Ordres médians et ordres de Slater des tournois

Charon, Irène; Hudry, Olivier; Woirgard, Frédéric

doi:10.4000/msh.2740

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…This idea dates back at least to Barbut (1959), Kemeny (1959), Kemeny and Snell (1962) and Slater (1961). Although it raises fascinating deep combinatorial questions and difficult algorithmic problems (see Barthélémy, Guénoche and Hudry, 1989;Monjardet, 1981, 1988;Bermond, 1972;Charon-Fournier, Germa and Hudry, 1992;Charon, Hudry and Woirgard, 1996;Hudry, 1989;Monjardet, 1990), this line of research raises other difficulties. As argued in Perny (1992) and Roy and Bouyssou (1993), -the choice of the distance function should be analyzed with care as soon as one leaves the, easy, case of a distance between tournament and linear orders (see, e.g.…”

Section: Discussionmentioning

confidence: 99%

Monotonicity of ?ranking by choosing?: A progress report

Bouyssou

2004

Soc Choice Welfare

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Procedures designed to select alternatives on the basis of the results of pairwise contests between them have received much attention in literature. The particular case of tournaments has been studied in depth. More recently weak tournaments and valued generalizations thereof have been investigated. The purpose of this paper is to investigate to what extent these choice procedures may be meaningfully used to define ranking procedures via their repeated use, i.e. when the equivalence classes of the ranking are determined by successive applications of the choice procedure. This is what we call "ranking by choosing". As could be expected, such ranking procedures raise monotonicity problems. We analyze these problems and show that it is nevertheless possible to isolate a large class of well-behaved choice procedures for which failures of monotonicity are not overly serious. The hope of finding really attractive ranking by choosing procedures is however shown to be limited. Our results are illustrated on the case of tournaments. Key words Ranking procedures-Choice procedures-Monotonicity-Strong Superset Property-Ranking by choosing-Tournaments This is what we call "ranking by choosing". An example may help clarify the process.

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Section: Discussionmentioning

confidence: 99%

Monotonicity of ?ranking by choosing?: A progress report

Bouyssou

2004

Soc Choice Welfare

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“…In the tournament of Fig. 2, for which the missing arcs are assumed to be oriented from the left to the right, it is easy to show that b is the only Slater winner while its score is not the highest one (see Charon et al 1996c, for more details). On the other hand, we may check easily (for instance from the list of the different patterns of non-isomorphic tournaments given in Moon 1968) that:…”

Section: Theorem 10 a Tournament T Is Regular (Hence With An Odd Numbmentioning

confidence: 99%

A survey on the linear ordering problem for weighted or unweighted tournaments

Charon

Hudry

2007

4OR

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In this paper, we survey some results, conjectures and open problems dealing with the combinatorial and algorithmic aspects of the linear ordering problem. This problem consists in finding a linear order which is at minimum distance from a (weighted or not) tournament. We show how it can be used to model an aggregation problem consisting of going from individual preferences defined on a set of candidates to a collective ranking of these candidates.MSC classification 05C20 · 05C38 · 05C90 · 06A05 · 06A07 · 68Q17 · 68Q25 · 68R10 · 90C10 · 90C27 · 90C35 · 90C57 · 90C59 · 91F10

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“…In fact, such a situation can occur for any n ≥ 6 (see [21] or [22]). More precisely, these two sets are equal for n ≤ 3, the set of Copeland winners contains the one of Slater winners for n = 4, and the intersection of the two sets is non-empty for n = 5 but there is no systematic inclusion between them.…”

Section: Introductionmentioning

confidence: 96%

Maximum Distance Between Slater Orders and Copeland Orders of Tournaments

Charon

Hudry

2010

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Given a tournament T = (X, A), we consider two tournament solutions applied to T: Slater's solution and Copeland's solution. Slater's solution consists in determining the linear orders obtained by reversing a minimum number of directed edges of T in order to make T transitive. Copeland's solution applied to T ranks the vertices of T according to their decreasing out-degrees. The aim of this paper is to compare the results provided by these two methods: to which extent can they lead to different orders? We consider three cases: T is any tournament, T is strongly connected, T has only one Slater order. For each one of these three cases, we specify the maximum of the symmetric difference distance between Slater orders and Copeland orders. More precisely, thanks to a result dealing with arc-disjoint circuits in circular tournaments, we show that this maximum is equal to n(n − 1)/2 if T is any tournament on an odd number n of vertices, to (n 2 − 3n + 2)/2 if T is any tournament on an even number n of vertices, to n(n − 1)/2 if T is strongly connected with an odd number n of vertices, to (n 2 − 3n − 2)/2 if T is strongly connected with an even number n of vertices greater than or equal to 8, to (n 2 − 5n + 6)/2 if T has an odd number n of vertices and only one Slater order, to (n 2 − 5n + 8)/2 if T has an even number n of vertices and only one Slater order.

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Ordres médians et ordres de Slater des tournois

Cited by 10 publications

References 7 publications

Monotonicity of ?ranking by choosing?: A progress report

Monotonicity of ?ranking by choosing?: A progress report

A survey on the linear ordering problem for weighted or unweighted tournaments

Maximum Distance Between Slater Orders and Copeland Orders of Tournaments

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