The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution

Abstract

We investigate the quality of Condorcet solutions when compared to a central decision maker solution in the context of a facility location model in the plane. We perform an extensive set of experiments and conclude that if each population member votes according to his/her own self interest, then the Weber objective at the Condorcet solution point is very close to the optimal Weber objective value. Reducing the set of voters has little impact on the quality of the Condorcet solution. Being short of a good candidate has some impact but the final decision is still a good one. The distance metric seems to be of little relevance as well. As long as candidates are diverse, the Condorcet solution results in a good decision when compared to the decision by a benevolent dictator.