Date on Master's Thesis/Doctoral Dissertation

8-2014

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Committee Chair

Powers, Robert C.

Committee Member

Riedel, Thomas

Committee Member

Wildstrom, David J.

Committee Member

McMorris, Fred R.

Committee Member

Desoky, Ahmed

Subject

Social choice--Decision making

Abstract

Arrow's classic theorem shows that any collective choice function satisfying independence of irrelevant alternatives (IIA) and Pareto (P), where the range is a subset of weak orders, is based on a dictator. This thesis focuses on Arrovian collective choice functions in which the range is generalized to include acyclic, indifference-transitive (ACIT) relations on the set of alternatives. We show that Arrovian ACIT collective choice functions with domains satisfying the free-quadruple property are based on a unique weakly decisive voter; however, this is not necessarily true for ACIT collective choice functions where Arrow's independence condition is weakened. For ACIT collective choice functions with linear order domains, we present a complete characterization, as well as a recursive formula for counting the number of Arrovian ACIT collective choice functions with two voters.

Included in

Mathematics Commons

Share

COinS