Framing Contingencies ∗

The subjective likelihood of a contingency often depends on the manner in which it is described to the decision maker. To accommodate this dependence, we introduce a model of decision making under uncertainty which takes as primitive a family of preferences indexed by partitions of the state space. Each partition corresponds to a description of the state space. We characterize the following partition-dependent expected utility representation. The decision maker has a nonadditive set function ν over events. Given a partition of the state space, she computes expected utility with respect to her partition-dependent belief, which weights each cell in the partition by ν. Nonadditivity of ν allows the probability of an event to depend on the way in which the state space is described. We propose behavioral definitions for those events which are transparent to the decision maker and those which are completely overlooked, and connect these definitions to conditions on the representation. ∗This paper supersedes an earlier draft titled “Unawareness and Framing.” Comments from anonymous referees, Eddie Dekel, Raphaël Giraud, and Todd Sarver were very helpful. Klaus Nehring deserves special thanks for discovering and carefully explaining the relationship between binary bet acyclicity and the product rule to us, leading to the material in Section 4.4. We thank the National Science Foundation for financial support under Grants SES-0550224 and SES-0835944. †Department of Economics, University of California, 508-1 Evans Hall #3880, Berkeley, CA 94720-3880. Email: dahn@econ.berkeley.edu. ‡Department of Economics, Washington University in Saint Louis, Campus Box 1208, Saint Louis, MO 63130. Email: hergin@artsci.wustl.edu.