Condorcet efficiency: Weighted Bucklin vs. weighted scoring and Borda

Abstract

We ask how good Bucklin-related procedures can be at identifying Condorcet winners in ranked-ballot, single-winner elections. Bucklin procedures can have a wide range of weighting vectors and thresholds; one, for example, applies Borda weights, analogous to the Borda Count in weighted scoring elections. Using simulation, we estimate the maximum Condorcet efficiency of both weighted Bucklin and weighted scoring elections as the number of voters becomes very large; these measures depend of course on the underlying distribution of ballots. For the impartial anonymous culture distribution, weighted Bucklin exhibits higher Condorcet efficiency than weighted scoring when there are 3 candidates, but is not as good when there are 4 candidates, and about equal when there are 5 or 6. We also compare them under the impartial culture distribution (equally good), and under a one-dimensional spatial model (weighted Bucklin is usually better, sometimes much better).