Lewis, Peter J. (2008) Probability, Self-Location and Quantum Branching. In:  Philosophy of Science Assoc. 21st Biennial Mtg (Pittsburgh, PA).
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, since they presuppose Reflection.
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