Belief Update across Fission

Abstract

When an agent undergoes fission, how should the beliefs of the fission results relate to the pre-fission beliefs? This question is important for the Everett interpretation of quantum mechanics, but it is of independent philosophical interest. Among other things, fission scenarios demonstrate that "self-locating" information can affect the probability of uncentred propositions even if an agent has no essentially self-locating uncertainty. I present a general update rule for centred beliefs that gives sensible verdicts in cases of fission, without relying on controversial metaphysical or linguistic assumptions. The rule is supported by the same considerations that support standard conditioning in the traditional framework of uncentred propositions. * This paper once fissioned from [Schwarz 2012], which presents the same update rule, but (in the published version) sets aside cases of fission. Thanks to Christopher Meacham, Paolo Santorio and two anonymous referees for helpful comments and discussion.

Self-locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics

“…z À Á , where t É P" ! " z À Á is a 'transition probability', capturing something like the degree to which the copies of Alice on " z branches are Alice's successors if the initial wave function is É P" ; or, more operationally, specifying how much of Alice's credence in É P" should shift to the " z branches at t 3 before she takes account of any new evidence (Schwarz [2015]). If Schwarz's suggestion is adopted, one could argue that the transition probabilities should be given by the amplitude-squared of the wave function, by requiring that belief update when there is no period self-locating uncertainty agree with the case of an arbitrarily small period of self-locating uncertainty.…”

Can rational choice guide us to correct de se beliefs?

“…Perhaps the best we can hope for is to identify the happy medium and gradually accumulate bits of evidence that, while each not entirely convincing on its own, gradually tilt the balance in favor of one or the other position. 14 13 Perhaps such examples are more palatable when we consider variants of the Sleeping Beauty problem that involve clones-see, e.g., Elga [2004] and Schwarz [2014]. The example where she hopes that today is Tuesday then is analogous to the "After the Train Crash" case in Hare [2007], where a victim of a train crash who has forgotten his name, upon learning that the victim named "A" will have to undergo painful surgery, hopes that he is victim "B".…”

Collectives’ and individuals’ obligations: a parity argument

“…Nazi Germany became East Germany and West Germany (fission), and later reunified (fusion). In such cases, we have change that is the result of an earlier decision procedure, with substantial continuity in membership, but we have a different number of entities than we had previously (Schwarz 2014a, 2014b). 7…”