Objectively Reliable Subjective Probabilities

Author: Juhl C.F.  

Publisher: Springer Publishing Company

ISSN: 0039-7857

Source: Synthese, Vol.109, Iss.3, 1996-12, pp. : 293-309

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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.