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A DUTCH BOOK THEOREM AND CONVERSE DUTCH BOOK THEOREM FOR KOLMOGOROV CONDITIONALIZATION

Published online by Cambridge University Press:  28 May 2018

MICHAEL RESCORLA
MICHAEL RESCORLA*
Affiliation:
Department of Philosophy, University of California, Los Angeles
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CALIFORNIA LOS ANGELES, CA 90095-1555, USA E-mail: rescorla@ucla.edu
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Abstract

This article discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

Keywords

03A1003A0503A99Bayesian decision theoryformal epistemologyconditionalizationsubjective probabilityregular conditional distribution
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 4 , December 2018 , pp. 705 - 735
Copyright
Copyright © Association for Symbolic Logic 2018 

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