Uncovered choice functions

Abstract

An abiding problem in choice theory has been one of characterizing those choice function which are obtained as a result of some kind of optimization. Specifically, the endeavour has concentrated largely on finding a binary relation (if there be any) whose best elements coincide with observed choices. An adequate survey of this line of research till the mid eighties is available in Moulin [1985]. More recently, the emphasis has focused on binary relations defined on non-empty subsets of a given set, such that the choice function coincides with the best subset corresponding to a feasible set of alternatives. This problem has been provided with a solution in Lahiri (Forthcoming), although the idea of binary relations defined on subsets is a concept which owes its analytical origins to Pattanaik and Xu [1990].