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Bayesian Decision Theory and Stochastic Independence

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  • Mongin, Philippe

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.

Suggested Citation

  • Mongin, Philippe, 2017. "Bayesian Decision Theory and Stochastic Independence," HEC Research Papers Series 1228, HEC Paris, revised 28 Nov 2017.
    • Handle: RePEc:ebg:heccah:1228
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    Cited by:

    1. Philippe Mongin & Marcus Pivato, 2020. "Social preference under twofold uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 633-663, October.

    More about this item

    Keywords

    Stochastic Independence; Probabilistic Independence; Bayesian Decision Theory; Savage;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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