Voting for Voters: A Model of Electoral Evolution

S. Barberà; M. Maschler; J. Shalev

doi:10.1006/game.2000.0827

Voting for Voters: A Model of Electoral Evolution

S. Barberà, M. Maschler, J. Shalev

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Abstract

We model decision problems faced by the members of societies whose new members are determined by vote. We examine a simple model: the founders and the candidates are fixed, the society operates and holds elections for a fixed number of periods, one vote is sufficient for admission, and voters can support as many candidates as they wish. We show through theorems and examples that interesting strategic behavior is implied by the dynamic structure of the problem. In particular, the vote for friends may be postponed, and it may be advantageous to vote for enemies. We characterize all pure strategy Nash equilibria outcomes and show that they can also be obtained as subgame perfect equilibria. We present conditions for existence of pure strategy (trembling hand) perfect equilibrium profiles and show that they always exist in a two-stage scheme under appropriate assumptions on utilities. We discuss the need for further refinements and extensions of our game theoretic analysis. Journal of Economic Literature Classification Numbers: C7, D7, D71.

Original language	English
Pages (from-to)	40-78
Number of pages	39
Journal	Games and Economic Behavior
Volume	37
Issue number	1
DOIs	https://doi.org/10.1006/game.2000.0827
Publication status	Published - Oct 2001

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10.1006/game.2000.0827Licence: C In Copyright

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La formació de grups i coalicions: Vots, negociacions i provisió de serveis
Barberà, S. (Principal Investigator), Burani , N. (Scholar), Domínguez Manzano, B. (Scholar), Mestre Ferrandiz, J. (Scholar), Rata , S. C. (Scholar), Beviá Baeza, M. D. C. (Investigator), Massó, J. (Investigator), Nicolo, A. (Investigator), Ponsati Obiols, C. (Investigator) & Vila Carnicero, F. J. (Investigator)
Dirección General de Enseñanza Superior e Investigación Científica (DGESIC)
30/12/99 → 30/12/02
Project: Research Projects and Other Grants
Cooperació i Competència: Estudis sobre el comportament estratègic i el disseny institucional
Barberà, S. (Principal Investigator), Berga Colom, D. (Scholar), Bogomolnaia, A. (Scholar), Caballero Jurado, J. (Scholar), Villar Febré, J. P. (Scholar), Beviá Baeza, M. D. C. (Investigator), Cardona Coll, D. (Investigator), Gonzalez Maestre, M. (Investigator), Jelovac ., I. (Investigator), Macho Stadler, I. (Investigator), Martínez Giralt, X. (Investigator), Massó, J. (Investigator), Olivella, P. (Investigator), Perez Castrillo, J. D. (Investigator), Ponsati Obiols, C. (Investigator) & Vila Carnicero, F. J. (Investigator)
Dirección General de Enseñanza Superior e Investigación Científica (DGESIC)
15/12/97 → 15/12/99
Project: Research Projects and Other Grants

Cite this

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title = "Voting for Voters: A Model of Electoral Evolution",

abstract = "We model decision problems faced by the members of societies whose new members are determined by vote. We examine a simple model: the founders and the candidates are fixed, the society operates and holds elections for a fixed number of periods, one vote is sufficient for admission, and voters can support as many candidates as they wish. We show through theorems and examples that interesting strategic behavior is implied by the dynamic structure of the problem. In particular, the vote for friends may be postponed, and it may be advantageous to vote for enemies. We characterize all pure strategy Nash equilibria outcomes and show that they can also be obtained as subgame perfect equilibria. We present conditions for existence of pure strategy (trembling hand) perfect equilibrium profiles and show that they always exist in a two-stage scheme under appropriate assumptions on utilities. We discuss the need for further refinements and extensions of our game theoretic analysis. Journal of Economic Literature Classification Numbers: C7, D7, D71.",

keywords = "voting, elections, clubs, game theory, noncooperative games, pure-strategy, equilibrium profiles, equilibrium refinements",

