UTA Department of Mathematics

Lattices and Social Choice Seminar

Date/Time/Room: Friday (5/3/2002) at 1:00pm in 487 Pickard Hall

Speaker: Prof Mark Johnson, Department of Economics, Tulane University

``Path Independent Choice Functions and LLD Lattices''

Abstract: The concept of Path Indepence (PI) was first introduced by Arrow (Social Choice and Individual Values, Yale Univ Press, New Haven, 1963), as a defense of his requirement that collective choices be rationalized by a weak ordering. Plott (Econometrica 41 (1973), 1075-1091) highlighted the dynamic aspects of PI implicit in Arrow's initial discussion. Throughout these investigations, two questions remained ananswered. What are the precise mathematical foundations for path independence? How can PI choice functions be constructed? We give complete answers to both these questions for finite domains and provide necessary conditions for infinite domains.