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Cooperation and punishment under repeated majority voting


  • Dennis Epple
  • Michael Riordan


In light of the extensive theoretical evidence suggesting absence of equilibrium in voting models, Tullock (1981) asks "Why So Much Stability?" Our results suggest the following answer: Political agents engaged in long-term relationships can sustain highly stable allocations if there are strongly held norms for punishment of defectors. Moreover, recent work by Cremer (1986) suggests that even if decisionmakers have finite horizons, significant cooperation is nevertheless feasible if institutions are indefinitely-lived. Our results show that a wide range of allocations can be sustained as equilibria by the threat of political banishment. The following anecdote suggests that something like a political banishment punishment has in fact been employed in practice: "Senator James L. Buckley...tried to delete forty-four public works projects at the committee stage in the Senate. The members voted down all his amendments except the ones cutting out projects in New York; these latter they adopted." Quoted from Mayhew (1974, pp. 91–92) who cites Reeves (1974) Ferejohn (1974, p. 114) cites an example in which Senator Proximre was similarly punished for supporting proposals to cut appropriations for the Department of the Interior—a House-Senate Conference Committee deleted the Senator's favored project from the Interior appropriations bill. Our results indicate not only that stable cooperative outcomes are possible but also that a wide range of allocations can be sustained. This is a liability rather than an asset; the theory provides weak predictions. One way to augment the model is to assume that the chosen contract is a member of the ex ante optimal set of feasible contracts. This assumption can be expected to give strong predictions. In our model, when the conditions of Proposition 3 are satisfied, the assumption that the ex ante optimal contract is chosen leads to a prediction of equal division of the cake each period. The assumption that the ex ante optimal contract is chosen is a natural one when agreements are indeed made "behind the veil of ignorance"; under such conditions the ex ante optimal contract would receive unanimous support. When individuals are differently situated at the time contracting occurs, the assumption of ex ante optimality of the contract might better be replaced by a characterization of the bargaining problem individuals confront in attempting to agree upon a contract. The analysis of Baron and Ferejohn (1986) is in this spirit. Our model has two related features, both of which may seem unrealistic: The punishment for defection from a cooperative agreement is eternal banishment, and punishment never occurs. Both features are inconsistent with at least the second of our two anecdotes. Less severe punishments than eternal banishment could no doubt be devised, e.g., temporary banishment. However, the range of cooperative agreements that could be supported by the weaker punishment would be smaller, and defection from agreements that would be supported by the weaker punishment would never occur. Thus, while a weaker punishment might seem more "realistic," the introduction of such a punishment in the current framework is artificial and does not alter the prediction that punishment never occurs in equilibrium. Similar problems arise in models of self-enforcing private agreements when there is neither uncertainty nor private information. To address these problems, Green and Porter (1984) developed a model of cartel enforcement with uncertainty and private information in which punishment occurs, and Abreu, Pierce, and Stachetti (1986) have shown that the optimal punishment period in the Green-Porter model is finite. (See also Porter (1983).) In the Green-Porter model, an unobserved random shock introduces variation in outcomes. However, since the shock is unobserved and individual actions are private information, the players cannot tell whether the variation is due to the random shock or to a defection by another player. If a sufficiently adverse outcome occurs, the punishment regime is invoked. However, since the punishment regime may (and in equilibrium will) be triggered by the random shock, it is in the players' interests to engage in a limited period of punishment and then revert to the cooperative regime. The introduction of uncertainty and private information in the model developed in this paper may also motivate occasional finite punishments. If our anecdotes are to serve as a guide, however, the identity of defectors in the political arena will sometimes be known—in contrast to the Green-Porter model in which the identity of defectors cannot be observed. This suggests that a somewhat different motivation for finite, observed punishments will be more appropriate in our setting than in the cartel setting studied by Green and Porter. We view this as a fruitful area for extension of the model. Copyright Martinus Nijhoff Publishers 1987

Suggested Citation

  • Dennis Epple & Michael Riordan, 1987. "Cooperation and punishment under repeated majority voting," Public Choice, Springer, vol. 55(1), pages 41-73, September.
  • Handle: RePEc:kap:pubcho:v:55:y:1987:i:1:p:41-73
    DOI: 10.1007/BF00156810

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    References listed on IDEAS

    1. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    2. Thomas Romer & Howard Rosenthal, 1978. "Political resource allocation, controlled agendas, and the status quo," Public Choice, Springer, vol. 33(4), pages 27-43, December.
    3. Daniel Ingberman, 1985. "Running against the status quo: Institutions for direct democracy referenda and allocations over time," Public Choice, Springer, vol. 46(1), pages 19-43, January.
    4. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    5. Jacques Cremer, 1986. "Cooperation in Ongoing Organizations," The Quarterly Journal of Economics, Oxford University Press, vol. 101(1), pages 33-49.
    6. Epple, Dennis & Spatt, Chester, 1986. "State restrictions on local debt : Their role in preventing default," Journal of Public Economics, Elsevier, vol. 29(2), pages 199-221, March.
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    8. Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, January.
    9. Peter Coughlin, 1986. "Elections and income redistribution," Public Choice, Springer, vol. 50(1), pages 27-91, January.
    10. Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
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    Cited by:

