An analogy for the simulation argument

To people already familiar with the argument, this may be old news. It’s an analogy to help people feel the intuitive force of the argument.

Suppose the following: New diseases appear inside people all the time. Only one in ten diseases is contagious, but the contagious diseases spread to a thousand other people, on average, before dying out. The non-contagious ones don’t spread to anyone else. You get sick. You haven’t yet gone to the doctor or googled your symptoms; given the above facts, part of you wonders whether you should bother… after all, 90% of diseases only ever infect one person. So, how likely is it that someone else has had your disease before?

Draw a Venn diagram with two circles: “First victim” and “contagious.” This makes three interesting categories:

A = First victims of noncontagious diseases

B = First victims of contagious diseases

C = Nonfirst victims of contagious diseases

 Since only one in ten diseases is contagious, B/A = 1/9.Since contagious diseases spread to a thousand people on average, B/C is 1/1000. It follows that C/(A+B+C) = 100/101.

Since you know you are diseased, you should assign credence to each hypothesis “I’m in A” “I’m in B” “I’m in C” equal to the fraction of diseased people who are in that category, at least until you get evidence that you would be more likely to get in one category than another.

(For example, if you google your symptoms and get zero hits, that’s evidence that is more likely to happen to people in group A or B, so you should update to be less confident that you are in group C than the base rate would suggest.)

So you are almost certain to be in category C, since they make up 100/101 of the total population of diseased people, and at the moment you don’t have any evidence that is less likely to happen to people in category C than people in the other categories. So it’s almost certain that other people have had your disease already, even though 90% of diseases only ever infect one person.

In the simulation argument, the reasoning is similar.

Suppose that 90% of non-simulated civilizations never create ancestor sims, but that the remaining 10% create 1000 each on average. Then most civilizations are ancestor-simulated.

Do we have any evidence that is more likely to happen to people who are ancestor-simulated than people who are not, or vice versa?

You might think the answer is yes: For example, simulated people are more likely to see things that appear to break the laws of physics, more likely to see pop-up windows saying “you are in a simulation,” etc. 

But Bostrom anticipates this when he restricts his argument to ancestor simulations. Ancestor simulations are designed to perfectly mimic real history, so the answer is no: Someone in category C is just as likely to see what we see as someone in category B or A.

So even if we rule out non-ancestor-simulations entirely, the argument goes through: Most civilizations with evidence like ours are ancestor-simulated, and we don’t have any reason to think we are special, so we are probably ancestor-simulated. And of course, we shouldn’t rule out non-ancestor-simulations entirely, so the probability that we are simulated should be even higher than the probability we are ancestor-simulated.

(Clarificatory caveat: Bostrom’s argument is NOT for the conclusion that we are in a simulation; rather, it is a triple-disjunct. In the framing discussed here, Bostrom leaves open the possibility that Group A is extremely large relative to Group B, large enough that it is bigger than B and C combined.)

Great Map of the Mind



Here is the link in case you want to look at it more closely or spin off a copy to make a version of your own.

Moral realism and AI alignment

Abstract”: Some have claimed that moral realism – roughly, the claim that moral claims can be true or false – would, if true, have implications for AI alignment research, such that moral realists might approach AI alignment differently than moral anti-realists. In this post, I briefly discuss different versions of moral realism based on what they imply about AI. I then go on to argue that pursuing moral-realism-inspired AI alignment would bypass philosophical and help resolve non-philosophical disagreements related to moral realism. Hence, even from a non-realist perspective, it is desirable that moral realists (and others who understand the relevant realist perspectives well enough) pursue moral-realism-inspired AI alignment research.

Different forms of moral realism and their implications for AI alignment

Roughly, moral realism is the view that “moral claims do purport to report facts and are true if they get the facts right.” So for instance, most moral realists would hold the statement “one shouldn’t torture babies” to be true. Importantly, this moral claim is different from a claim about baby torturing being instrumentally bad given some other goal (a.k.a. a “hypothetical imperative”) such as “if one doesn’t want to land in jail, one shouldn’t torture babies.” It is uncontroversial that such claims can be true or false. Moral claims, as I understand them in this post, are also different from descriptive claims about some people’s moral views, such as “most Croatians are against babies being tortured” or “I am against babies being tortured and will act accordingly”. More generally, the versions of moral realism discussed here claim that moral truth is in some sense mind-independent. It’s not so obvious what it means for a moral claim to be true or false, so there are many different versions of moral realism. I won’t go into more detail here, though we will revisit differences between different versions of moral realism later. For a general introduction on moral realism and meta-ethics, see, e.g., the SEP article on moral realism.

