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.
Recommended Citation
Bjurstrom, Katey, "Acyclic and indifference-transitive collective choice functions." (2014). Electronic Theses and Dissertations. Paper 114.
https://doi.org/10.18297/etd/114
