Regression to the mean and Judy Benjamin

Synthese:1-13 (2018)
Download Edit this record How to cite View on PhilPapers
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.
Categories
(categorize this paper)
PhilPapers/Archive ID
MCCRTT-2
Revision history
Archival date: 2018-04-30
View upload history
References found in this work BETA
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.
Entropy and Uncertainty.Seidenfeld, Teddy

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2018-04-30

Total views
94 ( #23,167 of 38,881 )

Recent downloads (6 months)
54 ( #7,672 of 38,881 )

How can I increase my downloads?

Monthly downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.