A class of simple games

Isbell, John

doi:10.1215/s0012-7094-58-02537-7

Cited by 153 publications

(98 citation 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%

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%

Voting games with abstention: Linking completeness and weightedness

Freixas

Tchantcho

Tedjeugang

2014

Decision Support Systems

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“…(Isbell, [5]) Let (N, W) be a simple game, i and j be two voters. Player i is said to be more desirable than j, denoted by i j if the following two conditions are fulfilled:…”

Section: Complete Simple Gamesmentioning

confidence: 99%

Some Advances in the Theory of Voting Systems Based on Experimental Algorithms

Freixas

Molinero

2006

Experimental Algorithms

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Abstract. In voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker [8] establishes the equivalence between weighted voting games and k-trade robust games for each positive integer k. Moreover, they also construct, in [9], a succession of games G k based on magic squares which are (k − 1)-trade robust but not k-trade robust, each one of these games G k has k 2 players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is (k − 1)-trade robust but not k-trade robust for all values of k. As a consequence it will we showed the existence of games with less than k 2 players which are (k − 1)-trade robust but not k-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.

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“…If j strictly dominates i (j W i), then j is said more desirable than i (Isbell, 1958). In a voting rule W, seat i is a seat with veto if for any S ∈ W , i ∈ S. Obviously a seat with veto dominates any other seat.…”

Section: Freixas and Puente (2003))mentioning

confidence: 99%

A critical reappraisal of some voting power paradoxes

Laruelle

Valenciano

2005

Public Choice

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Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed 'natural' postulates that a measure of a priori voting power 'should' satisfy, the violations of which are called 'voting power paradoxes'. In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.

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A class of simple games

Cited by 153 publications

References 0 publications

Voting games with abstention: Linking completeness and weightedness

Voting games with abstention: Linking completeness and weightedness

Some Advances in the Theory of Voting Systems Based on Experimental Algorithms

A critical reappraisal of some voting power paradoxes

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