# Bayesian Decision Theory and Stochastic Independence

*TARK 2017*(2017)

**Abstract**

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory.

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References found in this work BETA

A Nonpragmatic Vindication of Probabilism.Joyce, James

An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy.Leitgeb, Hannes & Pettigrew, Richard

Decision Theory with a Human Face.Bradley, Richard

Philosophical Theories of Probability.Gillies, Donald

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2017-10-20

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