Abstract

A simple rule of probability revision ensures that the final result of a sequence of probability revisions is undisturbed by an alteration in the temporal order of the learning prompting those revisions. This Uniformity Rule dictates that identical learning be reflected in identical ratios of certain new-to-old odds, and is grounded in the old Bayesian idea that such ratios represent what is learned from new experience alone, with prior probabilities factored out. The main theorem of this paper includes as special cases Field's theorem on commuting probability-kinematical revisions and the equivalence of two strategies for generalizing Jeffrey 's solution to the old evidence problem to the case of uncertain old evidence and probabilistic new explanation