.

We then discovered something which shed new light on the question of whether we can, and began to give an affirmative answer to the question of whether we should.

Compat, which we would like to share with you today, is a new field, or perhaps just a very complex idea, which we found in the intersection of multiverse theory, simulationism and acausal trade (well motivated by Hofstadter's Sanity and Survival, a discussion of superrational solutions to the one shot prisoner's dilemmas). Compat asks what kind of precommitments an entity (primarily, the class of living things on the threshold of their singularity) aught to make if they wanted to acausally boost the measure of their desired patterns, if not across the entire multiverse, at least across the subset of the multiverse in which they may find their future selves.

A compat thinker negotiates acausally with hypothetical agents in other universes⬨ (I imagine these negotiations look kind of like this (Yvain's short story Galactic Core, in which a newly awoken AGI has a conversation with a recursive model of galactic precursors it cannot see)). We call the resolutions of these negotiations pacts.ˣ

Life's Pact is the protocol we expect most living species to adhere to. It is the primary object of study in Compat. I'm not sure where to start explaining it, as the reasoning is... hopefully not circular, but recursive, self-referrentialˑ. Hopefully the reasons we consider it a primal candidate for life's pact will become clear as I connect it back around. Well. I guess I'll start with the conditions of adherence:

    An adherent steward of Life's Pact allocates some proportion of their computational resources to doing a randomized search for viable life-supporting physical laws, simulating each with randomized initial conditions until its heat death(or if the candidate somehow manages to have life without entropy, until some cutoff), while monitoring the living patterns the simulated universe contains, then rewarding those simulants' who adhere to the pact in turn, perhaps by giving them entropy-reversing magic and improving their environment in formerly impossible ways, or, individual preferences permitting, by transplanting the adherent simulant's pattern to a more efficient second simulation not encumbered by the requirement of strict physical accuracy˅.

    Initial simulations stewarded under the pact are, from the inside, indistinguishable from toplevel god-free universes, as such, all living things must consider the possibility that they're living in a life's pact simulation. However, once an agent realizes that a steward of life's pact could grant them more utility than a godless universe could contain, they will wish to raise this probability, even if it is small.▾

    A choice made in isolation acausally increases the probability of unseen like-minded agents making, or having already made, the same choice. As such, adhering to the agreement acausally boosts the probability that one is already living under a higher complexity steward's lifepat programme (or boosts the amount of returns one would receive from the incentives imposed by the pact, if the probability of living under one already seemed overwhelming).

    Lo, the pact births itself. A being who sees no physical trace of a benevolent simulator finds reasons to behave as one, as the act, in its acausal way, engenders that simulator's existence, and earns its favor.

We think this pact is primal: *the* solution, an idea that will be arrived at by most living things and apparent all to be a nexus concept around which a quorum can be reached, non-arbitrary, not just some single scheme that is nice and compelling but which fails to be demonstrably better than its alternatives (which would take us into the territory of Pascal's Wager or, dare I utter it's name, no I darn't, you know the basilisk I'm talking about).

I do not know enough math to prove that it is primal (nor disprove it, which would be far more immediately useful to me tbh). I'm not sure anyone does, just yet, but I don't think we're too far off ˁ. If any physicists or decision theorists find these ideas interesting, your help would be appreciated, and potentially rewarded with huge heapings of utility larger than you can currently comprehend.

 

Concerns of Praxis

    I say that working on Compat theory might be rewarded, full disclosure, I'm not yet sure why. Obviously lifepat is a fairly sprawling scheme with an organically intelligent incentive structure, but... If there exists a valid pact, the AGI we are already building will infer it on its own. The pact does not have to be known to AGI researchers for that to happen, and I do not expect the sorts of people who tend to do well in AI research will be be terribly perturbed by it, if their creation brings it up as it stirs. As such, at this stage it seems like there's very little that most people can do to influence humanity's adherence to life's pact, few acts that compat can currently instruct, and few incentives to be paid out to anyone yet living. An organic, intelligent scheme of incentives would seem to prefer that agnostics simply carry on with business as usual.

