Regression to the Mean and Judy Benjamin

Synthese 197 (3):1343-1355 (2020)
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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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Belief and the Will.van Fraassen, Bas C.
A New Resolution of the Judy Benjamin Problem.Douven, Igor & Romeijn, Jan-Willem
Stopping to Reflect.Schervish, M. J.; Seidenfeld, T. & Kadane, J. B.

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