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
11 Pages Posted: 21 Nov 2017 Last revised: 28 Nov 2017
Date Written: August 1, 2017
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: Suggested Citation