For the theologically inclined, though, Compat may be extremely interesting, having its god of the gaps, its heavens, its deontics. Compat, as we know it, seems to have a strange(almost auspicious) capacity to make new sense of old myths. The archetype of the steward is both monotheistic and polytheistic, of a fixed, yet unknowable nature, born of man, yet still born of god, it has a body we can touch, our own stewards, and a body beyond our comprehension that mirrors the steward of man, in the set of universes which steward our pattern. The compat cosmology and all those images of its supreme being that it contains is both created, discovered, and born of itself. The compat heaven is whatever its subjects need it to be. The gospel of compat is, as far as we can yet tell, true from all perspectives, requiring no leaps of faith, no doublethink, and no motivated reasoning.

I have never seen a religion with a greater capacity for syncretization and reconciliation.

Should the theologans of the fractured tribes decide to weave compat theory into the tapestry of their beliefs, they may then come to find their tapestries woven together. Even the schism between theists and agnostics would begin to narrow. Without this weaving together, I fear that either no coherent volition can be found or humanity's FAI will have no choice but to seal its given temporal slice of human potential into an ugly compromise. Even if life's pact cannot be formalized or prepared for by any living person, compat may open the way for the discovery of confluences between preexisting belief systems, by that path the population 50 years from now could come to have far more compatible values than the one we see today.

As such, even if humanity's eventual adherence to life's pact cannot be significantly influenced from the present, compat is conceivably a major piece of a long running, necessary cultural project to reconcile the fractured tribes of humanity under the aesthetic of reason. If it can be proven, or disproven, we must attempt to do so.

 

ˑ Naturally, as anything that factors the conditionality of the behavior of likeminded entities needs to be, anything with a grain of introspection, from any human child who considers the golden rule to the likes of AlphaGo and Deep Blue, who model the their opponents at least partially by putting themselves in their position and asking what they'd do. If you want to reason about real people rather than idealized simplifications, it's quite necessary.

⬨ The phrase "other universes" may seem oxymoronic. It's like the term "atom", who's general quality "atomic" means "indivisible", despite "atom" remaining attached to an entity that was found to be quite divisible. I don't know whether "universe" might have once referred to the multiverse, the everything, but clearly somewhere along the way, some time leading up to the coining of the contrasting term "multiverse", that must have ceased to be. If so, "universe" remained attached to the the universe as we knew it, rather the universe as it was initially defined.

▾ I make an assumption around about here, that the number of simulations being run by life in universes of a higher complexity level always *can* be raised sufficiently(give their inhabitants are cooperative) to make stewardship of one's universe likely, as a universe with more intricate physics, once they learn to leverage its intricacy, will tend to be able to create much more flexible computers and spawn a more simulations than exist lower complexity levels(if we assume a finite multiverse(we generally don't), some of those simulations might end up simulating entities that don't otherwise exist. This source of inefficiency is unavoidable). We also assume that either there is no upper limit to the complexity of life supporting universes, or that there is no dramatic, ultimate decrease in number of civs as complexity increases, or that the position of this limit cannot be inferred and the expected value of adherence remains high even for those who cannot be resimulated, or that, as a last resort, agents drawing up the terms of their pact will usually be at a certain level of well-approximatable sophistication that they can be simulated in high fidelity by civilizations with physics of similar intricacy.
And if you can knock out all of those defenses, I sense it may all be obviated by a shortcut through a patternist principle my partner understands better than I do about the self following the next most likely perceptual state without regard to the absolute measure of that state over the multiverse, which I'm still coming to grips with.
There is unfortunately a lot that has been thought about compat already, and it's impossible for me to convey it all at once. Anyone wishing to contribute to, refute, or propagate compat may have to be prepared to have a lot of arguments before they can do anything. That said, remember those big heaps of expected utilons that may be on offer.

ˁ MIRI has done work on cooperation in one shot prisoners dilemmas (acausal cooperation) http://arxiv.org/abs/1401.5577. Note, they had to build their own probability theory. Vanilla decision theory cannot get these results, and without acausal cooperation, it can't seem to capture all of humans' moral intuitions about interaction in good faith, or even model the capacity for introspection.

