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Journal Articles Electronic Notes in Discrete Mathematics Year : 2013

Complexity of computing median linear orders and variants

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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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Dates and versions

hal-02286384 , version 1 (13-09-2019)

Identifiers

  • HAL Id : hal-02286384 , version 1

Cite

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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