I should note right here that I myself find at least “strong versions” of moral realism implausible. But in this post, I don’t want to argue about meta-ethics. Instead, I would like to discuss an implication of some versions of moral realism. I will later say more about why I am interested in the implications of a view I believe to be misguided, but for now suffice it to say that “moral realism” is a majority view among professional philosophers (though I don’t know how popular the versions of moral realism studied in this post are), which makes it interesting to explore the view’s possible implications.

The implication that I am interested in here is that moral realism helps with AI alignment in some way. One very strong version of the idea is that the orthogonality thesis is false: if there is a moral truth, agents (e.g., AIs) that are able to reason successfully about a lot of non-moral things will automatically be able to reason correctly about morality as well and will then do what they infer to be morally correct. On p. 176 of “The Most Good You Can Do”, Peter Singer defends such a view: “If there is any validity in the argument presented in chapter 8, that beings with highly developed capacities for reasoning are better able to take an impartial ethical stance, then there is some reason to believe that, even without any special effort on our part, superintelligent beings, whether biological or mechanical, will do the most good they possibly can.” In the articles “My Childhood Death Spiral”, “A Prodigy of Refutation” and “The Sheer Folly of Callow Youth” (among others), Eliezer Yudkowsky says that he used to hold such a view.

Of course, current AI techniques do not seem to automatically include moral reasoning. For instance, if you develop an automated theorem prover to reason about mathematics, it will not be able to derive “moral theorems”. Similarly, if you use the Sarsa algorithm to train some agent with some given reward function, that agent will adapt its behavior in a way that increases its cumulative reward regardless of whether doing so conflicts with some ethical imperative. The moral realist would thus have to argue that in order to get to AGI or superintelligence or some other milestone, we will necessarily have to develop new and very different reasoning algorithms and that these algorithms will necessarily incorporate ethical reasoning. Peter Singer doesn’t state this explicitly. However, he makes a similar argument about human evolution on p. 86f. in ch. 8:

The possibility that our capacity to reason can play a critical role in a decision to live ethically offers a solution to the perplexing problem that effective altruism would otherwise pose for evolutionary theory. There is no difficulty in explaining why evolution would select for a capacity to reason: that capacity enables us to solve a variety of problems, for example, to find food or suitable partners for reproduction or other forms of cooperative activity, to avoid predators, and to outwit our enemies. If our capacity to reason also enables us to see that the good of others is, from a more universal perspective, as important as our own good, then we have an explanation for why effective altruists act in accordance with such principles. Like our ability to do higher mathematics, this use of reason to recognize fundamental moral truths would be a by-product of another trait or ability that was selected for because it enhanced our reproductive fitness—something that in evolutionary theory is known as a spandrel.

A slightly weaker variant of this strong convergence moral realism is the following: Not all superintelligent beings would be able to identify or follow moral truths. However, if we add some feature that is not directly normative, then superintelligent beings would automatically identify the moral truth. For example, David Pearce appears to claim that “the pain-pleasure axis discloses the world’s inbuilt metric of (dis)value” and that therefore any superintelligent being that can feel pain and pleasure will automatically become a utilitarian. At the same time, that moral realist could believe that a non-conscious AI would not necessarily become a utilitarian. So, this slightly weaker variant of strong convergence moral realism would be consistent with the orthogonality thesis.

I find all of these strong convergence moral realisms very implausible. Especially given how current techniques in AI work – how value-neutral they are – the claim that algorithms for AGI will all automatically incorporate the same moral sense seems extraordinary and I have seen little evidence for it1 (though I should note that I have read only bits and pieces of the moral realism literature).2

It even seems easy to come up with semi-rigorous arguments against strong convergence moral realism. Roughly, it seems that we can use a moral AI to build an immoral AI. Here is a simple example of such an argument. Imagine we had an AI system that (given its computational constraints) always chooses the most moral action. Now, it seems that we could construct an immoral AI system using the following algorithm: Use the moral AI to decide which action of the immoral AI system it would prevent from being taken if it could only choose one action to be prevented. Then take that action. There is a gap in this argument: perhaps the moral AI simply refuses to choose the moral actions in “prevention” decision problems, reasoning that it might currently be used to power an immoral AI. (If exploiting a moral AI was the only way to build other AIs, then this might be the rational thing to do as there might be more exploitation attempts than real prevention scenarios.) Still (without having thought about it too much), it seems likely to me that a more elaborate version of such an argument could succeed.