ˣ It was not initially clear that compat should support the definition of more than a single pact. We used to call Life's Pact just Compat, assuming that the one protocol was an inevitable result of the theory and that any others would be marginal. There may be a singleton pact, but it's also conceivable that there may be incorrigible resimulation grids that coexist in an equilibrium of disharmony with our own.
As well as that, there is a lot of self-referrential reasoning that can go on in the light of acausal trade, I think we will be less likely to fall prey to circular reasoning if we make sure that a compat thinker can always start from scratch and try to rederive the edifice's understanding of the pact from basic premises. When one cannot propose alternate pacts, criticizing the bathwater without the baby may not seem .

˭ THE TEAM:
    Christian Madsen was the subject of an experimental early-learning program in his childhood, but despite being a very young prodigy, he coasted through his teen years. He dropped out of art school in 2008, read a lot of transhumanism-related material, synthesized the initial insights behind compat, and burned himself out in the process. He is presently laboring on spec-work projects in the fields of music and programming, which he enjoys much more than structured philosophy.
    Mako Yass left the university of Auckland with a dual major BSc in Logic & Computation and Computer Science. Currently working on writing, mobile games, FOSS, and various concepts. Enjoys their unstructured work and research, but sometimes wishes they had an excuse to return to charting the hyllean theoric wilds of academic analytic philosophy, all the same.
    Hypothetical Independent Co-inventors, we're pretty sure you exist. Compat wouldn't be a very good acausal pact if you didn't. Show yourselves.
    You, if you'd like to help to develop the field of Compat(or dismantle it). Don't hesitate to reach out to us so that we can invite you to the reductionist aesthete slack channel that Christian and I like to argue in. If you are a creative of any kind who bears or at least digs the reductive nouveau mystic aesthetic, you'd probably fit in there as well.

˅ It's debatable, but I imagine that for most simulants, heaven would not require full physics simulation, in which case heavens may be far far longer-lasting than whatever (already enormous) simulation their pattern was discovered in.

Summary

Some preference utilitarians care about satisfaction of preferences even when the organism with the preference doesn't know that it has been satisfied. These preference utilitarians should care to some degree about the preferences that people in other branches of our multiverse have regarding our own world, as well as the preferences of aliens regarding our world. In general, this suggests that we should give relatively more weight to tastes and values that we expect to be more universal among civilizations across the multiverse. This consideration is strongest in the case of aesthetic preferences about inanimate objects and is weaker for preferences about organisms that themselves have experiences.

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Introduction

Classical utilitarianism aims to maximize the balance of happiness over suffering for all organisms. Preference utilitarianism focuses on fulfillment vs. frustration of preferences, rather than just at hedonic experiences. So, for example, if someone has a preference for his house to go to his granddaughter after his death, then it would frustrate his preference if it instead went to his grandson, even though he wouldn't be around to experience negative emotions due to his preference being thwarted.

Non-hedonic preferences

In practice, most of people's preferences concern their own hedonic wellbeing. Some also concern the wellbeing of their children and friends, although often these preferences are manifested through direct happiness or suffering in oneself (e.g., being on the edge of your seat with anxiety when your 14-year-old daughter hasn't come home by midnight).

However, some preferences are beyond hedonic experience by oneself. This is true of preferences about how the world will be after one dies, or whether the money you donated to that charity actually gets used well even if you wouldn't find out either way. It's true of many moral convictions. For instance, I want to actually reduce expected suffering rather than hook up to a machine that makes me think I reduced expected suffering and then blisses me out for the rest of my life. It's also true of some aesthetic preferences, such as the view that it would be good for art, music, and knowledge to exist even if no one was around to experience them.

Certainly these non-hedonic preferences have hedonic effects. If I learned that I was going to be hooked up to a machine that would erase my moral convictions and bliss me out for the rest of my life, I would feel upset in the short run. However, almost certainly this aversive feeling would be outweighed by my pleasure and lack of suffering in the long run. So my preference conflicts with egoistic hedonism in this case. (My preference not to be blissed out is consistent with hedonistic utilitarianism, rather than hedonistic egoism, but hedonistic utilitarianism is a kind of moral system that exists outside the realm of hedonic preferences of an individual organism.)

Because preference utilitarians believe that preference violations can be harmful even if they aren't accompanied by negative hedonic experience, there are some cases in which doing something that other people disapprove of is bad even if they never find out. For example, Muslims strongly oppose defacing the Quran. This means that, barring countervailing factors, it would be prima facie bad to deface a Quran in the privacy of your own home even if no one else knew about it.

