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dc.contributor.authorFreixas Bosch, Josep
dc.contributor.authorPons Vallès, Montserrat
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.identifier.citationFreixas, J.; Pons, M. Hierarchies achievable in simple games. "Theory and decision", Abril 2010, vol. 68, núm. 4, p. 393-404.
dc.description.abstractA 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.
dc.format.extent12 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
dc.subject.lcshGame theory
dc.subject.lcshVoting -- Mathematical models
dc.titleHierarchies achievable in simple games
dc.subject.lemacJocs, Teoria de
dc.subject.lemacVot -- Models matemàtics
dc.contributor.groupUniversitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
dc.subject.amsClassificació AMS::91 Game theory, economics, social and behavioral sciences
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
local.citation.authorFreixas, J.; Pons, M.
local.citation.publicationNameTheory and decision

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