Reexamination on Updating Choquet Beliefs

Abstract

Eichberger, Grant, and Kelsey (2007) characterize the full Bayesian update rule for capacities. This paper shows that a conditional preference relation represented by the Choquet expected utility with respect to the updated capacity through the rule does not satisfy the axiom of Conditional Certainty Equivalence Consistency. A counterexample is provided and it is proved that a relaxation of the axiom maintains their results.