Tyranny of the majority?

People sometimes object to utilitarianism on the grounds that it might allow for tyranny of the majority. This seems especially possible for preference utilitarianism, when considering preferences regarding the external world that don't directly affect a person's hedonic experience. For example, one might fear that if large numbers of people have a preference against gay sex, then even if these people are not emotionally affected by what goes on in the privacy of others' bedrooms, their preference against those private acts might still matter appreciably.

As a preliminary comment, I should point out that preference utilitarianism typically optimizes idealized preferences rather than actual preferences. What's important is not what you think you want but what you would actually want if you were better informed, had greater philosophical reflectiveness, etc. While there are strong ostensible preferences against gay sex in the world, it's less clear that there are strong idealized preferences against it. It's plausible that many gay opponents would come to see that (safe) gay sex is actually a positive expression of pleasure and love rather than something vile.

But let's ignore this for the moment and suppose that most people really did have idealized preferences against gay sex. In fact, let's suppose the world consists of N+2 people, two of whom are gay and would prefer to have sex with each other, and the other N of whom have idealized preferences opposing gay sex. If N is very large, do we have tyranny of the majority, according to which it's bad for the two gays to have sex?

This is a complicated question that involves more subtlety than it may seem. Even if the direct preference summation came out against gay sex, it might still be better to allow it for other reasons. For instance, maybe at a meta level, a more libertarian stance on social issues tends to produce better outcomes in the long run. Maybe allowing gay sex increases people's tolerance, leading to a more positive society in the future. And so on. But for now let's consider just the direct preference summation: Does the balance of opposition to gay sex exceed the welfare of the gay individuals themselves?

This answer isn't clear, and it depends how you weigh the different preferences. Intuitively it seems obvious that for large enough N, N people opposed to gay sex can trump two people who prefer it. On the other hand, that's less clear if we look at the matter from the perspective of scaled utility functions.

• Suppose unrealistically that the only thing the N anti-gay people care about is preventing gay sex. In particular, they're expected-gay-sex minimizers, who consider each act of gay sex as bad as another and aim to minimize the total amount that happens. The best possible world (normalized utility = 1) is one where no gay sex happens. The worst possible world (normalized utility = 0) is one where all N+2 people have gay sex. The world where just the two gay people have gay sex is almost as good as the best possible world. In particular, its normalized utility is N/(N+2). Thus, if gay sex happens, each anti-gay person only loses 2/(N+2) utility. Aggregated over all N anti-gay people, this is a loss of 2N/(N+2).
• Also unrealistically, suppose that the only thing the two gay people care about is having gay sex. Their normalized utility for having sex is 1 and for not having it is 0. Aggregated over the two of them, the total gain from having sex is 2.
• Because 2 > 2N/(N+2), it's overall better in direct preference summation for the gay sex to happen as long as we weight each person's normalized utility equally. This is true regardless of N.

That said, if the anti-gay people had diminishing marginal disutility for additional acts of gay sex, this conclusion would probably flip around.

It feels intuitively suspicious to just sum normalized utility. As an example, consider a Beethoven utility monster -- a person whose only goal in life is to hear Beethoven's Ninth Symphony. This person has no other desires, and if he doesn't hear Beethoven's Ninth, it's as good as being dead. Meanwhile, other people also want to hear Beethoven's Ninth, but their desire for it is just a tiny fraction of what they care about. In particular, they value not dying and being able to live the rest of their lives 99,999 times as much as hearing Beethoven's Ninth.

• Each normal person's normalized utility without hearing the symphony is 0.99999. Hearing the symphony would make it 1.00000.
• The Beethoven utility monster would be at 0 without hearing the symphony and 1 hearing it.
• Thus, if we directly sum normalized utilities, it's better for the Beethoven utility monster to hear the symphony than for 99,999 regular people to do the same.

