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Voting for voters: the unanimity case


  • Jonathan Shalev

    () (10 Gonen Street Ra'anana 43399, Israel)

  • Daniel Granot

    () (Faculty of Commerce and Business Administration, University of British Columbia Vancouver, B. C., Canada V6T 1Y2)

  • Michael Maschler

    () (Department of Mathematics and Center for Rationality and Interactive Decision Theory, The Hebrew University of Jerusalem Jerusalem 91904, Israel)


We present a simplified model of the evolution of a society which is regulated by a formal unanimity voting procedure. We examine several protocols, which depend on whether admission or expulsion are permissible, and on the order with which they are implemented. Conditions which ensure the existence of pure-strategy perfect equilibrium profiles for some voting protocols, and counter examples for the existence of such profiles in other protocols are presented. Finally, we prove that, if the agents insist on perfect equilibrium strategy profiles in a one-stage play, the original founders would prefer a protocol in which expulsion precedes admission to protocols in which either admission precedes expulsion, or the two are treated simultaneously. The paper concludes with an overview and a discussion on the results and suggestions for further research.

Suggested Citation

  • Jonathan Shalev & Daniel Granot & Michael Maschler, 2003. "Voting for voters: the unanimity case," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 155-202.
  • Handle: RePEc:spr:jogath:v:31:y:2003:i:2:p:155-202 Note: Received: December 2001

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    References listed on IDEAS

    1. Abraham Neyman & Rann Smorodinsky, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
    2. Mertens, J F, 1988. "The Shapley Value in the Non Differentiable Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(1), pages 1-65.
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    Cited by:

    1. Guillermo Owen, 2010. "Michael Maschler’s bibliography," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 301-308, March.
    2. D. Berga & G. Bergantiños & J. Massó & A. Neme, 2006. "On Exiting After Voting," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 33-54, April.
      • Dolors Berga & Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2003. "On exiting after voting," Estudios de Economia, University of Chile, Department of Economics, vol. 30(2 Year 20), pages 261-288, December.
    3. Dolors Berga & Alejandro Neme & Jordi Massó & Gustavo Bergantiños, 2008. "On two basic properties of equilibria of voting with exit," Economics Bulletin, AccessEcon, vol. 4(21), pages 1-9.
    4. Gilbert Laffond & Jean Lainé, 2014. "Triple-consistent social choice and the majority rule," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 784-799, July.
    5. Berga, Dolors & Bergantinos, Gustavo & Masso, Jordi & Neme, Alejandro, 2007. "An undominated Nash equilibrium for voting by committees with exit," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 152-175, September.


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