On the equilibrium of voting games with abstention and several levels of approval

Tchantcho, Bertrand; Lambo, Lawrence Diffo; Pongou, Roland; Moulen, Joël

doi:10.1007/s00355-009-0403-7

Cited by 11 publications

(5 citation statements)

References 13 publications

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“…From the minimal winning coalitions of the game, the obtention of certain stable sets is established. With respect to the core, Branzei (2005) studied the core for multichoice games, and, more recently, Tchantcho et al (2010) introduced the core for ( j, 2) simple games. Both models are particular cases of our framework.…”

Section: Introductionmentioning

confidence: 99%

Stable sets and cores for multi-criteria simple games and for their extensions

Fernández

2011

Soc Choice Welf

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In this article we deal with multi-criteria simple games which constitute an extension of the basic framework of voting systems and related social-choice situations. We generalize two closely related solution concepts for these games, the stable sets and the core. A relationship between stable sets and minimal winning coalitions is established. Two generalizations of the core for multi-criteria simple games are characterized in terms of veto players. In addition, extended multi-criteria simple games obtained from different aggregation operations, such as union, intersection, marginalization, and composition, are introduced. It is shown that a voting system can be established when these operations are applied to complex voting systems.

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Section: Introductionmentioning

confidence: 99%

Stable sets and cores for multi-criteria simple games and for their extensions

Fernández

2011

Soc Choice Welf

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“…[Freixas and Zwicker, 2003]. The notion of the Nakamura number and a first set of stability results for (j, 2)-simple games have been transfered by [Tchantcho et al, 2010].…”

Section: Introductionmentioning

confidence: 99%

Bounds for the Nakamura number

Freixas

Kurz

2018

Soc Choice Welf

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The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of simple games the corresponding Nakamura number has also been characterized. However, in general, not much is known about lower and upper bounds depending on invariants of simple, complete or weighted games. Here, we survey such results and highlight connections with other game theoretic concepts.2000 Mathematics Subject Classification. Primary: 91A12; Secondary: 91B14, 91B12. Key words and phrases. Nakamura number and stability and simple games and complete simple games and weighted games and bounds.

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“…Peleg () and Nakamura () characterize the structure of acyclic social choice, but they focus on a special class of rules (see Tchantcho et al . () for further development). Cato and Hirata () characterize a class of acyclic rules that satisfy neutrality and anonymity by extending the work by Bossert and Suzumura ().…”

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confidence: 99%

Remarks on a Procedural Condition for the Voting Paradox

Cato

2019

Bulletin of Econ Res

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Schwartz [A Procedural Condition Necessary and Sufficient for Cyclic Social Preference, J. Econ. Theory 137 (2007), 688–695] provides a generalization of the voting paradox by using the impotence‐partition condition. This paper aims to clarify his result by providing several remarks. We show that a main result of Schwartz can be strengthened by replacing strong Pareto by weak Pareto. We also discuss how the impotence partition is related to the standard concept of decisiveness, which is widely employed in the literature on social choice.

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On the equilibrium of voting games with abstention and several levels of approval

Cited by 11 publications

References 13 publications

Stable sets and cores for multi-criteria simple games and for their extensions

Stable sets and cores for multi-criteria simple games and for their extensions

Bounds for the Nakamura number

Remarks on a Procedural Condition for the Voting Paradox

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