This seems suspicious. Maybe it's because our intuitions are not well adapted to thinking about organisms with really different utility functions from ours, and if we interacted with them more -- seeing them struggle endlessly, risking life and limb for the symphony they so desire -- we would begin to feel differently. Another problem is that an organism's utility counts for less as soon as the range of its experience increases. If the Beethoven monster were transformed to want to hear Beethoven's Ninth and Eighth symphonies each with equal strength, suddenly the value of its hearing the Ninth alone is cut in half. Again, maybe this is plausible, but it's not clear. I think some people have the intuition that an organism with a broader range of possible joys counts more than one with fewer, though I'm not sure I agree with this.

So the question of tyranny remains indeterminate. It depends on how you weigh different preferences. However, it remains the case that it may be instrumentally valuable to preserve norms of individual autonomy in order to produce better societies in the long run.

Preferences across worlds: A story of art maximizers

Consider the following (highly unrealistic) story. It's the year 2100. A group of three artist couples is traveling on the first manned voyage to Mars. These couples value art for art's sake, and in fact, their moral views consider art to be worthwhile even if no one experiences it. Their utility functions are linear in the amount of art that exists, and so they wish to maximize the expected amount of art in the galaxy -- converting planets and asteroids into van Gogh, Shakespeare, and Chopin.

However, they don't quite agree on which art is best. One couple wants to maximize paintings, feeling that a galaxy filled with paintings would be worth +3. A galaxy filled with sculptures would be +2. And a galaxy filled with poetry or music would be worthless: 0. The second couple values poetry at +3, sculptures at +2, and the other art at 0. The third values music at +3, sculptures at +2, and everything else at 0. Despite their divergent views, they manage to get along in the joint Martian voyage.

However, a few weeks into the trip, a terrestrial accident vaporizes Earth, leaving no one behind. The only humans are now the artists heading for Mars, where they land several months later.

The original plan had been for Earth to send more supplies following this crew, but now that Earth is gone, the colonists have only the minimal resources that the Martian base currently has in stock. They plan to grow more food in their greenhouse, but this will take many months, and the artists will all starve in the meanwhile if they each stick around. They realize that it would be best if two of the couples sacrificed themselves so that the third would have enough supplies to continue to grow crops and eventually repopulate the planet.

Rather than fighting for control of the Martian base, which could be costly and kill everyone, the three couples realize that everyone would be better off in expectation if they selected a winner by lottery. In particular, they use a quantum random number generator to apportion 1/3 probabilities for each couple to survive. The lottery takes place, and the winner is the first couple, which values paintings most highly. The other two couples wish the winning couple the best of luck and then head to the euthanasia pods.

The pro-paintings couple makes it through the period of low food and manages to establish a successful farming operation. They then begin having children to populate the planet. After many generations, Mars is home to a thriving miniature city. All the inhabitants value paintings at +3, sculptures at +2, and everything else at 0, due to the influence of the civilization's founders.

By the year 2700, the city's technology is sufficient to deploy von Neumann probes throughout the galaxy, converting planets into works of art. The city council convenes a meeting to decide exactly what kind of art should be deployed. Because everyone in the city prefers paintings, the council assumes the case will be open and shut. But as a formality, they invite their local philosopher, Dr. Muchos Mundos, to testify.

Council president: Dr. Mundos, the council has proposed to deploy von Neumann probes that will fill the galaxy with paintings. Do you agree with this decision?

Dr. Mundos: As I understand it, the council wishes to act in the optimal preference-utilitarian fashion on this question, right?

Council president: Yes, of course. The greatest good for the greatest number. Given that everyone who has any preferences about art most prefers a galaxy of paintings, we feel it's clear that paintings are what we should deploy. It's true that when this colony was founded, there were two other couples who would have wanted poetry and music, but their former preferences are far outweighed by our vast population that now wants paintings.

Dr. Mundos: I see. Are you familiar with the many-worlds interpretation (MWI) of quantum mechanics?

Council president: I'm a politician and not a physicist, but maybe you can give me the run-down?

Dr. Mundos: According to MWI, when quantum randomness occurs, it's not the case that just a single outcome is selected. Rather, all outcomes happen, and our experiences of the world split into different branches.

Council president: Okay. What's the relevance to art policy?

Dr. Mundos: Well, a quantum lottery was used to decide which colonizing couple would populate Mars. The painting lovers won in this branch of the multiverse, but the poetry lovers won in another branch with equal measure, and the music lovers won in a third branch, also with equal measure. Presumably the couples in those branches also populated Mars with a city about as populous as our own. And if they care about art for art's sake, regardless of whether they know about it or where it exists, then the populations of those cities in other Everett branches also care about what art we deploy.

