I assume some familiarity with basic concepts in the area of anthropics (a.k.a. self-locating beliefs or imperfect recall) and decision theory.

A pragmatist maxim of action relevance

Consider the following form of pragmatism, which I think is close to Peircian pragmatism:

The pragmatist maxim of action relevance: You should only ask yourself questions that are (in principle) decision-relevant. That is, you should only ask yourself a question Q if there is some (hypothetical) decision situation where you take different actions depending on how you answer Q.

I am aware that this is quite vague and has potential loopholes. (For any question Q, does it count as a decision situation if someone just asks you what you think about Q? We have to rule this out somehow if we don’t want the maxim to be vacuous.) For the purpose of this post, a fairly vague notion of the maxim will suffice.

The action relevance maxim rules out plenty of definitional questions. E.g., it recommends against most debates on the question, “If a tree falls in a forest and no one is around to hear it, does it really make a sound?”. (It does allow asking the question, “What meaning should we give to the word ‘sound’?”) Importantly, it allows asking normative ethical questions such as, “should we kill murderers or put them in jail?”. By allowing hypothetical scenarios, you can still ask questions about time travel and so forth. Perhaps it has some controversial implications for when and why one should discuss consciousness. (If you already fully understand how, say, a biological system works, then how will it matter for your actions whether that system is conscious? I can only think of ethical implications – if a system is conscious, I don’t want to harm it. Therefore, consciousness becomes primarily a question of what systems we should care about. This seems similar to some eliminativist views, e.g., that of Brian Tomasik.) That said, for every definitional question (what is “sound”, “consciousness”, etc.), there are pragmatically acceptable questions, such as, “What is a rigorous/detailed definition of ‘consciousness’ that agrees with (i.e., correctly predicts) our intuitions about whether a system is conscious?”.) I think the implications for anthropics / self-locating beliefs are also controversial. Anyway, I find the above pragmatist maxim compelling.

It is worth noting that there are also other pragmatist principles under which none of the below applies. For example, Eliezer Yudkowsky has a post titled “Making Beliefs Pay Rent in Anticipated Experiences”. Self-locating beliefs anticipate experiences. So even without action relevance they “pay rent” in this sense.

Successful pragmatist critiques of anthropics

I think some pragmatist critiques of anthropics are valid. Here’s the most important critique that I think is valid: (It uses some terms that I’ll define below.)

If you have non-indexical preferences and you think updateless decision theory – i.e., maximizing ex ante expected utility (expected utility from the perspective of the prior probability distribution) – is the only relevant normative decision criterion, then the philosophical question of what probabilities you should assign in scenarios of imperfect recall disappears.

First, some explanations and caveats: (I’ll revisit the first two later in this post.)

• By non-indexical preferences I mean preferences that don’t depend on where in the scenario you are. For example, in Sleeping Beauty, an indexical preference might be: “I prefer to watch a movie tonight.” This is indexical because the meaning of “tonight” differs between the Monday and Tuesday instantiations of Beauty. The Tuesday instantiation will want Beauty to watch a movie on Tuesday night, while the Monday instantiation will not care whether Beauty watches a movie on Tuesday night.
• I’ll leave it to another post to explain what I consider to be a “philosophical” question. (Very roughly, I mean: questions for which there’s no agreed-upon methodology for evaluating proposed answers and arguments.) I’ll give some questions below about self-locating beliefs that I consider to be non-philosophical, such as how to compute optimal policies.
• Of course, scenarios of imperfect recall may also involve other (philosophical) issues that aren’t addressed by UDT (the maxim of following the ex ante optimal policy) and that don’t arise in, say, Sleeping Beauty or the absent-minded driver. For example, we still have to choose a prior, deal with problems of game theory (such as equilibrium selection), deal with infinities (e.g., as per infinite ethics) and so on. I’m not claiming that UDT addresses any of these problems.

As an example, optimizing ex ante utility is sufficient to decide whether to accept or reject any given bet in Sleeping Beauty. Also, one doesn’t need to answer the question, “what is the probability that it is Monday and the coin came up Heads?” (On other questions it is a bit unclear whether the ex ante perspective commits to an answer or not. In some sense, UDTers are halfers: in variants of Sleeping Beauty with bets, the UDTers expected utility calculations will have ½ in place of probabilities and the calculation overall looks very similar to someone who uses EDT and (double) halfing (a.k.a. minimum-reference-class SSA). On the other hand, in Sleeping Beauty without bets, UDTers don’t give any answer to any question about what the probabilities are. On the third hand, probabilities are closely tied to decision making anyway. So even (“normal”, non-UDT) halfers might say that when they talk about probabilities in Sleeping Beauty, all they’re talking about is what numbers they’re going to multiply utilities with when offered (hypothetical) bets. Anyway: Pragmatism! There is no point in debating whether UDTers are halfers or not.)

