Regression to the mean and Judy Benjamin


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 k→ ∞, recommends a posterior converging to P(A| A∪ 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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