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

  • MICHAEL RESCORLA (a1)
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.

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*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CALIFORNIA LOS ANGELES, CA 90095-1555, USA E-mail: rescorla@ucla.edu
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