Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Committee Chair

Powers, Robert C.

Committee Co-Chair (if applicable)

Riedel, Thomas

Committee Member

Riedel, Thomas

Committee Member

Wildstrom, David J.

Committee Member

McMorris, Fred R.

Committee Member

Desoky, Ahmed


Social choice--Decision making


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