A unified representation of conditioning rules for convex capacities

This paper proposes a unified representation, called the G-updating rule, which includes three conditioning rules as special cases, the naïve Bayes rule, the Dempster-Shafer rule (Shafer(1976)), and the generalized Bayes' updating rule introduced by Dempster(1967) or Fagin and Halpern(1991). It is shown that the G-updating rule constitutes a three-step conditioning, where one of the three rules is applied in each step.

CEU Preferences and Dynamic Consistency

This paper investigates the dynamic consistency of CEU preferences. A decision maker is faced with an information structure represented by a fixed filtration. If beliefs are represented by a convex capacity, we show that a necessary and sufficient condition for dynamic consistency is that beliefs be additive over the final stage in the filtration.

A General Update Rule for Convex Capacities

A characterization of a general update rule for convex capacities, the G-updating rule, is investigated. We introduce a consistency property which bridges between unconditional and conditional preferences, and deduce an update rule for unconditional capacities. The axiomatic basis for the G-updating rule is established through consistent counterfactual acts, which take the form of trinary acts expressed in terms of G, an ordered tripartition of global states.ambiguous belief, Bayes' rule, update rule, convex capacity, Choquet ex- pected utility, conditional preference