Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: I construct minimal subjective state spaces S for any complete and transitive preference over finite menus. The construction of S identifies two endogenous components for such preferences: the revealed dominance relation and the family F of focal menus. It also identifies all Pareto representations for the revealed dominance. Uniqueness is obtained for some minimal spaces. The aggregation of minimal spaces satisfies a novel condition called coherence. Coherent aggregation of minimal spaces has many special cases, such as the Strotz-like model of changing tastes and a version of the costly self-control model studied by Gul and Pesendorfer (2001, 2005). Another application is a lexicographic aggregation model. Moreover, the difference between any pair of preferences can be modeled in terms of minimal spaces and coherent aggregation. The well-known additive model of Kreps (1979) and its extension with negative states by Gorno (2016) are both coherent, but they are not guaranteed for minimal spaces S. I derive some non-binding constraints for state spaces in additive models.