MP-Aggregation MP(R,2-WO) is Polynomial-Time Solvable When the Output Should Be Dichotomous Weak Preference Order

We consider the median procedure (Barthelemy and Monjardet, 1981) that aggregates a sequence n of binary relations from some input class into a single binary relation from some (possibly different) output class, minimizing the number of disagreed order pairs. We show that if the output class should be a dichotomous weak order (2-WO), then the problem is polynomial-time solvable.