McCutcheon, Randall G.
(2018)
Regression to the mean and Judy Benjamin.
[Preprint]
Abstract
Van Fraassen's Judy Benjamin problem asks how one ought to update one's credence in A upon receiving evidence of the sort ``A may or may not obtain, but B is k times likelier than C'', where {A,B,C} is a partition. Van Fraassen's
solution, in the limiting case of increasing k, recommends a posterior converging to the probability of A conditional on A union B, where P is one's prior probability function. Grove and Halpern, and more recently Douven and Romeijn, have argued that one ought to leave credence in A unchanged, i.e. fixed at P(A). We argue that while the former approach is superior, it brings about a reflection violation due in part to neglect of a ``regression to the mean'' phenomenon, whereby when C is eliminated by random evidence that leaves A and B alive, the ratio P(A):P(B) ought to drift in the direction of 1:1.
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