Fair infinite lotteries, qualitative probability, and regularity

Date
2022-02-11
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Source Title
Philosophy of Science
Print ISSN
0031-8248
Electronic ISSN
1539-767X
Publisher
Cambridge University Press
Volume
89
Issue
4
Pages
824 - 844
Language
English
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Abstract

A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating countable additivity. In this article, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than continuous uniform distributions. Along the way, I provide a novel argument for a weak qualitative, epistemic version of regularity.

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Published Version (Please cite this version)