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Hierarchies achievable in simple games
Freixas Bosch, Josep; Pons Vallès, Montserrat
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
A previous work by Friedman et al. (Theory and Decision, 61:305–318, 2006) introduces the concept of a hierarchy of a simple voting game and characterizes which hierarchies, induced by the desirability relation, are achievable in linear games. In this paper, we consider the problem of determining all hierarchies, conserving the ordinal equivalence between the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices, achievable in simple games. It is proved that only four hierarchies are non-achievable in simple games.Moreover, it is also proved that all achievable hierarchies are already obtainable in the class of weakly linear games. Our results prove that given an arbitrary complete pre-ordering defined on a finite set with more than five elements, it is possible to construct a simple game such that the pre-ordering induced by the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices coincides with the given pre-ordering.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
Game theory
Voting--Mathematical models
Jocs, Teoria de
Vot -- Models matemàtics
Classificació AMS::91 Game theory, economics, social and behavioral sciences
info:eu-repo/semantics/publishedVersion
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