Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Powers, Robert

Committee Co-Chair (if applicable)

McMorris, Fred

Committee Member

McMorris, Fred

Committee Member

Gill, Ryan

Committee Member

Gainous, Jason

Author's Keywords

voting theory; difference of votes; electoral college; probability of agreement; popular vote


In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. In addition, we state and prove Llamazares' theorem in voting models where either there is an infinite number of votes or each voter is allowed to express an intensity level for one alternative over the other. Finally, we will use a computer simulation to compare different voting methods to simple majority rule, in order to analyze the probability that the voting rules would output different results.