A Comparison of Efficiency of Multicandidate Electoral Systems

Abstract

A variety of electoral systems for single-winner, multicandidate elections are evaluated according to their tendency to (a) select the Condorcet candidate-the candidate who could beat each of the others in a two-way race-if one exists, and (b) select a candidate with high social (average) utility. The proportion of Condorcet candidates selected and a measure of social-utility efficiency under either random society or spatial model assumptions are estimated for seven electoral systems using Monte Carlo techniques. For the spatial model simulations, the candidates and voters are generated from multivariate normal distributions. Numbers of candidates and voters are varied, along with the number of spatial dimensions, the correlation structure, and the relative dispersion of candidates to voters. The Borda, Black, and Coombs methods perform well on both criteria, in sharp contrast to the performance of the plurality method. Approval voting, plurality with runoff, and the Hare system (preferential voting) provide mixed, but generally intermediate results. Finally, the results of the spatial model simulations suggest a multicandidate equilibrium for winningoriented candidates (under plurality, runoff, and Hare) that is not convergent to the median.