An updated survey on the linear ordering problem for weighted or unweighted tournaments

Charon, Irène; Hudry, Olivier

doi:10.1007/s10479-009-0648-7

Cited by 62 publications

(44 citation statements)

References 201 publications

(223 reference statements)

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“…The extension of the method of Kemeny to rankings with ties (and to tournaments and to binary relations) is a common problem in social choice [8,21,30,31], usually referred to as the search for 'median orders' or 'median relations'. These extensions are obtained by allowing the relations in the profile to be rankings with ties (or tournaments, or binary relations) or by allowing the winning relations to be rankings with ties (or tournaments, or binary relations).…”

Section: Definition 841mentioning

confidence: 99%

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

Pérez‐Fernández¹

2017

4OR-Q J Oper Res

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Section: Definition 841mentioning

confidence: 99%

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

Pérez‐Fernández¹

2017

4OR-Q J Oper Res

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“…There are many publications addressing this problem, for a review of the literature see, for example, Charon & Hudry (2010).…”

Section: Two Measures Of the Dependence Of Preferential Rankings On Cmentioning

confidence: 99%

Two Measures of the Dependence of Preferential Rankings on Categorical Variables

Lissowski

2017

Studies in Logic, Grammar and Rhetoric

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Abstract. The aim of this paper is to apply a general methodology for constructing statistical methods, which is based on decision theory, to give a statistical description of preferential rankings, with a focus on the rankings' dependence on categorical variables. In the paper, I use functions of description errors that are based on the Kemeny and Hamming distances between preferential orderings, but the proposed methodology can also be applied to other methods of estimating description errors.Keywords: decision theory, individual preferential ordering (ranking), group (social) preferential ordering (ranking), Kemeny distance, Hamming distance, generalized regression, measure of the intensity of a dependence, computational complexity.

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“…Finding these linear orders is equivalent to solving an instance of the NP-complete problem feedback arc set [1,14,20], which implies that checking membership in the Slater set is NP-hard [16]. Yet, there are implementations that are sufficiently fast on small instances (e.g., [17]).…”

Section: Top Cycle a Nonempty Subset Of Alternativesmentioning

confidence: 99%

Bounds on the disparity and separation of tournament solutions

Brandt

Dau

Seedig

2015

Discrete Applied Mathematics

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A tournament solution is a function that maps a tournament, i.e., a directed graph representing an asymmetric and connex relation on a finite set of alternatives, to a non-empty subset of the alternatives. Tournament solutions play an important role in social choice theory, where the binary relation is typically defined via pairwise majority voting. If the number of alternatives is sufficiently small, different tournament solutions may return overlapping or even identical choice sets. For two given tournament solutions, we define the disparity index as the order of the smallest tournament for which the solutions differ and the separation index as the order of the smallest tournament for which the corresponding choice sets are disjoint. Isolated bounds on both values for selected tournament solutions are known from the literature. In this paper, we address these questions systematically using an exhaustive computer analysis. Among other results, we provide the first tournament in which the bipartisan set and the Banks set are not contained in each other.

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An updated survey on the linear ordering problem for weighted or unweighted tournaments

Cited by 62 publications

References 201 publications

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

Two Measures of the Dependence of Preferential Rankings on Categorical Variables

Bounds on the disparity and separation of tournament solutions

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