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Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules

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  • Cardona, Daniel
  • Ponsati, Clara

Abstract

We consider negotiations selecting one-dimensional policies. Individuals have instantaneous preferences represented by continuous, concave and single-peaked utility functions, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. We provide sufficient conditions that guarantee the existence of a unique stationary subgame perfect equilibrium, and we provide its explicit characterization. The uniqueness of the equilibrium permits an analysis of the set of Pareto optimal voting rules. For symmetric distributions of peaks and uniform recognition probabilities unanimity is the unanimously preferred majority rule.

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  • Cardona, Daniel & Ponsati, Clara, 2011. "Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules," Games and Economic Behavior, Elsevier, vol. 73(1), pages 65-75, September.
    • Handle: RePEc:eee:gamebe:v:73:y:2011:i:1:p:65-75
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    1. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    3. Banks, Jeffrey S. & Duggan, John, 2006. "A General Bargaining Model of Legislative Policy-making," Quarterly Journal of Political Science, now publishers, vol. 1(1), pages 49-85, January.
    4. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    5. Sam Bucovetsky, 2003. "The optimal majority with an endogenous status quo," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 131-148, August.
    6. Predtetchinski, Arkadi, 2011. "One-dimensional bargaining," Games and Economic Behavior, Elsevier, vol. 72(2), pages 526-543, June.
    7. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-399, March.
    8. Cho, Seok-ju & Duggan, John, 2009. "Bargaining foundations of the median voter theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 851-868, March.
    9. Tasos Kalandrakis, 2006. "Proposal Rights and Political Power," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 441-448, April.
    10. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
    11. Jackson, Matthew O. & Moselle, Boaz, 2002. "Coalition and Party Formation in a Legislative Voting Game," Journal of Economic Theory, Elsevier, vol. 103(1), pages 49-87, March.
    12. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    13. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
    14. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(1), pages 73-88, March.
    15. Baron, David P., 1996. "A Dynamic Theory of Collective Goods Programs," American Political Science Review, Cambridge University Press, vol. 90(2), pages 316-330, June.
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    Cited by:

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    2. Kalandrakis, Tasos, 2015. "Computation of equilibrium values in the Baron and Ferejohn bargaining model," Games and Economic Behavior, Elsevier, vol. 94(C), pages 29-38.
    3. Daniel Cardona & Arnold Polanski, 2013. "Voting rules and efficiency in one-dimensional bargaining games with endogenous protocol," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 217-240, July.
    4. Ortner, Juan, 2017. "A theory of political gridlock," Theoretical Economics, Econometric Society, vol. 12(2), May.
    5. Le Breton, Michel & Thomas, Alban & Zaporozhets, Vera, 2012. "Bargaining in River Basin Committees: Rules Versus Discretion," TSE Working Papers 12-324, Toulouse School of Economics (TSE).
    6. Zapal, Jan, 2020. "Simple Markovian equilibria in dynamic spatial legislative bargaining," European Journal of Political Economy, Elsevier, vol. 63(C).
    7. Alessandro Riboni & Francisco Ruge‐Murcia, 2023. "The Power Of The Federal Reserve Chair," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(2), pages 727-756, May.
    8. P. Herings & Arkadi Predtetchinski, 2015. "Procedural fairness and redistributive proportional tax," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 333-354, June.
    9. Nicolás Porteiro & Antonio Villar, 2015. "Appointing high-court judges by political parties," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(1), pages 91-99, March.
    10. Daniel Diermeier & Carlo Prato & Razvan Vlaicu, 2016. "A bargaining model of endogenous procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 985-1012, December.
    11. Daniel Cardona & Antoni Rubí-Barceló, 2014. "On the efficiency of equilibria in a legislative bargaining model with particularistic and collective goods," Public Choice, Springer, vol. 161(3), pages 345-366, December.
    12. Chen, Daniel L. & Michaeli, Moti & Spiro, Daniel, 2020. "Legitimizing Policy," TSE Working Papers 20-1123, Toulouse School of Economics (TSE).
    13. Daniel Cardona & Clara Ponsatí, 2014. "Super-Majorites, One-Dimensional Policies, and Social Surplus," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(6), pages 884-898, December.
    14. Giri Parameswaran & Hunter Rendleman, 2022. "Redistribution under general decision rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(1), pages 159-196, February.
    15. Daniel Cardona & Clara Ponsatí, 2013. "Super-majorites and collective surplus in one-dimensional bargaining: Numerical simulations," Economics Bulletin, AccessEcon, vol. 33(1), pages 278-288.
    16. Jan Zápal, 2017. "Crafting consensus," Public Choice, Springer, vol. 173(1), pages 169-200, October.
    17. Kazuo Yamaguchi, 2022. "Spatial bargaining in rectilinear facility location problem," Theory and Decision, Springer, vol. 93(1), pages 69-104, July.
    18. Juan Ortner, 2014. "Political Bargaining in a Changing World," 2014 Meeting Papers 445, Society for Economic Dynamics.

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