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 | ||||||
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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 |
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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 |
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Date: | October 2017 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/14082 |
Available Versions of this Item
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A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization. (deposited 27 Oct 2017 17:14)
- A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization. (deposited 01 Nov 2017 15:56) [Currently Displayed]
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