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Achievable hierarchies in voting games with abstention
Freixas Bosch, Josep; Tchantcho, Bertrand; Tedjeugang, Narcisse
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley-Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable in the class of complete VGA. The aim of this paper is twofold. Firstly, we show that all hierarchies are achievable in a subclass of weighted VGA, the class of weighted games for which a single weight is assigned to voters. Secondly, we conduct a partial study of achievable hierarchies within the subclass of H-complete games, that is, complete games under stronger versions of influence relation. (C) 2013 Elsevier B.V. All rights reserved.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
Decision making--Mathematical models
Voting--Mathematical models
Voting - Abstention
Game theory
2) Voting rules
Decision support systems
Weightedness and completeness
Ordinal equivalence
Decisió, Presa de -- Models matemàtics
Vot -- Models matemàtics
Abstencionisme electoral
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::94 Information And Communication, Circuits::94C Circuits, networks

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