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Whose Opinion Counts? Political Processes and the Implementation Problem

Author

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  • Rene Saran

    () (Department of Economics, University of Maastricht, The Netherlands)

  • Norovsambuu Tumennasan

    () (Department of Economics and Business, Aarhus University, Denmark)

Abstract

We augment the mechanism used in Nash implementation with a political process that collects the opinions of a subset of individuals with a xed probability distribution. The outcome is a function of only the collected opinions. We show that the necessary - and sometimes sufficient - condition for implementation by a specic political process can be either weaker or stronger than Maskin monotonicity. We study three such processes: oligarchy, oligarchic democracy and random sampling. Oligarchy collects only the opinions of the oligarchs (a strict subset of the individuals). We present a Nash implementable social choice rule (SCR) that cannot be implemented by any oligarchy. Oligarchic democracy "almost always" collects the opinions of the oligarchs but sometimes, there is a referendum (i.e., everyone's opinions are collected). We show that in economic environments, every Nash implementable SCR can be implemented by oligarchic democracy in which any three individuals act as oligarchs. In random sampling, a sample of opinions are collected randomly. We show that in economic environments, every Nash implementable SCR can be implemented by randomly sampling opinions of 4 individuals. We also provide necessary and sufficient conditions for implementation when the planner has the exibility to choose any political process.

Suggested Citation

  • Rene Saran & Norovsambuu Tumennasan, 2011. "Whose Opinion Counts? Political Processes and the Implementation Problem," Economics Working Papers 2011-06, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2011-06
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    References listed on IDEAS

    as
    1. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
    2. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    3. Bergemann, Dirk & Morris, Stephen, 2008. "Ex post implementation," Games and Economic Behavior, Elsevier, vol. 63(2), pages 527-566, July.
    4. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    5. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    6. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    7. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    8. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    9. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    10. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May.
    11. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
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    More about this item

    Keywords

    Nash Implementation; Political Process; p-Implementation; Direct Democracy; Oligarchy; Oligarchic Democracy; Random Sampling;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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