Relative Efficiency of Voting Systems

Abstract

Most comparisons of voting systems have focused on the outcomes of the elections and on the propensity of the systems to elect Condorcet winners. In this analysis, the emphasis is on the voters and the effectiveness of sincere voting on their part. The relative efficiency of sincere voting is defined to be the ratio of the maximum expected “gain” (in utility or impact) obtainable by the voter by voting sincerely to the maximum expected gain obtainable by the voter using any vote(s) allowed by the system. It represents the degree to which sincere voting behavior by the voter is encouraged by the voting system itself. Lower bounds for the relative efficiency are calculated for plurality voting, negative voting, preferential voting, the Borda method, and approval voting. Of the single-stage election systems considered, approval voting is shown to least penalize sincere voting.