Exactly What Happens After The Anscombe-aumann Race? Representing Preferences In Vague Environments

This paper derives a representation of preferences for a choice theory with vague environments; vague in the sense that the agent does not know the precise probability distributions over outcomes conditional on states. Instead, he knows only a possible set of these probabilities for each state. Thus, the paper relaxes an assumption about the environment, which is done while maintaining the independence axiom. The behavior implied by this model is different from both the behavior implied by standard subjective expected utility models and the behavior implied by ambiguity aversion models. To illustrate these differences and the importance of allowing for vagueness, the consequences of the developed theory for a simple contracting problem are considered. The paper also provides a defense of the independence axiom against the usual Ellsberg critique.