Borda and the Maximum Likelihood Approach to Vote Aggregation

Abstract

Drissi-Bakhkhat and Truchon [“Maximum Likelihood Approach to Vote Aggregation with Variable Probabilities,” Social Choice and Welfare, 23 (2004), 161-185.] extend the Condorcet-Kemeny-Young maximum likelihood approach to vote aggregation by relaxing the assumption that the probability of correctly ordering two alternatives is the same for all pairs of alternatives. They let this probability increase with the distance between the two alternatives in the true order, to reflect the intuition that a judge or voter is more prone to errors when confronted to two comparable alternatives than when confronted to a good alternative and a bad one. In this note, it is shown that, for a suitably chosen probability function, the maximum likelihood rule coincides with the Borda rule, thus, partially reconciling the Borda and the Condorcet methods.