A Structure of Joint Irreducible Sets for Classically Rationalizable Choice Operators

Abstract

Decomposition of choice functions into some choice functions rationalizable by linear orders, and ordinal representaion of closure operators are two concepts independently developed in the literature. Koshevoy (1999) defined a map which is a correspondence between path independent choice functions and anti-exchange closure operators. In this study the Koshevoy map is redefined for some special cases of classically rationalizable choice functions. For these cases, the width concept in the decomposition of choice functions, introduced by Aleskerov et al. (1979), and the structure of joint irreducible sets in ordinal representation of closure operators, studied by Monjardet and Raderanirina (1999), are combined.