Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom

First, consider a single-universe theory h_U on which our universe is fine-tuned, so that conditional on h_U there was only a very small probability that an observer-containing universe should exist. If we compare h_U with a multiverse theory h_M, on which it was quite likely that an observer-containing universe should exist, we find that if h_U and h_M had similar prior probabilities, then there are prima facie grounds for thinking h_M to be more probable than h_U given the evidence we have. Whether these prima facie grounds hold up on closer scrutiny depends on the distributions of observer-moments that h_U and h_M make probable. Supposing that the nature of the observer-moments that would tend to exist on h_U (if there were any observer-moments at all, which would improbable on h_U) are similar to the observer-moments that (most likely) exist on h_M, then we do in fact have such grounds.

We see here the sense in which fine-tuning suggests a multiverse in a way that mere free parameters do not. In the former case, h_M tends to be strongly supported by the evidence we have (given comparable priors); in the latter case, not.

On this story, how does one fit in the scenario where we discover a simple single-universe theory h_U^* that accounts well for the evidence? Well, if h_U^* is elegant and simple, then we would assign it a relatively high prior probability. Since h_U^* by assumption implies or at least gives a rather high probability to e, the conditional probability of h_U^* given e would thus be high. This would be support for the single-universe hypothesis and against the multiverse hypothesis.

One kind of candidate for such a single-universe theory are theories involving a creator who chose to create only one universe. If one assigned one such theory h_C^* a reasonably high prior probability, and if it could be shown to give a high probability to there being one universe precisely like the one we observe and no other universes, then one would have support for h_C^*. Creator-hypotheses on which the creator creates a whole ensemble of observer-containing universes would be less supported than h_C^*. However, if our universe is not of the sort that one might have suspected a creator to create if he created only one universe (if our universe is not the nicest possible one in any sense, for example), then the conditional probability of e on any creator-hypothesis involving the creation of only one universe might well so slim that even if one assigned such a creator-hypothesis a high prior probability it would still not be tenable in light of e if there were some plausible alternative theory giving a high conditional probability to e (e.g. a multiverse theory successfully riding on fine-tuning and its concomitant selection effects, or a still-to-be-discovered simple and elegant single-universe theory that fits the facts). If there were no such plausible alternative theory, then one may believe either a fine-tuned single-universe theory, a multiverse-theory not benefiting from observation selection effects, or a creator hypothesis (either of the single-universe or the multiverse kind) – these would be roughly on a par regarding how well they’d fit with the evidence (quite poorly for all of them) and the choice between them would be determined mainly by one’s prior probability function.

In chapter 2 we also touched on the case where our universe is discovered to have some “special feature” F. One example of this is if we were to find inscriptions saying “God created this universe and it’s the only one he created.” in places where it seems only a divine being would have made them (and we thought that there was a significant chance that the creator was being honest). Another example is if we find specific evidence that favors on ordinary (non-anthropic) grounds some physical theory that either implies a single-universe world or a multiverse. Such new evidence e’ would be conjoined with the evidence e we already have. What we should believe in the light of this depends on what conditional probability various hypotheses give to e&e’ and on the prior probabilities we give to these hypotheses. With e’ involving special features, e&e’ might well be such as to preferentially favor hypotheses that specifically accounts for the special features, and this favoring may be strong enough to dominate any of the considerations mentioned above. For example, if we find all those inscriptions, that would make the creator-hypothesis seem very attractive even if one assigned it a low prior probability and even if the conditional probability of there being a single universe with F given the creator-hypotheses would be small; for other plausible hypotheses would presumably give very much smaller conditional probabilities to our finding that our universe has F. (On h_U, it would be extremely unlikely that there would be any universe with F. On h_M, it might be likely that there should be some universe with F, but it would nonetheless be extremely unlikely that we should be in that universe, since on any plausible multiverse theory not involving a creator it would seem that if it were likely that there should be one universe with F then it would also be most likely that there are a great many other universes not having F and in which the observers, although many of them would be in the same reference class as us, would thus not be compatible with the evidence we have.) Similar considerations hold if F is not divine-looking inscriptions but something more of the nature of ordinary physical evidence for some particular physical theory.

Finally, we have to tackle the question of how the existence of freak observers affects the story. The answer is: hardly at all. Although once we take account of freak observers there will presumably be a broad class of single-universe theories that make probable that some observers compatible with e should exist, this doesn’t help the case for such theories. For freak observers are random. Whether they are generated by Hawking radiation or by thermal fluctuations or some other phenomena of a similar kind, these freak observers would not be preferentially generated to be compatible with e. Only an extremely minute fraction of all freak observers would be compatible with e. The case would therefore be essentially the same as if we have a multiverse where many universes contain observers (that are in our reference class) but only a tiny fraction of them contain observers who are compatible with e. Just as e didn’t especially favor such multiverse-theories over ad hoc single-universe theories, so likewise e is not given a sufficiently high probability by the there-is-a-single-universe-sufficiently-big-to-contain-all-kinds-of-freak observers theory (h_F) to make such a theory supported by our evidence. In fact, the case for h_F is much worse than the case for such a multiverse theory. For the multiverse theory, even if not getting any assistance from fine-tuning, would at least have a bias towards observers who have evolved (i.e. most observers would be of that kind). Evolved observers would tend to be in epistemic states that to some degree reflect the nature of the universe they are living in. Thus if not every logically possible universe is instantiated (with equal frequency) in the multiverse but instead the universes it contains tend to share at least some basic features with our actual universe, then a much greater fraction of the observers existing in the multiverse would be compatible with e than of the observers existing given h_F. On h_F the observers would be distributed roughly evenly over all logically possible epistemic states (of a given complexity)⁹³ whereas on the multiverse theory they’d be distributed over the smaller space of epistemic states that are likely to be instantiated in observers evolving in universes that share at least some basic features (maybe physical laws, or some physical laws, depending on the particular multiverse theory) with our universe. So h_F is strongly disfavored by e.