Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom
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In principle, it is possible for a hypothesis h- that makes it less likely that there should be some observer-moment compatible with e to get preferential support from e vis-à-vis a hypothesis h+ which makes that more likely. For example, if h+ makes it likely that there should be one observer-moment compatible with e but at the same time makes it very likely that there are very many other observer-moments in our reference class which are not compatible with e, then h+ may be disfavored by e compared to a hypothesis h- on which it is quite unlikely that there should be any observer-moment compatible with e but on which also it is highly unlikely that there should be a substantial number of observer-moments in our reference class which are not compatible with e. In practice (i.e. regarding (3)), if we think of h+ as a multiverse theory and h- as a single-universe theory, it seems that the concrete details will sometimes be such that (£) follows from ($$) together with the facts about these concrete details. This is the case when h+ entails a higher probability than does h- to there being some actual observer-moment that is compatible with e while at the same time the expected ratio between the number of actual observer-moments that are compatible with e that are in our reference class and the number of actual observer-moments that are in our reference class that are incompatible with e is about the same on h+ as on h- (or greater on h+ than on h-). Crudely put: it is ok to infer a bigger cosmos in order to make it probable that at least some observer-moment compatible with e exists, but only if this can be done without sacrificing too much of the desideratum of making it probable that a large fraction of the actual observer-moments that are in our reference class are compatible with e. We’ll continue the discussion of (3) in a moment, but first let’s direct the spotlight on the second preliminary thesis. The analysis of (2) follows a path parallel to that of (1). Suppose that 
Since the first expression implies that 
we get, in a similar way to above,  ($$*)
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