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Whose Opinion Counts? Political Processes and the Implementation Problem

  • Rene Saran

    ()

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

  • Norovsambuu Tumennasan

    ()

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

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.

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Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2011-06.

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Length: 44
Date of creation: 23 May 2011
Date of revision:
Handle: RePEc:aah:aarhec:2011-06
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. 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.
  2. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  3. 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.
  4. 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.
  5. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  7. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
  8. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Levine's Bibliography 784828000000000018, UCLA Department of Economics.
  9. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
  10. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
  11. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
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