Author

Lucas Hoots

Date on Master's Thesis/Doctoral Dissertation

8-2015

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Powers, Robert

Committee Member

Sahoo, Prasanna

Committee Member

McMorris, Fred

Committee Member

Wildstrom, David

Committee Member

Gainous, Jason

Subject

Semilattices; Majorities; Voting

Abstract

Kenneth May [16], in 1952, characterized simple majority rule in terms of three conditions: anonymity, neutrality, and positive responsiveness. In this thesis, we remove the condition of neutrality and obtain a characterization of the class of voting rules that satisfy anonymity and positive responsiveness. The key concept in this characterization is the notion of a strong quota pair system. The situation with two alternatives studied by May can be thought of as a very simple example of a finite median semilattice. The main result of this thesis is an extension of May’s theorem to the domain of all finite median semilattices.

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