Contraction consistent stochastic choice correspondence

We model a general choice environment via probabilistic choice correspondences, with (possibly)incomplete domain and infinite universal set of alternatives. We offer a consistency restrictionregarding choice when the feasible set contracts. This condition, ‘contraction consistency’, subsumesearlier notions such as Chernoff’s Condition, Sen’s α and β , and regularity. We identify arestriction on the domain of the stochastic choice correspondence, under which contractionconsistency is equivalent to the weak axiom of revealed preference in its most general form. Whenthe universal set of alternatives is finite, this restriction is also necessary for such equivalence.Analogous domain restrictions are also identified for the special case where choice is deterministicbut possibly multi-valued. Results due to Sen (Rev Econ Stud 38: 307-317, 1971) and Dasgupta andPattanaik (Econ Theory 31: 35-50, 2007) fall out as corollaries. Thus, conditions are established,under which our notion of consistency, articulated only in reference to contractions of the feasible set,suffices as the axiomatic foundation for a general revealed preference theory of choice behaviour.