    1. Marco Battaglini & Stephen Coate, 2007. "Inefficiency in Legislative Policymaking: A Dynamic Analysis," American Economic Review, American Economic Association, vol. 97(1), pages 118-149, March.
    2. Rosenthal, Howard & Zame, William R., 2022. "Sequential referenda with sophisticated voters," Journal of Public Economics, Elsevier, vol. 212(C).
    3. Lars P. Feld & Justina A.V. Fischer & Gebhard Kirchgässner, 2010. "The Effect Of Direct Democracy On Income Redistribution: Evidence For Switzerland," Economic Inquiry, Western Economic Association International, vol. 48(4), pages 817-840, October.
    4. B. D. Bernheim & S. N. Slavov, 2009. "A Solution Concept for Majority Rule in Dynamic Settings," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 33-62.
    5. Tasos Kalandrakis, 2010. "Minimum winning coalitions and endogenous status quo," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 617-643, October.
    6. Baron, David P. & Bowen, T. Renee & Nunnari, Salvatore, 2017. "Durable coalitions and communication: Public versus private negotiations," Journal of Public Economics, Elsevier, vol. 156(C), pages 1-13.
    7. Hülya Eraslan & Kirill S. Evdokimov & Jan Zápal, 2022. "Dynamic Legislative Bargaining," Springer Books, in: Emin Karagözoğlu & Kyle B. Hyndman (ed.), Bargaining, chapter 0, pages 151-175, Springer.
    8. Epple, Dennis, 1998. "Rent control with reputation: theory and evidence," Regional Science and Urban Economics, Elsevier, vol. 28(6), pages 679-710, November.
    9. Dahm, Matthias & Glazer, Amihai, 2015. "A carrot and stick approach to agenda-setting," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 465-480.
    10. Hans Grüner, 2009. "Inequality and Political Consensus," Theory and Decision, Springer, vol. 67(3), pages 239-265, September.
    11. T. Renee Bowen & Ying Chen & H?lya Eraslan, 2014. "Mandatory versus Discretionary Spending: The Status Quo Effect," American Economic Review, American Economic Association, vol. 104(10), pages 2941-2974, October.
    12. Justin Fox, 2006. "Legislative Cooperation among Impatient Legislators," Journal of Theoretical Politics, , vol. 18(1), pages 68-97, January.
    13. Tasos Kalandrakis, 2016. "Pareto efficiency in the dynamic one-dimensional bargaining model," Journal of Theoretical Politics, , vol. 28(4), pages 525-536, October.
    14. David P. Baron, 2019. "Simple dynamics of legislative bargaining: coalitions and proposal power," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 319-344, February.
    15. Tasos Kalandrakis, 2007. "Majority Rule Dynamics with Endogenous Status Quo," Wallis Working Papers WP46, University of Rochester - Wallis Institute of Political Economy.
    16. Matthias Dahm & Amihai Glazer, 2012. "How An Agenda Setter Induces Legislators to Adopt Policies They Oppose," Working Papers 111211, University of California-Irvine, Department of Economics.
    17. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
    18. Zapal, Jan, 2020. "Simple Markovian equilibria in dynamic spatial legislative bargaining," European Journal of Political Economy, Elsevier, vol. 63(C).
    19. Grüner, Hans Peter, 2003. "Inequality and Political Consensus," CEPR Discussion Papers 4159, C.E.P.R. Discussion Papers.
    20. Marina Azzimonti & Gabriel P. Mihalache & Laura Karpuska, 2020. "Bargaining over Taxes and Entitlements," NBER Working Papers 27595, National Bureau of Economic Research, Inc.
    21. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    22. Dahm, Matthias & Glazer, Amihai, 2010. "Repeated Agenda Setting and the Unanimous Approval of Bad Policies," Working Papers 2072/151549, Universitat Rovira i Virgili, Department of Economics.
    23. Harms, Philipp & Zink, Stefan, 2003. "Limits to redistribution in a democracy: a survey," European Journal of Political Economy, Elsevier, vol. 19(4), pages 651-668, November.
    24. Marina Azzimonti & Laura Karpuska & Gabriel Mihalache, 2020. "Bargaining over Mandatory Spending and Entitlements," Department of Economics Working Papers 20-02, Stony Brook University, Department of Economics.
    25. Daniel E. Ingberman & Robert P. Inman, 1987. "The Political Economy of Fiscal Policy," NBER Working Papers 2405, National Bureau of Economic Research, Inc.

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