Maximum likelihood approach to vote aggregation with variable probabilities

The Condorcet-Kemeny-Young statistical approach to vote aggregation is based on the assumption that voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e., the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent and does not satisfy local independence of irrelevant alternatives. Yet, it is anonymous, neutral, and paretian. It also appears that its performance in selecting the alternative most likely to be the best improves with the rate at which the probability increases.We would like to thank Michel Le Breton for his encouragement to examine this question and for his comments, as well as Philippe De Donder, Jean-Yves Duclos, Stephen Gordon, Cyril Téjédo and an anonymous referee for their comments.