Teddy Seidenfeld, Mark Schervish and Joseph Kadane

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Two theories of conditional probability and non-conglomerability

Abstract

Conglomerability of conditional probabilities is suggested by some (e.g., Walley, 1991) as necessary for rational degrees of belief. Here we give sufficient conditions for non-conglomerability of conditional probabilities in the de Finetti/Dubins sense of conditional probability. These sufficient conditions cover familiar cases where P(.) is a continuous, countably additive probability. In this regard, we contrast the de Finetti/Dubins sense of conditional probability with the more familiar account of regular conditional distributions, in the fashion of Kolmogorov.

Keywords

Non-conglomerability, conditional probability, k-additive probability, regular conditional distribution

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E-mail addresses

Teddy Seidenfeld		teddy@stat.cmu.edu
Mark Schervish		mark@stat.cmu.edu
Joseph Kadane		kadane@stat.cmu.edu