Some other, less central critiques succeed as well. In general, it’s common to imagine purely definitional disputes arising about any philosophical topic. So, if you show me a (hypothetical) paper titled, “Are SIA probabilities really probabilities?”, I will be a little skeptical of the paper’s value.

(There are also lots of other possible critiques of various pieces of work on anthropics that are outside the scope of this post. Arguably too many papers rely too much on intuition pumps. For instance, Bostrom’s PhD thesis/book on anthropics is sometimes criticized for this (anonymous et al., personal communication, n.d.). I also think that anthropic arguments applied to the real world (the Doomsday argument, the simulation argument, arguments from fine tuning, etc.) often don’t specify that they use specific theories of self-locating beliefs.)

The defense

I now want to defend some of the work on anthropics against pragmatist critiques. The above successful critique already highlights, to some extent, three caveats. Each of these gives rise to a reason why someone might think about how to reason de se (from “within” the scenario, “updatefully”) about games of imperfect recall:

1. Indexical preferences. Ex ante optimization (UDT) alone doesn’t tell you what to do if you have indexical preferences, because it’s not clear how to aggregate preferences between the different “observer moments”. Armstrong (2011) shows a correspondence between methods of assigning self-locating beliefs (SIA, etc.) and methods of aggregating preferences across copies (average and total utilitarianism). That’s a great insight! But it doesn’t tell you what to do. (Perhaps it’s an argument for relativism/antirealism: you can choose whatever way of aggregating preferences across observer moments you like, and so you could also choose whatever method of assigning self-locating beliefs that you like. But even if you buy into this relativist/antirealist position, you still need to decide what to do.)
2. Rejecting updatelessness (e.g., claiming it’s irrational to pay in counterfactual mugging). If the ex ante optimal/updateless choice is not the unambiguously correct one, then you have to ask yourself what other methods of decision making you find more compelling.
3. Asking non-philosophical questions of what procedures work. One might want to know which kinds of reasoning “work” for various notions of “work” (satisfying the reflection principle; when used for decision making: avoiding synchronic or diachronic Dutch books, being compatible with the ex ante optimal/updatelessness policy). Why?
   • I’m sure some philosophers do this just out of curiosity. (“Non-minimum reference class SSA seems appealing. I wonder what happens if we use it to make decisions.” (It mostly doesn’t work.))
   • But there are also lots of very practical reasons that apply even if we fully buy into updatelessness. In practice, even those who buy fully into updatelessness talk about updating their probabilities on evidence in relatively normal ways, thus implicitly assigning the kind of self-locating beliefs that UDT avoids. (For example, they might say, “I read a study that caused me to increase my credence in vitamin D supplements being beneficial even in the summer. Therefore, I’ve ordered some vitamin D tablets.” Not: “From my prior’s perspective, the policy of ordering vitamin D tablets upon reading such and such studies is greater than the policy of not taking vitamin D tablets when exposed to such studies.”) Updating one’s beliefs normally seems more practical. But if in the end we care about ex ante utility (UDT), then does updating even make sense? What kind of probabilities are useful in pursuit of the ex ante optimal/updateless policy? And how should we use such probabilities?
     
     As work in this area shows: both SIA probabilities (thirding) and minimum-reference class SSA probabilities (double halfing) can be useful, while non-minimum-reference class SSA probabilities (single halfing) probably aren’t. Of the two that work, I think SIA actually more closely matches intuitive updating. (In sufficiently large universes, every experience occurs at least once. Minimum-reference class SSA therefore makes practically no updates between large universes.) But then SIA probabilities need to be used with CDT! We need to be careful not to use SIA probabilities with EDT.
     
     Relatedly, some people (incl. me) think about this because they wonder how to build artificial agents that choose correctly in such problems. Finding the ex ante optimal policy directly is generally computationally difficult. Finding CDT+SIA policies is likely theoretically easier than finding an ex ante optimal policy (CLS-complete as opposed to NP-hard), and also can be done using practicable modern ML techniques (gradient descent). Of course, in pursuit of the ex ante optimal policy we need not restrict ourselves to methods that correspond to methods involving self-locating beliefs. There are some reasons to believe that these methods are computationally natural, however. For example, CDT+SIA is roughly computationally equivalent to finding local minima of the ex ante expected utility function.

Acknowledgments

I thank Emery Cooper, Vince Conitzer and Vojta Kovarik for helpful comments.