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 Co-Chair (if applicable)
Riedel, Thomas
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
