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 Co-Chair (if applicable)

Sahoo, Prasanna

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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