Consequentialism and Dynamic Consistency in Updating Ambiguous Beliefs

Abstract

By proposing the notions of upper-constrained dynamic consistency and lower-constrained dynamic consistency that are weaker axioms than dynamic consistency, this paper axiomatizes the Dempster-Shafer updating rule and naive Bayes' updating rule within the framework of Choquet expected utility. Based on the notion of conditional comonotonicity, this paper also provides an axiomatization of consequentialism under Choquet expected utility. Furthermore, based on the idea of the mean preserving rule, this paper provides a unified approach for distinguishing capacity updating rules (the Dempster-Shafer updating rule, naive Bayes' updating rule, and Fagin-Halpern updating rule) according to the degree of dynamic consistency.