Commuting Probability Revisions: The Uniformity Rule: In Memoriam Richard Jeffrey, 1926-2002

Commuting Probability Revisions: The Uniformity Rule

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 le...

Probability Revision, the Uniformity Rule, and the Chan-Darwiche Metric

The author has proposed a rule of probability revision dictating that identical learning be reflected in identical ratios of new to old odds. Following this rule ensures that the final result of a sequence of probability revisions is undisturbed by an alteration in the temporal order of the learning prompting these revisions. There is also a close connection between this rule and an intriguing ...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

Comments on Carl Wagner’s Jeffrey Conditioning and External Bayesianity

In “Jeffrey conditioning and external Bayesianity”, Carl Wagner provides further support from mathematical elegance for what he calls the uniformity rule: namely, that Bayesians should represent “identical learning” by sameness of odds ratios across atomic events. Put another way, if something prompts both you and me to change our subjective probabilities, and as a result we learn the same thin...

Generalizing Jeffrey Conditionalization

Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this gen­ eralization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise disjoint. We discuss a twofold extension of th...