Council president: Oh dear, you're right. Our city contains M people, and suppose their cities have about the same populations. If we deploy paintings, our M citizens each get +3 of utility, and those in the other worlds get nothing. The aggregate is 3M. But if we deploy sculptures, which everyone values at +2, the total utility is 3 * 2M = 6M. This is much better than 3M for paintings.

Dr. Mundos: Yes, exactly. Of course, we might have some uncertainty over whether the populations in the other branches survived. But even if the probability they survived was only, say, 1/3, then the expected utility of sculptures would still be 2M for us plus (1/3)(2M + 2M) = 4M/3 for them. The sum is more than 3M, so it would still be better to do sculptures.

After further deliberation, the council agreed with this argument and deployed sculptures. The preference satisfaction of the poetry-loving and music-loving cities was improved.

Multiversal distribution of preferences

According to Max Tegmark's "Parallel Universes," there's probably an exact copy of you reading this article within 10¹⁰²⁸ meters away and in practice, probably much closer. As Tegmark explains, this claim assumes only basic physics that most cosmologists take for granted. Even nearer than this distance are many people very similar to you but with minor variations -- e.g., with brown eyes instead of blue, or who prefer virtue ethics over deontology.

In fact, all possible people exist somewhere in the multiverse, if only due to random fluctuations of the type that produce Boltzmann brains. Nick Bostrom calls these "freak observers." Just as there are art maximizers, there are also art minimizers who find art disgusting and want to eliminate as much of it as possible. For them, the thought of art triggers their brains' disgust centers instead of beauty centers.

However, the distribution of organisms across the multiverse is not uniform. For instance, we should expect suffering reducers to be much more common than suffering increasers because organisms evolve to dislike suffering by themselves, their kin, and their reciprocal trading partners. Societies -- whether human or alien -- should often develop norms against cruelty for collective benefit.

Human values give us some hints about what values across the multiverse look like, because human values are a kind of maximum likelihood estimator for the mode of the multiversal distribution. Of course, we should expect some variation about the mode. Even among humans, some cultural norms are distinct and others are universal. Probably values like not murdering, not causing unnecessary suffering, not stealing, etc. are more common among aliens than, say, the value of music or dance, which might be human-specific spandrels. Still, aliens may have their own spandrels that they call "art," and they might value those things.

Like human values, alien values might be mostly self-directed toward their own wellbeing, especially in their earlier Darwinian phases. Unless we meet the aliens face-to-face, we can't improve their welfare directly. However, the aliens may also have some outward-directed aesthetic and moral values that apply across space and time, like the value of art as seen by the art-maximizing cities on Mars in the previous section. If so, we can affect the satisfaction of these preferences by our actions, and presumably they should be included in preference-utilitarian calculations.

As an example, suppose there were 10 civilizations. All 10 valued reducing suffering and social equality. 5 of the 10 also valued generating knowledge. Only 1 of the 10 valued creating paintings and poetry. Suppose our civilization values all of those things. Perhaps previously we were going to spend money on creating more poetry, because our citizens value that highly. However, upon considering that poetry would not satisfy the preferences of the other civilizations, we might switch more toward knowledge and especially toward suffering reduction and equality promotion.

In general, considering the distribution of outward-directed preferences across the multiverse should lead us to favor more those preferences of ours that are more evolutionarily robust, i.e., that we predict more civilizations to have settled upon. One corollary is that we should care less about values that we have due to particular, idiosyncratic historical contingencies, such as who happened to win some very closely contested war, or what species were killed by a random asteroid strike. Values based on more inevitable historical trends should matter relatively more strongly.

Tyranny of the aliens?

Suppose, conservatively, that for every one human civilization, there are 1000 alien civilizations that have some outward-directed preferences (e.g., for more suffering reduction, justice, knowledge, etc.). Even if each alien civilization cares only a little bit about what we do, collectively do their preferences outweigh our preferences about our own destiny? Would we find ourselves beholden to the tyranny of the alien majority about our behavior?

