Pairwise consensus and the Borda rule

Abstract

We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the Kemeny distance of the profile to the former is not greater than its distance to the latter. We show that if a preference profile exhibits pairwise consensus around a preference relation, then this preference relation coincides with the binary relation induced by the Borda count. We also show that no other scoring rule always selects the top ranked alternative of the preference relation around which there is consensus when such consensus exists.