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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Bibliographic Details
Published in:European journal of operational research Vol. 236; no. 1; pp. 254 - 260
Main Authors: Freixas, Josep, Tchantcho, Bertrand, Tedjeugang, Narcisse
Format: Journal Article Publication
Language:English
Published: Amsterdam Elsevier B.V 01.07.2014
Elsevier Sequoia S.A
Elsevier
Subjects:
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
Online Access:Get full text
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Summary:•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.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2013.11.030