Commuting Probability Revisions: The Uniformity Rule

A simple rule of probability revision ensures that the final result ofa sequence of probability revisions is undisturbed by an alterationin the temporal order of the learning prompting those revisions.This Uniformity Rule dictates that identical learning be reflectedin identical ratios of certain new-to-old odds, and is grounded in the oldBayesian idea that such ratios represent what is learned from new experiencealone, with prior probabilities factored out. The main theorem of this paperincludes as special cases (i) Field's theorem on commuting probability-kinematical revisions and (ii) the equivalence of two strategiesfor generalizing Jeffrey's solution to the old evidence problem tothe case of uncertain old evidence and probabilistic new explanation.