Date on Master's Thesis/Doctoral Dissertation
Applied and Industrial Mathematics, PhD
Semilattices; Majorities; Voting
Kenneth May , 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.
Hoots, Lucas, "Strong quota pair systems and May's theorem on median semilattices." (2015). Electronic Theses and Dissertations. Paper 2253.