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A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization

Rescorla, Michael (2017) A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization. [Preprint]

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Abstract

This paper 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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Rescorla, Michaelrescorla@ucla.edu
Additional Information: Forthcoming in "The Review of Symbolic Logic"
Keywords: Conditionalization; Bayesian decision theory; conditional probability; regular conditional distributions; Borel-Kolmogorov paradox; diachronic Dutch books
Subjects: Specific Sciences > Mathematics > Epistemology
General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Depositing User: Michael Rescorla
Date Deposited: 01 Nov 2017 15:56
Last Modified: 01 Nov 2017 17:41
Item ID: 14082
Subjects: Specific Sciences > Mathematics > Epistemology
General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Date: October 2017
URI: http://philsci-archive.pitt.edu/id/eprint/14082

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