The self-sampling assumption can be seen as an indifference principle of self-locating belief: it instructs us to treat all the possibilities that might be in the reference class of observers as equally likely. Indifference principles of self-locating belief are regarded as suspect by some philosophers because they appear to have paradoxical consequences. Notably, an indifference principle of self-locating belief is usually appealed to in the notorious Doomsday Argument, and it also plays a role in the derivation of apparent “anomalous causal powers” in Nick Bostrom's Adam and Eve thought experiments. The recommendation that we should sometimes act as if there were anomalous causal powers seems very hard to accept. I show that reasoning akin to that used in the Doomsday Argument and in the Adam and Eve thought experiments leads to a similar recommendation in a version of the famous Sleeping Beauty problem. All these unattractive recommendations can be avoided if, as required by the BIC, one pays careful attention to the background evidence based on which one assigns probabilities to competing hypotheses and chooses the observer reference class in accordance with that background evidence.

This chapter discusses further types of multiverse hypotheses: the branching worlds of Everettian quantum theory, the totality of possible worlds according to David Lewis’s modal realism, and the totality of mathematical structures, which – according to Max Tegmark – are all physically realized. I argue that suggested solutions to the probability problem in Everettian quantum theory are unconvincing. A recent proposal by Sebens and Carroll to derive the Born rule in the Everettian framework using considerations about self-locating belief turns out to suffer from a circularity problem because the central principle on which the derivation is based has no independent motivation besides, possibly, appeal to the Born rule itself. I further argue that it is not possible to coherently, in full seriousness, believe David Lewis's modal realism. Nor is it possible to coherently believe Max Tegmark's thesis that there is a multiverse of all mathematical structures in which they are physically realized. Tegmark's claim that our universe is itself a mathematical universe hypothesis is found to be incoherent.