Voting games with abstention: Linking completeness and weightedness

Weighted games for several levels of approval in input and output were introduced in [9]. An extension of the desirability relation for simple games, called the influence relation, was introduced for games with several levels of approval in input in [24] (see also [18]). However, there are weighted...

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Vydané v:Decision Support Systems Ročník 57; s. 172 - 177
Hlavní autori: Freixas, Josep, Tchantcho, Bertrand, Tedjeugang, Narcisse
Médium: Journal Article Publikácia
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.01.2014
Elsevier
Elsevier Sequoia S.A
Predmet:
05 Combinatorics
05C Graph theory
90 Operations research, mathematical programming
90B Operations research and management science
91 Game theory, economics, social and behavioral sciences
91A Game theory
94 Information And Communication, Circuits
94C Circuits, networks
Abstencionisme electoral
Abstention
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approval
Classificació AMS
Completeness
Computer science; control theory; systems
Decision making
Decision making process
Decision theory. Utility theory
Decisió, Presa de
Desirability relations
Exact sciences and technology
Game theory
Input
Input output
Investigació operativa
Matemàtiques i estadística
Mathematical models
Models matemàtics
Multiple levels of approval
Operational research and scientific management
Operational research. Management science
Output
Power
Representation
Studies
Systems
Teoria de jocs
Theoretical computing
Vot
Voting
Voting systems in democratic organizations
Weightedness and completeness
Àrees temàtiques de la UPC
91A12
05C65
91A35
Multiple levels of approval
Weightedness and completeness
Decision making process
Desirability relations
Voting systems in democratic organizations
MSC
90B50
94C10
Input output
Voting
Decision making
Completeness
Democracy
Game theory
ISSN:0167-9236, 1873-5797
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Shrnutí:Weighted games for several levels of approval in input and output were introduced in [9]. An extension of the desirability relation for simple games, called the influence relation, was introduced for games with several levels of approval in input in [24] (see also [18]). However, there are weighted games not being complete for the influence relation, something different to what occurs for simple games. In this paper we introduce several extensions of the desirability relation for simple games and from the completeness of them it follows the consistent link with weighted games, which solves the existing gap. Moreover, we prove that the influence relation is consistent with a known subclass of weighted games: strongly weighted games. •We study voting systems in democratic institutions in which abstention is allowed.•Some weighted systems are not complete for the influence relation.•We consider three new relations, each of them weaker than the influence relation.•We determine the desired notion of completeness being coherent with weightedness.•The research carried out is related with the determination of importance rankings.
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ISSN:0167-9236
1873-5797
DOI:10.1016/j.dss.2013.08.015