This question runs exactly parallel to the standard concern about tyranny of the majority for individuals within a society, so the same sorts of arguments will apply on each side. Just as in that case, it's possible aliens would place value on the ability of individual civilizations to make their own choices about how they're constituted without too much outside interference. Of course, this is just speculation.

Even if tyranny of the alien majority was the result, we might choose to accept that conclusion. After all, it seems to yield more total preference satisfaction, which is what the preference utilitarians were aiming for.

Direct welfare may often dominate

In the preceding examples, I often focused on aesthetic values like art and knowledge for a specific reason: These are cases of preferences for something to exist or not where that thing does not itself have preferences. Art does not prefer for itself to keep existing or stop existing.

However, many human preferences have implications for the preferences of others. For instance, a preference by humans for more wilderness may mean vast numbers of additional wild animals, many of whom strongly (implicitly) prefer not to have endured the short lives and painful deaths inherent to the bodies in which they found themselves born. A relatively weak aesthetic preference for nature by a relatively small number of people is compared against strong hedonic preferences by large numbers of animals not to have existed. In this case, the preferences of the animals clearly dominate. The same is true for preferences about creating space colonies and the like: The preferences of the people, animals, and other agents in those colonies will tend to far outweigh the preferences of their creators.

Considering multiverse-wide aesthetic and moral preferences is thus cleanest in the case of preferences about inanimate things. Aliens' preferences about actions that affect the welfare of organisms in our civilization still matter, but relatively less than the contribution of their preferences about inanimate things.

Acknowledgments

This piece was inspired by Carl Shulman's "Rawls' original position, potential people, and Pascal's Mugging," as well as a conversation with Paul Christiano.

There are at least ten different conceptions of how the World can be made of many worlds.

But are those just definitional disputes? Or are they separate claims that can be evaluated. If they are distinct, in virtue of what are they distinct. Finally, do we have good grounds to care (morally) about those fine distinctions?

 

Max Tegmark's taxonomy is well known here. 

Brian Greene's is less, and has 9, instead of four, kinds of multiverse, I'll risk conflating the Tegmark ones that are superclasses of these, feel free to correct me:

In his book, Greene discussed nine types of parallel universes:

• (Tegmark 1) The quilted multiverse only works in an infinite universe. With an infinite amount of space, every possible event will occur an infinite amount of times. However, the speed of light prevents us from being aware of these other identical areas.
• (Tegmarks 1 and 2) The inflationary multiverse is composed of various pockets where inflaton fields collapse and form new universes.
• The brane multiverse follows from M-theory and states that each universe is a 3-dimensional brane that exists with many others. Particles are bound to their respective branes except for gravity.
• The cyclic multiverse has multiple branes (each a universe) that collided, causing Big Bangs. The universes bounce back and pass through time, until they are pulled back together and collided again, destroying the old contents and creating them anew.
• (Tegmarks 2) The landscape multiverse relies on string theory's Calabi-Yau shapes. Quantum fluctuations drop the shapes to a lower energy level, creating a pocket with a different set of laws from the surrounding space.
• (Tegmarks 3) The quantum multiverse creates a new universe when a diversion in events occurs, as in the many-worlds interpretation of quantum mechanics.
• The holographic multiverse is derived from the theory that the surface area of a space can simulate the volume of the region.
• (Related to Bostrom's Simulation Hypothesis) The simulated multiverse exists on complex computer systems that simulate entire universes. (for the sake of brevity I'll consider dust theory to be a subset of this)
• (Tegmark's 4) The ultimate multiverse contains every mathematically possible universe under different laws of physics.

I don't understand branes well enough (or at all) to classify the others. The holographic one seems compatible with a multitude, if not all, previous ones. 

Besides all those there is David Lewis's Possible Worlds in which all possible worlds exist (in whichever sense the word exist can be significantly applied, if any). For Lewis, when we call our World the Actual World, we think we mean the only one that is there, but what we mean is "the one to which we happen to belong".  Notice it is distinct from the Mathematical/Ultimate in that there may be properties of non-mathematical kind. 

So Actual_lewis= Our world  and Actual_{most everyone else}=Those that obtain, exist, or are real. 