Here’s a weaker moral realist convergence claim about AI alignment: There’s moral truth and we can program AIs to care about the moral truth. Perhaps it suffices to merely “tell them” to refer to the moral truth when deciding what to do. Or perhaps we would have to equip them with a dedicated “sense” for identifying moral truths. This version of moral realism again does not claim that the orthogonality thesis is wrong, i.e. that sufficiently effective AI systems will automatically behave ethically without us giving them any kind of moral guidance. It merely states that in addition to the straightforward approach of programming an AI to adopt some value system (such as utilitarianism), we could also program the AI to hold the correct moral system. Since pointing at something that exists in the world is often easier than describing that thing, it might be thought that this alternative approach to value loading is easier than the more direct one.

I haven’t found anyone who defends this view (I haven’t looked much), but non-realist Brian Tomasik gives this version of moral realism as a reason to discuss moral realism:

Moral realism is a fun philosophical topic that inevitably generates heated debates. But does it matter for practical purposes? […] One case where moral realism seems problematic is regarding superintelligence. Sometimes it’s argued that advanced artificial intelligence, in light of its superior cognitive faculties, will have a better understanding of moral truth than we do. As a result, if it’s programmed to care about moral truth, the future will go well. If one rejects the idea of moral truth, this quixotic assumption is nonsense and could lead to dangerous outcomes if taken for granted.

(Below, I will argue that there might be no reason to be afraid of moral realists. However, my argument will, like Brian’s, also imply that moral realism is worth debating in the context of AI.)

As an example, consider a moral realist view according to which moral truth is similar to mathematical truth: there are some axioms of morality which are true (for reasons I, as a non-realist, do not understand or agree with) and together these axioms imply some moral theory X. This moral realist view suggests an approach to AI alignment: program the AI to abide by these axioms (in the same way as we can have automated theorem provers assume some set of mathematical axioms to be true). It seems clear that something along these lines could work. However, this approach’s reliance on moral realism is also much weaker.

As a second example, divine command theory states that moral truth is determined by God’s will (again, I don’t see why this should be true and how it could possibly be justified). A divine command theorist might therefore want to program the AI to do whatever God wants it to do.

Here are some more such theories:

  • Social contract
  • Habermas’ discourse ethics
  • Universalizability / Kant’s categorical imperative
  • Applying human intuition

Besides pointing being easier than describing, another potential advantage of such a moral realist approach might be that one is more confident in one’s meta-ethical view (“the pointer”) than in one’s object-level moral system (“one’s own description”). For example, someone could be confident that moral truth is determined by God’s will but be unsure that God’s will is expressed via the Bible, the Quran or something else, or how these religious texts are to be understood. Then that person would probably favor AI that cares about God’s will over AI that follows some particular interpretation of, say, the moral rules proposed in the Quran and Sharia.

A somewhat related issue which has received more attention in the moral realism literature is the convergence of human moral views. People have given moral realism as an explanation for why there is near-universal agreement on some ethical views (such as “when religion and tradition do not require otherwise, one shouldn’t torture babies”). Similarly, moral realism has been associated with moral progress in human societies, see, e.g., Huemer (2016). At the same time, people have used the existence of persisting and unresolvable moral disagreements (see, e.g., Bennigson 1996 and Sayre-McCord 2017, sect. 1) and the existence of gravely immoral behavior in some intelligent people (see, e.g., Nichols 2002) as arguments against moral realism. Of course, all of these arguments take moral realism to include a convergence thesis where being a human (and perhaps not being affected by some mental disorders) or a being a society of humans is sufficient to grasp and abide by moral truth.

Of course, there are also versions of moral realism that have even weaker (or just very different) implications for AI alignment and do not make any relevant convergence claims (cf. McGrath 2010). For instance, there may be moral realists who believe that there is a moral truth but that machines are in principle incapable of finding out what it is. Some may also call very different views “moral realism”, e.g. claims that given some moral imperative, it can be decided whether an action does or does not comply with that imperative. (We might call this “hypothetical imperative realism”.) Or “linguistic” versions of moral realism which merely make claims about the meaning of moral statements as intended by whoever utters these moral statements. (Cf. Lukas Gloor’s post on how different versions of moral realism differ drastically in terms of how consequential they are.) Or a kind of “subjectivist realism”, which drops mind-independence (cf. Olson 2014, ch. 2).

