Cardinal Utility Representation Separating Ambiguous Beliefs and Utility

Abstract

This paper proposes the weaker axioms which admit a cardinal utility representa- tion under ambiguity separating ambiguous beliefs and utility over consequences in a purely subjective setting. The representation is obtained in an implicit form, which corresponds to the disappointment aversion utility (Gul, 1991) with respect to a non- additive measure in place of a probability measure. It includes all the properties of cardinality, ambiguity aversion, reference dependency, gain/loss asymmetry, and the distortion in probability evaluations. It enables us to capture varying attitude to- ward ambiguity such as the subjective common ratio e¤ect and to explain Machina s examples (2009, 2014) in the simplest way.