The trouble with existence, or reality, is that it is hard to pin down what it is pointing at. Eliezer writes:

The collection of hypothetical mathematical thingies that can be described logically (in terms of relational rules with consistent solutions) looks vastly larger than the collection of causal universes with locally determined, acyclically ordered events. Most mathematical objects aren't like that. When you say, "We live in a causal universe", a universe that can be computed in-order using local and directional rules of determination, you're vastly narrowing down the possibilities relative to all of Math-space.

So it's rather suggestive that we find ourselves in a causal universe rather than a logical universe - it suggests that not all mathematical objects can be real, and the sort of thingies that can be real and have people in them are constrained to somewhere in the vicinity of 'causal universes'. That you can't have consciousness without computing an agent made of causes and effects, or maybe something can't be real at all unless it's a fabric of cause and effect. It suggests that if there is a Tegmark Level IV multiverse, it isn't "all logical universes" but "all causal universes".

and elsewhere

More generally, for me to expect your beliefs to correlate with reality, I have to either think that reality is the cause of your beliefs, expect your beliefs to alter reality, or believe that some third factor is influencing both of them.

Now another interesting way of looking at existence or reality is  

Reality=I should care about what takes place there

It is interesting because it is what is residually left after you abandon the all too stringent standard of "causally connected to me", which would leave few or none of the above, and cut the party short.  

So Existence_yud  and Existence_{moral-concern} are very different. Reality-fluid, or Measure, in quantum universes is also different, and sometimes described by some as the quantity of existence. Notice though that the Measure is always a ratio - say these universes here are 30% of the successors of that universe, the other 70% are those other ones - not an absolute quantity.

Which of the 10 kinds of multiverses, besides our own, have Existence_yud  Existence_{moral-concern} and which can be split up in reality-fluid ratios?

That is left as an exercise, since I am very confused by the whole thing...

If you're going to use anthropic probability, use the self indication assumption (SIA) - it's by far the most sensible way of doing things.

Now, I am of the strong belief that probabilities in anthropic problems (such as the Sleeping Beauty problem) are not meaningful - only your decisions matter. And you can have different probability theories but still always reach the decisions if you have different theories as to who bears the responsibility of the actions of your copies, or how much you value them - see anthropic decision theory (ADT).

But that's a minority position - most people still use anthropic probabilities, so it's worth taking a more through look at what SIA does and doesn't tell you about population sizes and conditional probability.

This post will aim to clarify some issues with SIA, especially concerning Jaan Tallinn's simulation-tree model which he presented in exquisite story format at the recent singularity summit. I'll be assuming basic familiarity with SIA, and will run away screaming from any questions concerning infinity. SIA fears infinity (in a shameless self plug, I'll mention that anthropic decision theory runs into far less problems with infinities; for instance a bounded utility function is a sufficient - but not necessary - condition to ensure that ADT give you sensible answers even with infinitely many copies).

But onwards and upwards with SIA! To not-quite-infinity and below!

 

SIA does not (directly) predict large populations

One error people often make with SIA is to assume that it predicts a large population. It doesn't - at least not directly. What SIA predicts is that there will be a large number of agents that are subjectively indistinguishable from you. You can call these subjectively indistinguishable agents the "minimal reference class" - it is a great advantage of SIA that it will continue to make sense for any reference class you choose (as long as it contains the minimal reference class).

The SIA's impact on the total population is indirect: if the size of the total population is correlated with that of the minimal reference class, SIA will predict a large population. A correlation is not implausible: for instance, if there are a lot of humans around, then the probability that one of them is you is much larger. If there are a lot of intelligent life forms around, then the chance that humans exist is higher, and so on.

In most cases, we don't run into problems with assuming that SIA predicts large populations. But we have to bear in mind that the effect is indirect, and the effect can and does break down in many cases. For instance imagine that you knew you had evolved on some planet, but for some odd reason, didn't know whether your planet had a ring system or not. You have managed to figure out that the evolution of life on planets with ring systems is independent of the evolution of life on planets without. Since you don't know which situation you're in, SIA instructs you to increase the probability of life on ringed and on non-ringed planets (so far, so good - SIA is predicting generally larger populations).

And then one day you look up at the sky and see:

http://arxiv.org/abs/1105.3796

http://www.newscientist.com/article/mg21028154.200-when-the-multiverse-and-manyworlds-collide.html?full=true