Why moral-realism-inspired research on AI alignment might be useful

I can think of many reasons why moral realism-based approaches to AI safety have not been pursued much: AI researchers often do not have a sufficiently high awareness of or interest in philosophical ideas; the AI safety researchers who do – such as researchers at MIRI – tend to reject moral realism, at least the versions with implications for AI alignment; although “moral realism” is popular among philosophers, versions of moral realism with strong implications for AI (à la Peter Singer or David Pearce) might be unpopular even among philosophers (cf. again Lukas’ post on how different versions of moral realism differ drastically in terms of how consequential they are); and so on…

But why am I now proposing to conduct such research, given that I am not a moral realist myself? The main reason (besides some weaker reasons like pluralism and keeping this blog interesting) is that I believe AI alignment research from a moral realist perspective might actually increase agreement between moral realists and anti-realists about how (and to which extent) AI alignment research should be done. In the following, I will briefly argue this case for the strong (à la Peter Singer and David Pearce) and the weak convergence versions of moral realism outlined above.

Strong versions

Like most problems in philosophy, the question of whether moral realism is true lacks an accepted truth condition or an accepted way of verifying an answer or an argument for either realism or anti-realism. This is what makes these problems so puzzling and intractable. This is in contrast to problems in mathematics where it is pretty clear what counts as a proof of a hypothesis. (This is, of course, not to say that mathematics involves no creativity or that there are no general purpose “tools” for philosophy.) However, the claim made by strong convergence moral realism is more like a mathematical claim. Although it is yet to be made precise, we can easily imagine a mathematical (or computer-scientific) hypothesis stating something like this: “For any goal X of some kind [namely the objectively incorrect and non-trivial-to-achieve kind] there is no efficient algorithm that when implemented in a robot achieves X in some class of environments. So, for instance, it is in principle impossible to build a robot that turns Earth into a pile of paperclips.” It may still be hard to formalize such a claim and mathematical claims can still be hard to prove or disprove. But determining the truth of a mathematical statement is not a philosophical problem, anymore. If someone lays out a mathematical proof or disproof of such a claim, any reasonable person’s opinion would be swayed. Hence, I believe that work on proving or disproving this strong version of moral realism will lead to (more) agreement on whether the “strong-moral-realism-based theory of AI alignment” is true.

It is worth noting that finding out whether strong convergence is true may not resolve metaphysical issues. Of course, all strong versions of moral realism would turn out false if the strong convergence hypothesis were falsified. But other versions of moral realism would survive. Conversely, if the strong convergence hypothesis turned out to be true, then anti-realists may remain anti-realists (cf. footnote 2). But if our goal is to make AI moral, the convergence question is much more important than the metaphysical question. (That said, for some people the metaphysical question has a bearing on whether they have preferences over AI systems’ motivation system – “if no moral view is more true than any other, why should I care about what AI systems do?”)

Weak versions

Weak convergence versions of moral realism do not make such in-principle-testable predictions. Their only claim is the metaphysical view that the goals identified by some method X (such as derivation from a set moral axioms, finding out what God wants, discourse, etc.) have some relation to moral truths. Thinking about weak convergence moral realism from the more technical AI alignment perspective is therefore unlikely to resolve disagreements about whether some versions of weak convergence moral realism are true. However, I believe that by not making testable predictions, weak convergence versions of moral realism are also unlikely to lead to disagreement about how to achieve AI alignment.

Imagine moral realists were to propose that AI systems should reason about morality according to some method X on the basis that the result of applying X is the moral truth. Then moral anti-realists could agree with the proposal on the basis that they (mostly) agree with the results of applying method X. Indeed, for any moral theory with realist ambitions, ridding that theory of these ambitions yields a new theory which an anti-realist could defend. As an example, consider Habermas’ discourse ethics and Yudkowsky’s Coherent Extrapolated Volition. The two approaches to justifying moral views seem quite similar – roughly: do what everyone would agree with if they were exposed to more arguments. But Habermas’ theory explicitly claims to be realist while Yudkowsky is a moral anti-realist, as far as I can tell.

In principle, it could be that moral realists defend some moral view on the grounds that it is true even if it seems implausible to others. But here’s a general argument for why this is unlikely to happen. You cannot directly perceive ought statements (David Pearce and others would probably disagree) and it is easy to show that you cannot derive a statement containing an ought without using other statements containing an ought or inference rules that can be used to introduce statements containing an ought. Thus, if moral realism (as I understand it for the purpose of this paper) is true, there must be some moral axioms or inference rules that are true without needing further justification, similar to how some people view the axioms of Peano arithmetic or Euclidean geometry. An example of such a moral rule could be (a formal version of) “pain is bad”. But if these rules are “true without needing further justification”, then they are probably appealing to anti-realists as well. Of course, anti-realists wouldn’t see them as deserving the label of “truth” (or “falsehood”), but assuming that realists and anti-realists have similar moral intuitions, anything that a realist would call “true without needing further justification” should also be appealing to a moral anti-realist.

