Probability, self-location, and quantum branching

The main problem with the many-worlds theory is that it is not clear how the notion of probability should be understood in a theory in which every possible outcome of a measurement actually occurs. In this paper, I argue for the following theses concerning the many-worlds theory: (1) If probability can be applied at all to measurement outcomes, it must function as a measure of an agent's self-location uncertainty. (2) Such probabilities typically violate reflection. (3) Many-worlds branching does not have sufficient structure to admit self-location probabilities. (4) Decision-theoretic arguments do not solve this problem.