Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories

Tchantcho, Bertrand; Lambo, Lawrence Diffo; Pongou, Roland; Engoulou, Bertrand Mbama

doi:10.1016/j.geb.2007.10.014

Cited by 54 publications

(61 citation statements)

References 25 publications

(39 reference statements)

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“…In this paper, we will look at the extension of the desirability relation for simple games [13] to the ternary voting game (or more generally for (3, 2) games) given in [24], wherein such an extension was denominated influence relation. In [24], it is proved that the influence relation fails to be transitive and cycles for players are possible.…”

Section: Introductionmentioning

confidence: 99%

“…In [24], it is proved that the influence relation fails to be transitive and cycles for players are possible. We observe that one may easily find weighted (3, 2) games which are not complete for the influence relation, so that the completeness of the game for the influence relation is not a necessary condition for a (3, 2) game to be weighted.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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Voting games with abstention: Linking completeness and weightedness

Freixas

Tchantcho

Tedjeugang

2014

Decision Support Systems

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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.Keywords: Decision making process, Voting systems in democratic organizations, Multiple levels of approval, Weightedness and completeness, Desirability relations 2000 MSC: 91A12, 90B50, 91A35, 05C65, 94C10

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Voting games with abstention: Linking completeness and weightedness

Freixas

Tchantcho

Tedjeugang

2014

Decision Support Systems

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“…The I-in ‡uence relation introduced by Tchantcho et al [31] is a generalization of the desirability relation originally de…ned in simple games. It coincides with the extension of Shapley-Shubik and Banzhaf and Coleman indices de…ned by Felsenthal and Machover [9] and later on reconsidered in a general framework by Freixas ( [13] and [14]) in the class of swap-robust (3; 2) games.…”

Section: Resultsmentioning

confidence: 99%

“…They have moreover been generalized to the most general model of (j; k) games by Freixas ([13] and [14]). On the other hand, the desirability relation has been de…ned by Tchantcho et al [31] in terms of I-in ‡uence relation. These authors showed that the SS, BC and the I-in ‡uence relation are ordinally equivalent in the subclass of equitable swap-robust games.…”

Section: Introductionmentioning

confidence: 99%

Achievable hierarchies in voting games with abstention

Freixas

Tchantcho

Tedjeugang

2014

European Journal of Operational Research

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: It is well known that he in ‡uence 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 in ‡uence 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 in ‡uence relation.

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Power Indices

Freixas¹

2011

Wiley Encyclopedia of Operations Research and Management Science

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This paper deals with simple games, that is a voting situation in which a single alternative, such as a bill or amendment, is pitted against the status quo. In these systems, each voter responds with a vote “yea” or “nay.” A simple game is simply a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. After studying a little the mathematical structure of simple games, we proceed to introduce power, which is a central concept in political sciences. We revise some well‐known power indices as well as some existent background known in the literature.

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Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories

Cited by 54 publications

References 25 publications

Voting games with abstention: Linking completeness and weightedness

Voting games with abstention: Linking completeness and weightedness

Achievable hierarchies in voting games with abstention

Power Indices

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