As I have argued elsewhere, it’s unlikely we will ever come up with (formal) axioms (or methods, etc.) for morality that would be widely accepted by the people of today (or even among today’s Westerners with secular ethics). But I still think it’s worth a try. If it doesn’t work out, weak convergence moral realists might come around to other approaches to AI alignment, e.g. ones based on extrapolating from human intuition.

Other realist positions

Besides realism about morality, there are many other less commonly discussed realist positions, for instance, realism about which prior probability distribution to use, whether to choose according to some expected value maximization principle (and if so which one), etc. The above considerations apply to these other realist positions as well.

1. There are some “universal instrumental goal” approaches to justifying morality. Some are based on cooperation and work roughly like this: “Whatever your intrinsic goals are, it is often better to be nice to others so that they reciprocate. That’s what morality is.” I think such theories fail for two reasons: First, there seem to many widely accepted moral imperatives that cannot be fully justified by cooperation. For example, we usually consider it wrong for dictators to secretly torture and kill people, even if doing so has no negative consequences for them. Second, being nice to others because one hopes that they reciprocate is not, I think, what morality is about. To the contrary, I think morality is about caring things (such as other people’s welfare) intrinsically. I discuss this issue in detail with a focus on so-called “superrational cooperation” in chapter 6.7 of “Multiverse-wide Cooperation via Correlated Decision Making”. Another “universal instrumental goal” approach is the following: If there is at least one god, then not making these gods angry at you may be another universal instrumental goal, so whatever an agent’s intrinsic goal is, it will also act according to what the gods want. The same “this is not what morality is about” argument seems to apply.

2. Yudkowsky has written about why he now rejects this form of moral realism in the first couple of blog posts in the “Value Theory” series.

Goertzel’s GOLEM implements evidential decision theory applied to policy choice

I’ve written about the question of which decision theories describe the behavior of approaches to AI like the “Law of Effect”. In this post, I would like to discuss GOLEM, an architecture for a self-modifying artificial intelligence agent described by Ben Goertzel (2010; 2012). Goertzel calls it a “meta-architecture” because all of the intelligent work of the system is done by sub-programs that the architecture assumes as given, such as a program synthesis module (cf. Kaiser 2007).

Roughly, the top-level self-modification is done as follows. For any proposal for a (partial) self-modification, i.e. a new program to replace (part of) the current one, the “Predictor” module predicts how well that program would achieve the goal of the system. Another part of the system — the “Searcher” — then tries to find programs that the Predictor deems superior to the current program. So, at the top level, GOLEM chooses programs according to some form of expected value calculated by the Predictor. The first interesting decision-theoretical statement about GOLEM is therefore that it chooses policies — or, more precisely, programs — rather than individual actions. Thus, it would probably give the money in at least some versions of counterfactual mugging. This is not too surprising, because it is unclear on what basis one should choose individual actions when the effectiveness of an action depends on the agent’s decisions in other situations.

The next natural question to ask is, of course, what expected value (causal, evidential or other) the Predictor computes. Like the other aspects of GOLEM, the Predictor is subject to modification. Hence, we need to ask according to what criteria it is updated. The criterion is provided by the Tester, a “hard-wired program that estimates the quality of a candidate Predictor” based on “how well a Predictor would have performed in the past” (Goertzel 2010, p. 4). I take this to mean that the Predictor is judged based the extent to which it is able to predict the things that actually happened in the past. For instance, imagine that at some time in the past the GOLEM agent self-modified to a program that one-boxes in Newcomb’s problem. Later, the agent actually faced a Newcomb problem based on a prediction that was made before the agent self-modified into a one-boxer and won a million dollars. Then the Predictor should be able to predict that self-modifying to one-boxing in this case “yielded” getting a million dollar even though it did not do so causally. More generally, to maximize the score from the Tester, the Predictor has to compute regular (evidential) conditional probabilities and expected utilities. Hence, it seems that the EV computed by the Predictor is a regular EDT-ish one. This is not too surprising, either, because as we have seen before, it is much more common for learning algorithms to implement EDT, especially if they implement something which looks like the Law of Effect.

In conclusion, GOLEM learns to choose policy programs based on their EDT-expected value.


This post is based on a discussion with Linda Linsefors, Joar Skalse, and James Bell.

Three wagers for multiverse-wide superrationality


  1. There is a large or infinite universe or multiverse.
  2. Applying an acausal decision theory.


A wager for acausal decision theory and a large universe





A wager in favor of higher correlations







H1 H2
A1 n+c q×m







A wager against Solomonoff induction












UDT is “updateless” about its utility function









Is updating on your existence a sin?





UDT agents with differing priors








