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Sleeping beauty should be imprecise. (English) Zbl 1307.03006
Summary: The traditional solutions to the Sleeping Beauty problem say that Beauty should have either a sharp 1/3 or sharp 1/2 credence that the coin flip was heads when she wakes. But Beauty’s evidence is incomplete so that it doesn’t warrant a precise credence, I claim. Instead, Beauty ought to have a properly imprecise credence when she wakes. In particular, her representor ought to assign \(R(\mathrm{Heads})=[0,1/2]\). I show, perhaps surprisingly, that this solution can account for the many of the intuitions that motivate the traditional solutions. I also offer a new objection to A. Elga’s [“Self-locating belief and the Sleeping Beauty problem”, Anal. 60, No. 2, 143–147 (2000; doi:10.1093/analys/60.2.143)] restricted version of the principle of indifference, which an opponent may try to use to collapse the imprecision.

03A05 Philosophical and critical aspects of logic and foundations
60A05 Axioms; other general questions in probability
Full Text: DOI
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