Bayesian Decision Theory and Stochastic Independence

Forthcoming in J. Lang (ed.), Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), EPTCS 251, 2017

HEC Paris Research Paper No. ECO/SCD-2017-1228

11 Pages Posted: 21 Nov 2017 Last revised: 28 Nov 2017

See all articles by Philippe Mongin

Philippe Mongin

GREGHEC; CNRS & HEC Paris - Economics & Decision Sciences

Date Written: August 1, 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.

Keywords: Stochastic Independence, Probabilistic Independence, Bayesian Decision Theory, Savage

JEL Classification: C6, D81, D89

Suggested Citation

Mongin, Philippe, Bayesian Decision Theory and Stochastic Independence (August 1, 2017). Forthcoming in J. Lang (ed.), Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), EPTCS 251, 2017; HEC Paris Research Paper No. ECO/SCD-2017-1228. Available at SSRN: https://ssrn.com/abstract=3074448 or http://dx.doi.org/10.2139/ssrn.3074448

Philippe Mongin (Contact Author)

GREGHEC ( email )

1 rue de la Libération
Jouy-en-Josas, 78350
France

CNRS & HEC Paris - Economics & Decision Sciences ( email )

Paris
France

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