A note on permutations and rank aggregation

In this brief note we consider rank aggregation, a popular method in voting theory, social choice, business decisions, etc. Mathematically the problem is to find a permutation—viewed as a vector—that minimizes the sum of the ℓ1ℓ1-distances to a given family of permutations. The problem may be solved as an assignment problem and we establish several properties of optimal solutions in this problem.