Abstract
Subjective Bayesians typically find the following objection difficult to answer: some joint probability measures lead to intuitively irrational inductive behavior, even in the long run. Yet well-motivated ways to restrict the set of “reasonable” prior joint measures have not been forthcoming. In this paper I propose a way to restrict the set of prior joint probability measures in particular inductive settings. My proposal is the following: where there exists some successful inductive method for getting to the truth in some situation, we ought to employ a (joint) probability measure that is inductively successful in that situation, if such a measure exists. In order to do show that the restriction is possible to meet in a broad class of cases, I prove a “Bayesian Completeness Theorem”, which says that for any solvable inductive problem of a certain broad type, there exist probability measures that a Bayesian could use to solve the problem. I then briefly compare the merits of my proposal with two other well-known proposals for constraining the class of “admissible” subjective probability measures, the “leave the door ajar” condition and the “maximize entropy” condition.
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The author owes special thanks to Kevin Kelly, for a number of helpful ideas for the proof of the Bayesian Completeness Theorem, as well as other aspects of the paper. Thanks also to Clark Glymour for some helpful suggestions for improvement of an earlier draft. Part of the work leading to this paper was funded by a Summer Research Grant from the University Research Institute of the University of Texas at Austin.
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Juhl, C.F. Objectively reliable subjective probabilities. Synthese 109, 293–309 (1996). https://doi.org/10.1007/BF00413863
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DOI: https://doi.org/10.1007/BF00413863