Extending difference of votes rules on three voting models.

Abstract

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 nonnegative integer k, the difference of votes rule M k 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. v TABLE OF CONTENTS