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Monotonicity of "Ranking by Choosing": A progress report

Bouyssou, Denis (2004), Monotonicity of "Ranking by Choosing": A progress report, Social Choice and Welfare, 23, 2, p. 249-273. http://dx.doi.org/10.1007/s00355-003-0250-x

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Social Choice and Welfare
Volume
23
Number
2
Publisher
Springer
Pages
249-273
Publication identifier
http://dx.doi.org/10.1007/s00355-003-0250-x
Metadata
Show full item record
Author(s)
Bouyssou, Denis cc
Abstract (EN)
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 ldquoranking by choosingrdquo. 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.
Subjects / Keywords
monotonicity problems

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