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Bayesian Decision Theory and Stochastic Independence

Published online by Cambridge University Press:  01 January 2022

Philippe Mongin
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Abstract

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework.

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Articles
Information
Philosophy of Science , Volume 87 , Issue 1 , January 2020 , pp. 152 - 178
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

A first version of this article was presented at a seminar at the Munich Center for Mathematical Philosophy and at the Theoretical Aspects of Rationality and Knowledge (TARK) 2017 conference. The current version has particularly benefited from detailed comments made by Richard Bradley, Donald Gillies, Robert Nau, Marcus Pivato, Burkhard Schipper, Peter Wakker, Paul Weirich, two anonymous TARK referees, and two anonymous referees of this journal. I thank the Investissements d’Avenir (ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047) for supporting this research.

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