Generalizing Jeffrey Conditionalization

TL;DR

This paper extends Jeffrey's rule of probability updating to broader classes of lower probabilities and capacities, unifying and generalizing classical probability kinematics with new theoretical insights.

Contribution

It introduces a twofold extension of Jeffrey's rule, allowing for lower bounds as two-monotone capacities and priors as lower envelopes, broadening the scope of probability updating methods.

Findings

Generalizes Jeffrey's rule with Dempsterian lower probabilities

Unifies classical probability kinematics as a special case

Extends to two-monotone capacities and lower envelopes

Abstract

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 generalization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise disjoint. We discuss a twofold extension of this generalization, first allowing the lower bound to be any two-monotone capacity and then allowing the prior to be a lower envelope.