On the performance of voting systems in spatial voting simulations

Abstract

We study the performance of voting systems in terms of minimizing the overall social disutility of making a collective choice in an univariate voting space with ideological voting and perfect information. In order to obtain a distribution of the performance indicator for each of the 12 systems chosen for this study—Baldwin’s Method, Black’s Method, The Borda Count, Bucklin’s Grand Junction System, Coombs’ Method, Dodgson’s System, Instant Run-Off Voting, Plurality, Simpson’s MinMax, Tideman’s Ranked Pairs, Schulze’s Beatpath Method, and Two-Round Majority—we simulate elections using an Agent-Based Computational approach under several different distributions for voters and candidates positioning, with up to 15 available candidates. At each iteration, voters generate complete and strict ordinal utility functions over the set of available candidates, based on which each voting system computes a winner. We define the performance of a system in terms of its capability of choosing among the available candidates the one that minimizes aggregate voter disutility. As expected, the results show an overall dominance of Condorcet completion methods over the traditional and more widely used voting systems, regardless of the distributions of voter and candidate positions.