Comparison of Voting Methods Using Complexity Functions and the Weak Theta Asymptotic Notation

Computational social choice represents a new research area that brings together social choice theory and computer science. One of the most important topics in computational social choice is the use of the voting theory as part of the solutions for various problems in computer science. In this paper we propose a formal representation approach for voting methods using complexity functions. Also, using this representation and the Weak Theta asymptotic notation, we propose and prove several theorems related to the comparison of seven popular voting methods. The property of a voting method that we study in this paper is the following: a voting method is considered appropriate for a given voting scheme only if the method computes a single winner for that voting scheme, ´no winner´ or ´more than one winner´ are not acceptable results.