Bayesian update rules and minimal-change preference revision

This paper studies how minimal-change constraints on preference revision bear on credal revision, with special attention to imprecise priors. Working within a preference-revision framework inspired by the AGM belief revision theory of Alchourrón, Gärdenfors, and Makinson (Journal of Symbolic Logic 50(2): 510–530, 1985), we examine how admissible revisions of preference relations constrain revisions of the credal states represented by imprecise priors. The precise-prior case provides a baseline: under suitable conditions, Bayesian conditioning can be recovered from the relevant minimal-change postulates. The main focus of the paper is the imprecise-prior case, where credal states are represented by sets of probability functions and the orthodox update rule is Pointwise Bayesian conditioning. We characterize the posterior preferences induced by Pointwise Bayesian conditioning and show that this characterization reveals a divergence: Pointwise Bayesian conditioning may require the removal of preference judgments that admissible minimal-change revisions can preserve. The resulting divergence cases show that prior imprecision may stem from different sources, and that these different sources can warrant different posterior responses when new information is incorporated. The analysis also clarifies how dilation can be blocked when the relevant prior likelihood judgments remain part of the reference set. The framework therefore provides a preference-based perspective for assessing Pointwise Bayesian conditioning and for identifying admissible alternatives in the imprecise settings.