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Ranking sets of interacting objects via semivalues

Lucchetti, Roberto; Moretti, Stefano; Patrone, Fioravante (2015), Ranking sets of interacting objects via semivalues, TOP, 23, 2, p. 567-590. 10.1007/s11750-014-0357-5

Type
Article accepté pour publication ou publié
Date
2015
Journal name
TOP
Volume
23
Number
2
Publisher
Springer
Pages
567-590
Publication identifier
10.1007/s11750-014-0357-5
Metadata
Show full item record
Author(s)
Lucchetti, Roberto
MOX-Department of Mathematics "F.Brioschi", Politecnico di Milano, Italy.
Moretti, Stefano cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Patrone, Fioravante
University of Genova
Abstract (EN)
In this paper, we address the problem of how to extend a ranking over single objects to another ranking over all possible collections of objects, taking into account the fact that objects grouped together can have mutual interaction. An answer to this issue is provided by using game theory and, specifically, the fact that an extension (i.e., a total proorder on the set of all subsets of objects) must be aligned with some probabilistic value, in the sense that the ranking of the objects (according to some probabilistic value computed on a numerical representation of the extension) must also preserve the primitive preorder on the singletons, no matter which utility function is used to represent the extension. We characterize families of aligned extensions, we focus on their geometric properties and we provide algorithms to verify their alignments. We also show that the framework introduced in this paper may be used to study a new class of extension problems, which integrate some features dealing with risk and complete uncertainty within the class of preference extension problems known in the literature with the name of sets as final outcomes.
Subjects / Keywords
Preference extensions; Semivalues; Coalitional games

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