Rational choice and AGM belief revision

We establish a correspondence between the rationalizability of choice studied in the revealed preference literature and the notion of minimal belief revision captured by the AGM postulates. A choice frame consists of a set of alternatives Ω, a collection E of subsets of Ω (representing possible choice sets) and a function f:E→Ω2 (representing choices made). A choice frame is rationalizable if there exists a total pre-order R on Ω such that, for every E∈E, f(E) coincides with the best elements of E relative to R. We re-interpret choice structures in terms of belief revision. An interpretation is obtained by adding a valuation V that assigns to every atom p the subset of Ω at which p is true. Associated with an interpretation is an initial belief set and a partial belief revision function. A choice frame is AGM-consistent if, for every interpretation of it, the associated partial belief revision function can be extended to a full-domain belief revision function that satisfies the AGM postulates. It is shown that a finite choice frame is AGM-consistent if and only if it is rationalizable.