Making Right Decisions Based on Wrong Opinions

Abstract

We revisit the classic problem of designing voting rules that aggregate objective opinions, in a setting where voters have noisy estimates of a true ranking of the alternatives. Previous work has replaced structural assumptions on the noise with a worst-case approach that aims to choose an outcome that minimizes the maximum error with respect to any feasible true ranking. This approach underlies algorithms that have recently been deployed on the social choice website RoboVote.org. We take a less conservative viewpoint by minimizing the average error with respect to the set of feasible ground truth rankings. We derive (mostly sharp) analytical bounds on the expected error and establish the practical benefits of our approach through experiments.