Conditionalization and Rational Belief Change

Dissertation, University of California, Berkeley (1992)
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Abstract

I give a critique of the widely held Bayesian position that rational beliefs change by conditionalization. The conditionalization rules are intended to describe, in terms of probabilities, how degrees of belief should change in response to new information. First, I discuss the Simple Rule of Conditionalization, which states that when the probability of the proposition e changes to one the new probability of the proposition A is equal to the old probability of A given e . I then discuss Richard Jeffrey's generalization of the rule to cases where the probability of e changes to some value other than one. ;I present a variety of counterexamples which show that the conditionalization rules must be restricted if they are to describe only rational revisions. While there is a non-trivial way of characterizing how the simple rule of conditionalization should be applied, invoking a total evidence requirement, I argue that the characterization does not extend to Jeffrey's Rule because of difficulties with applying the total evidence requirement to his rule. The problems involved here also plague various attempts to show that one ought to change beliefs in accordance with Jeffrey's rule. I raise additional objections to efforts to justify the conditionalization rules, including David Lewis' Dutch Book Argument, which I argue is based on an unwarranted assumption about fair bets. Arguments of Paul Teller, Bas van Fraassen, Brad Armendt, and Brian Skyrms are also among those discussed. ;Ultimately, I argue that rational changes of belief need not be made in accordance with the principles of conditionalization. Furthermore, even where the conditionalization rules apply, they generally fail to capture all of the relevant reasoning involved in making the appropriate change of belief. I conclude that the Bayesian position, according to which only changes of belief which go by conditionalization are rational, is untenable. Nevertheless, rational belief change is often properly described by conditionalization and in the concluding sections I give a characterization of when it is rational to update by conditionalization.

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Susan Vineberg
Wayne State University

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