Objective Imprecise Probabilistic Information, Second Order Beliefs and Ambiguity Aversion: an Axiomatization

We axiomatize a model of decision under objective ambiguity or imprecise risk. The decision maker forms a subjective (non necessarily additive) belief aboutthe likelihood of probability distributions and computes the average expected utility of a given act with respect to this second order belief. We show that ambiguity aversion like the one revealed by the Ellsberg paradox requires that second order beliefs be nonadditive. Somespecial cases of the model are examined and different forms of ambiguity aversion are characterized.