Generalizing Jeffrey Conditionalization
This work provides a theoretical extension for researchers in probability theory and decision-making, but it appears incremental as it builds directly on existing generalizations.
The paper extends Jeffrey's rule of probability kinematics by generalizing it to cases where new evidence is bounded by a two-monotone capacity and the prior is a lower envelope, building on Wagner's prior work that used Dempsterian lower probabilities.
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.