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

Jiehua Chen

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.

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

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.
Paper Structure (2 sections, 1 theorem, 3 equations)

This paper contains 2 sections, 1 theorem, 3 equations.

Table of Contents

  1. Introduction
  2. Construction

Key Result

Theorem 1

If $(A,B)$ is a minimum cut, then the alternatives in $A$ and $B$ define a DWO with minimum disagreements. If $(A',B')$ is a DWO with minimum disagreements, then $(A,B)$ is a minimum cut, where $A$ consists of node $s$, the nodes corresponding to the alternatives in $A'$, and the nodes $v_{(x,y)}$ w

Theorems & Definitions (2)

  • Theorem 1
  • proof : Proof sketch.