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

TL;DR

This paper proves that the MP-aggregation problem for dichotomous weak orders can be solved efficiently in polynomial time, providing a computationally feasible method for certain preference aggregation scenarios.

Contribution

It establishes polynomial-time solvability of MP-aggregation when the output is a dichotomous weak order, extending previous complexity results.

Findings

The median procedure can be efficiently computed for dichotomous weak orders.

The problem is polynomial-time solvable under specific output class constraints.

This advances understanding of preference aggregation computational complexity.

Abstract

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.