Decision-making with partial information

Journal of Economic Theory . 2021. Vol. 198. Article 105369.

Jürgen Eichberger, Pasichnichenko I.

In this paper, we study choice under uncertainty with belief functions. Belief functions can capture par- tial information by describing what is objectively known about the probabilities of events. State-contingent acts together with a belief function over states induce belief functions over outcomes. We assume that de- cision 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 characterizing a preference rep- resentation for belief functions that captures what is (objectively) known about the likelihood of outcomes and combines it with subjective beliefs according to the “principle of insufficient reason” whenever the likelihood of events is unknown. This treatment of partial information yields a natural distinction between ambiguity and ambiguity attitudes. The approach is novel in its treatment of partial information and in its axiomatization of the uniform distribution in case of ignorance.
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Keywords: ambiguity, Belief functions, Principle of insufficient reason, Ambiguity attitude, Information about events