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Optimal Majority Rule in Referenda


  • Qingqing Cheng

    () (Department of Theory, Party School of Haimen Committee of CPC (Haimen Administration Institute), Haimen 226100, China)

  • Ming Li

    () (1455 Boulevard de Maisonneuve Ouest, Department of Economics, Concordia University, Montreal, QC H3G 1M8, Canada
    CIRANO, Montreal, QC H3A 2M8, Canada
    CIREQ, Montreal, QC H3T 1N8, Canada)


Adopting the group turnout model of Herrera and Mattozzi, J. Eur. Econ. Assoc. 2010 , 8 , 838–871, we investigate direct democracy with supermajority rule and different preference intensities for two sides of a referendum: Reform versus status quo. Two parties spend money and effort to mobilize their voters. We characterize the set of pure strategy Nash equilibria. We investigate the optimal majority rule that maximizes voters’ welfare. Using an example, we show that the relationship between the optimal majority rule and the preference intensity is not monotonic—the optimal majority rule is initially decreasing and then increasing in the preference intensity of the status quo side. We also show that when the preference intensity of the status quo side is higher, the easiness to mobilize voters on the status quo side is lower, or the payoff that the reform party receives is higher, the optimal majority rule is more likely to be supermajority.

Suggested Citation

  • Qingqing Cheng & Ming Li, 2019. "Optimal Majority Rule in Referenda," Games, MDPI, Open Access Journal, vol. 10(2), pages 1-23, June.
  • Handle: RePEc:gam:jgames:v:10:y:2019:i:2:p:25-:d:236869

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    References listed on IDEAS

    1. Matthias Messner & Mattias K. Polborn, 2004. "Voting on Majority Rules," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 115-132.
    2. Jörg L Spenkuch & David Toniatti, 2018. "Political Advertising and Election Results," The Quarterly Journal of Economics, Oxford University Press, vol. 133(4), pages 1981-2036.
    3. Barry Nalebuff & Ron Shachar, 1999. "Follow the Leader: Theory and Evidence on Political Participation," American Economic Review, American Economic Association, vol. 89(3), pages 525-547, June.
    4. Dal Bo, Ernesto, 2006. "Committees with supermajority voting yield commitment with flexibility," Journal of Public Economics, Elsevier, vol. 90(4-5), pages 573-599, May.
    5. Attanasi, Giuseppe & Corazzini, Luca & Passarelli, Francesco, 2017. "Voting as a lottery," Journal of Public Economics, Elsevier, vol. 146(C), pages 129-137.
    6. Martin J. Osborne & Matthew A. Turner, 2010. "Cost Benefit Analyses versus Referenda," Journal of Political Economy, University of Chicago Press, vol. 118(1), pages 156-187, February.
    7. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-660, May.
    8. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
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    More about this item


    referendum; majority rule; supermajority; mobilization; social welfare;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games


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