Philosophy of Science 87 (1):152-178 (2020)

Philippe Mongin
Last affiliation: Centre National de la Recherche Scientifique
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.
Keywords Probability theory  Stochastic independence  Probabilistic independence  Subjective probability  Subjective expected utility  Bayesian decision theory  Preference axiomatization  Representation theorems  Separability theory  Savage
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DOI 10.1086/706083
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References found in this work BETA

The Logic of Scientific Discovery.Karl Popper - 1959 - Studia Logica 9:262-265.
Decision Theory with a Human Face.Richard Bradley - 2017 - Cambridge University Press.
A Nonpragmatic Vindication of Probabilism.James M. Joyce - 1998 - Philosophy of Science 65 (4):575-603.
The Foundations of Statistics.Leonard J. Savage - 1959 - Synthese 11 (1):86-89.

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Philippe Mongin (1950-2020).Jean Baccelli & Marcus Pivato - 2021 - Theory and Decision 90 (1):1-9.

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