Decision-making with partial information

In this paper, we study choice under uncertainty with belief functions on a set of outcomes as objects of choice. Belief functions describe what is objectively known about the probabilities of outcomes. We assume that decision makers have preferences over belief functions that reflect both their valuation of outcomes and the information available about the likelihood of outcomes. We provide axioms which characterize a preference representation for belief functions that captures what is (objectively) known about the likelihood of outcomes and combines it with subjective beliefs about unknown probabilities according to the “principle of insufficient reason”. The approach is novel in its treatment of partial information and in its axiomatization of the uniform distribution in the case of ignorance. Moreover, our treatment of partial information yields a natural distinction between ambiguity and ambiguity attitude.