author = "S. Barber{\`a} and M. Maschler and J. Shalev",

note = "The authors thank R. J. Aumann, C. d{\textquoteright}Aspremont, D. Granot, S. Hart, and A. Perea for various comments and suggestions that helped improve this paper. 2 E-mail: [email protected]. This author gratefully acknowledges partial support from Spanish Ministry of Education DGICYT Grant PB-98-0870 and Comissionat per a Universitats i Recerca Grant SGR98-62. 3 E-mail: [email protected]. This author gratefully acknowledges DGICYT, Spanish Ministry of Education, for Grant SAB95-0276 that enabled him to participate in this research. 4 E-mail: [email protected]. This author gratefully acknowledges the support for his research given by the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister{\textquoteright}s Office, Science Policy Programming. This research was done when the author was working at CORE. 40",

year = "2001",

month = oct,

doi = "10.1006/game.2000.0827",

language = "English",

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journal = "Games and Economic Behavior",

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T1 - Voting for Voters

T2 - A Model of Electoral Evolution

AU - Barberà, S.

AU - Maschler, M.

AU - Shalev, J.

N1 - The authors thank R. J. Aumann, C. d’Aspremont, D. Granot, S. Hart, and A. Perea for various comments and suggestions that helped improve this paper. 2 E-mail: [email protected]. This author gratefully acknowledges partial support from Spanish Ministry of Education DGICYT Grant PB-98-0870 and Comissionat per a Universitats i Recerca Grant SGR98-62. 3 E-mail: [email protected]. This author gratefully acknowledges DGICYT, Spanish Ministry of Education, for Grant SAB95-0276 that enabled him to participate in this research. 4 E-mail: [email protected]. This author gratefully acknowledges the support for his research given by the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. This research was done when the author was working at CORE. 40

PY - 2001/10

Y1 - 2001/10

N2 - We model decision problems faced by the members of societies whose new members are determined by vote. We examine a simple model: the founders and the candidates are fixed, the society operates and holds elections for a fixed number of periods, one vote is sufficient for admission, and voters can support as many candidates as they wish. We show through theorems and examples that interesting strategic behavior is implied by the dynamic structure of the problem. In particular, the vote for friends may be postponed, and it may be advantageous to vote for enemies. We characterize all pure strategy Nash equilibria outcomes and show that they can also be obtained as subgame perfect equilibria. We present conditions for existence of pure strategy (trembling hand) perfect equilibrium profiles and show that they always exist in a two-stage scheme under appropriate assumptions on utilities. We discuss the need for further refinements and extensions of our game theoretic analysis. Journal of Economic Literature Classification Numbers: C7, D7, D71.

AB - We model decision problems faced by the members of societies whose new members are determined by vote. We examine a simple model: the founders and the candidates are fixed, the society operates and holds elections for a fixed number of periods, one vote is sufficient for admission, and voters can support as many candidates as they wish. We show through theorems and examples that interesting strategic behavior is implied by the dynamic structure of the problem. In particular, the vote for friends may be postponed, and it may be advantageous to vote for enemies. We characterize all pure strategy Nash equilibria outcomes and show that they can also be obtained as subgame perfect equilibria. We present conditions for existence of pure strategy (trembling hand) perfect equilibrium profiles and show that they always exist in a two-stage scheme under appropriate assumptions on utilities. We discuss the need for further refinements and extensions of our game theoretic analysis. Journal of Economic Literature Classification Numbers: C7, D7, D71.

KW - voting

KW - elections

KW - clubs

KW - game theory

KW - noncooperative games

KW - pure-strategy

KW - equilibrium profiles

KW - equilibrium refinements

U2 - 10.1006/game.2000.0827

DO - 10.1006/game.2000.0827

M3 - Article

SN - 0899-8256

VL - 37

SP - 40

EP - 78

JO - Games and Economic Behavior

JF - Games and Economic Behavior

IS - 1

ER -

Voting for Voters: A Model of Electoral Evolution

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La formació de grups i coalicions: Vots, negociacions i provisió de serveis

Cooperació i Competència: Estudis sobre el comportament estratègic i el disseny institucional

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