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Majority Rule Dynamics with Endogenous Status Quo

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Abstract

We analyze a stochastic bargaining game in which a new dollar is divided among committee members in each of an infinity of periods. In each period, a committee member is recognized and offers a proposal for the division of the dollar. The proposal is implemented if it is approved by a majority. If the proposal is rejected, then last period’s allocation is implemented. We show existence of equilibrium in Markovian strategies. It is such that irrespective of the initial status quo, the discount factor, or the probabilities of recognition, the proposer extracts the entire dollar in all periods but the initial two. We also derive a fully strategic version of McKelvey’s (1976), (1979) dictatorial agenda setting, so that a player with exclusive access to the formulation of proposals can extract the entire dollar in all periods except the first. The equilibrium collapses when within period payoffs are sufficiently concave. Winning coalitions may comprise players with high instead of low recognition probabilities, ceteris paribus.

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Bibliographic Info

Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP46.

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Length: 39 pages
Date of creation: May 2007
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Handle: RePEc:roc:wallis:wp46

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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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  1. Armando Gomes & Philippe Jehiel, 2005. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 626-667, June.
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  4. Tasos Kalandrakis, 2004. "Proposal Rights and Political Power," Wallis Working Papers WP38, University of Rochester - Wallis Institute of Political Economy.
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  6. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
  7. Marco Battaglini & Stephen Coate, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," NBER Working Papers 11495, National Bureau of Economic Research, Inc.
  8. B. Douglas Bernheim & Antonio Rangel & Luis Rayo, 2006. "The Power of the Last Word in Legislative Policy Making," Econometrica, Econometric Society, vol. 74(5), pages 1161-1190, 09.
  9. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
  10. Roger Lagunoff (Georgetown University), 2005. "Markov Equilibrium in Models of Dynamic Endogenous Political Institutions," Working Papers gueconwpa~05-05-07, Georgetown University, Department of Economics.
  11. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
  12. Banks, Jeffrey S. & Duggan, John, 2006. "A General Bargaining Model of Legislative Policy-making," International Quarterly Journal of Political Science, now publishers, vol. 1(1), pages 49-85, January.
  13. Dennis Epple & Michael Riordan, 1987. "Cooperation and punishment under repeated majority voting," Public Choice, Springer, vol. 55(1), pages 41-73, September.
  14. John Duggan & Tasos Kalandrakis, 2007. "Dynamic Legislative Policy Making," Wallis Working Papers WP45, University of Rochester - Wallis Institute of Political Economy.
  15. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
  16. Harrington, Joseph E, Jr, 1990. " The Role of Risk Preferences in Bargaining When Acceptance of a Proposal Requires Less than Unanimous Approval," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 135-54, June.
  17. Banks, Jeffrey S. & Duggan, John, 1999. "A Bargaining Model of Collective Choice," Working Papers 1053, California Institute of Technology, Division of the Humanities and Social Sciences.
  18. Banks, Jeffrey S. & Duggan, John, 2003. "A bargaining model of legislative policy-making," Working Papers 1162, California Institute of Technology, Division of the Humanities and Social Sciences.
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Cited by:
  1. Roger Lagunoff, 2004. "The Dynamic Reform of Political Institutions," Econometric Society 2004 Latin American Meetings 47, Econometric Society.
  2. David Baron & Daniel Diermeier & Pohan Fong, 2012. "A dynamic theory of parliamentary democracy," Economic Theory, Springer, vol. 49(3), pages 703-738, April.
  3. Roger Lagunoff, 2007. "Markov Equilibrium in Models of Dynamic Endogenous Political Institutions," Levine's Bibliography 122247000000000876, UCLA Department of Economics.
  4. Pohan Fong, 2008. "Endogenous Limits on Proposal Power," Discussion Papers 1465, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Tasos Kalandrakis, 2010. "Minimum winning coalitions and endogenous status quo," International Journal of Game Theory, Springer, vol. 39(4), pages 617-643, October.
  6. John Duggan & Tasos Kalandrakis, 2011. "A Newton collocation method for solving dynamic bargaining games," Social Choice and Welfare, Springer, vol. 36(3), pages 611-650, April.
  7. Lagunoff, Roger, 2009. "Dynamic stability and reform of political institutions," Games and Economic Behavior, Elsevier, vol. 67(2), pages 569-583, November.
  8. John Duggan & Tasos Kalandrakis, 2007. "Dynamic Legislative Policy Making," Wallis Working Papers WP45, University of Rochester - Wallis Institute of Political Economy.
  9. Jean Guillaume Forand, 2010. "Two-Party Competition with Persistent Policies," Working Papers 1011, University of Waterloo, Department of Economics, revised Nov 2010.
  10. Marco Battaglini & Thomas Palfrey, 2012. "The dynamics of distributive politics," Economic Theory, Springer, vol. 49(3), pages 739-777, April.
  11. Daniel Diermeier & Pohan Fong, 2011. "Legislative Bargaining with Reconsideration," The Quarterly Journal of Economics, Oxford University Press, vol. 126(2), pages 947-985.

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