Normally, this kind of subtle change in indexical information makes no difference to our inferences, so they can therefore usually be ignored. In special cases, however, including the thought experiments considered in this paper, which rely precisely on the peculiar evidential properties of indexical information, such changes can be highly relevant. This does not yet show that your beliefs at stage (b) about the outcome of the coin toss should differ from those obtained by conditionalizing Pr(tails|I’m in cell #1). But it defeats the 15 Bayesian argument for why they should be the same. If you regard these associated epistemic changes that occur in addition to your obtaining the information that “I’m in cell #1” when you move from stage (a) to stage (b) as relevant, then you can coherently assign a 1/2 posterior credence to tails. Let α be one of your observer-moments that exist before you discover which cell you are in. Let β be one of your observer-moments that exist after you have discovered that you are in cell #1 (but before you have learned about the outcome of the coin toss). What probabilities α and β assign to various hypotheses depends on reference classes in which they place themselves. For example, α can pick a reference class consisting of the observer-moments who are ignorant about which cell they are in, while β can pick the reference class consisting of all observer-moments who know they are in cell #1. α ’s conditional credences are then the same as before: Prα (α is in cell #1| tails) = 1 100 1 Prα (α is in cell #1| heads) = . But β ’s conditional probability of being in cell #1 given heads is now identical to that given tails: Prβ (β is in cell #1| tails) = 1 Prβ (β is in cell #1| heads) = 1. From this, it follows that β ’s posterior credence of tails after conditionalizing on β being in 16 cell #1 is the same as its posterior credence of heads, namely 1/2. SSSA does not by itself imply that this should be β ’s posterior credence of tails. It just shows that it is a coherent position to take. The actual credence assignment depends on which reference classes are chosen. In the case of Incubator, it may not be obvious which choice of reference class is best. But in the Serpent’s Advice, it is clear that Eve should select a reference class that puts her observer-moments existing at the time when she is pondering the possible consequences of the sinful act in a different reference class from those later observer-moments that may come to exist as a result of her transgression. For her to do otherwise would not be incoherent, but it would yield the strongly counterintuitive consequence discussed above. By selecting the more limited reference class, she can reject this consequence. The question arises whether it is possible to find some general principle that determines what reference class an observer-moment should use. We may note that the early Eve’s choice of a reference class that contains only her own early observer-moments and excludes the observermoments of all the billions of progeny that may come to exist later is not completely arbitrary. After all, the epistemic situation that the early Eve is in is very different from the epistemic situation of these later observer-moments. Eve doesn’t know whether she will get pregnant and whether all these other people will come to exist; her progeny, by contrast, would have no doubts about these issues. Eve is confronted with a very different epistemic problem than her possible children would be. It is thus quite natural to place Eve in a different reference class from these later people, even apart from the fact that this maneuver would explain why the serpent’s recommendation should be eschewed. Constraints on what could be legitimate choices of reference class can be established, but it is an open question whether these will always suffice to single out a uniquely correct reference class for every observer-moment. My suspicion is that there might remain a subjective element 17 in the choice of reference class in some applications. Furthermore, I suspect that the degree to which various applications of anthropic reasoning are sensitive to that subjective element is inversely related to how scientifically robust those applications are. The most rigorous uses of anthropic reasoning have the property that they give the same result for almost any choice of reference class (satisfying only some very weak constraints). In passing, we may note one interesting constraint on the choice of reference class. It turns out (for reasons that we do not have the space to elaborate on here) that a reference class definition according to which only subjectively indistinguishable observer-moments are placed in the same reference class is too narrow. (Two observer-moments are subjectively indistinguishable if they don’t have any information that enables them to tell which one is which.) In other words, there are cases in which you should reason as if your current observermoment were randomly selected from a class of observer-moments that includes ones of which you know that they are not your own current observer-moment. This fact makes anthropic reasoning a less simple affair than would otherwise have been the case. The use of SSSA and the relativization of the reference class that SSSA enables thus seem to make it possible to coherently reject both the presumptuous philosopher’s and the serpent’s arguments, while at the same time one can show how to get plausible results in Dungeon and several other thought experiments as well as in various scientific applications, some of them novel. The theory can be condensed into one general formula: the Observation Equation, which specifies the probabilistic bearing on hypotheses of evidence that contains an indexical component.5 Along with various constrains on permissible choices of reference classes, 5 ∑∈Ω ∩Ω Ω ∩Ω = h e w P w P h e σ σ σ α σ α γ | ( ) | 1 ( ) ( | ) (Observation Equation) 18 this forms the core of a theory of observation selection effects. 10. As a final example, let us consider an easy application of observation selection theory to a puzzle that many drivers on the motorway may have wondered about (and cursed). Why is it that the cars in the other lane seem to be getting ahead faster than you? One might be inclined to account for phenomenon by invoking Murphy’s Law (“If anything can go wrong, it will,” discovered by Edward A. Murphy, Jr, in 1949). However, a paper in Nature by Redelmeier and Tibshirani, published a couple of years ago,6 seeks a deeper explanation. They present some evidence that drivers on Canadian roadways (where faster cars are not expected to move into more central lanes) think that the next lane is typically faster. They seek to explain the drivers’ perceptions by appealing to a variety of psychological factors. For example: • “A driver is more likely to glance at the next lane for comparison when he is relatively idle while moving slowly;”