Regression to the mean and Judy Benjamin

Synthese:1-13 (2018)

Authors
Randall G. McCutcheon
University of Memphis
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.
Keywords Judy Benjamin Problem  Jeffrey Conditionalization  Conditionalization
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DOI 10.1007/s11229-018-1761-4
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References found in this work BETA

The Logic of Decision.R. C. Jeffrey & Richard C. Jeffrey - 1965 - Journal of Symbolic Logic 50 (1):247-248.
A Problem for Relative Information Minimizers in Probability Kinematics.Bas C. van Fraassen - 1981 - British Journal for the Philosophy of Science 32 (4):375-379.
Entropy and Uncertainty.Teddy Seidenfeld - 1986 - Philosophy of Science 53 (4):467-491.
Stopping to Reflect.M. J. Schervish, T. Seidenfeld & J. B. Kadane - 2004 - Journal of Philosophy 101 (6):315-322.

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