Achievable hierarchies in voting games with abstention

•We focus on two main notions of influence in voting rules with abstention.•We do a study of the achievable hierarchies for these two notions of influence.•Our results clarify which hierarchies are achievable in the context of abstention.•Our results contribute to the design of voting rules with abs...

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Veröffentlicht in:	European journal of operational research Jg. 236; H. 1; S. 254 - 260
Hauptverfasser:	Freixas, Josep, Tchantcho, Bertrand, Tedjeugang, Narcisse
Format:	Journal Article Verlag
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier B.V 01.07.2014 Elsevier Sequoia S.A Elsevier
Schlagworte:	05 Combinatorics 05C Graph theory 91 Game theory, economics, social and behavioral sciences 91A Game theory 94 Information And Communication, Circuits 94C Circuits, networks [formula omitted] Voting rules Abstencionisme electoral Abstention Approval Assignment problem Banzhaf Classificació AMS Decision making Decision support systems Decisió, Presa de Game theory Games Hierarchies Input Investigació operativa Matemàtiques i estadística Mathematical models Models matemàtics Operational research Ordinal equivalence Output Power Studies Systems Teoria de jocs Vot Voters Voting Voting rules Weightedness and completeness Àrees temàtiques de la UPC Decision support systems Hierarchies Weightedness and completeness Game theory (3,2) Voting rules Abstention
ISSN:	0377-2217, 1872-6860
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Abstract	•We focus on two main notions of influence in voting rules with abstention.•We do a study of the achievable hierarchies for these two notions of influence.•Our results clarify which hierarchies are achievable in the context of abstention.•Our results contribute to the design of voting rules with abstention. 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.
AbstractList	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 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. [PUBLICATION ABSTRACT] 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. •We focus on two main notions of influence in voting rules with abstention.•We do a study of the achievable hierarchies for these two notions of influence.•Our results clarify which hierarchies are achievable in the context of abstention.•Our results contribute to the design of voting rules with abstention. 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.
Author	Tedjeugang, Narcisse Freixas, Josep Tchantcho, Bertrand
Author_xml	– sequence: 1 givenname: Josep surname: Freixas fullname: Freixas, Josep email: josep.freixas@upc.edu organization: Departament de Matemàtica Aplicada 3 i, Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya, Spain – sequence: 2 givenname: Bertrand surname: Tchantcho fullname: Tchantcho, Bertrand email: btchantcho@yahoo.fr organization: University of Yaounde I, MASS Laboratory, Cameroon – sequence: 3 givenname: Narcisse surname: Tedjeugang fullname: Tedjeugang, Narcisse email: tedjeugang@yahoo.fr organization: University of Yaounde I, MASS Laboratory, Cameroon
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Snippet	•We focus on two main notions of influence in voting rules with abstention.•We do a study of the achievable hierarchies for these two notions of influence.•Our... 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...
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SubjectTerms	05 Combinatorics 05C Graph theory 91 Game theory, economics, social and behavioral sciences 91A Game theory 94 Information And Communication, Circuits 94C Circuits, networks [formula omitted] Voting rules Abstencionisme electoral Abstention Approval Assignment problem Banzhaf Classificació AMS Decision making Decision support systems Decisió, Presa de Game theory Games Hierarchies Input Investigació operativa Matemàtiques i estadística Mathematical models Models matemàtics Operational research Ordinal equivalence Output Power Studies Systems Teoria de jocs Vot Voters Voting Voting rules Weightedness and completeness Àrees temàtiques de la UPC
Title	Achievable hierarchies in voting games with abstention
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