Complexity of computing median linear orders and variants

Olivier Hudry 1, 2
Abstract :

Given a finite set X and a collection C of linear orders defined on X, computing a median linear order (Condorcet-Kemeny's problem) consists in determining a linear order O minimizing the remoteness from C. This remoteness is based on the symmetric distance, and measures the number of disagreements between O and C. In the context of voting theory, X can be considered as a set of candidates and the linear orders of C as the preferences of voters, while a linear order minimizing the remoteness from C can be adopted as the collective ranking of the candidates with respect to the voters' opinions. This paper studies the complexity of this problem and of several variants of it: computing a median order, computing a winner according to this method, checking that a given candidate is a winner and so on. We try to locate these problems inside the polynomial hierarchy.

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Submitted on : Friday, September 13, 2019 - 3:40:39 PM
Last modification on : Saturday, September 14, 2019 - 1:39:06 AM

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Olivier Hudry. Complexity of computing median linear orders and variants. Electronic Notes in Discrete Mathematics, 2013, 42, pp.57-64. ⟨hal-02286384⟩

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