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Social Choice in Large Populations with Single-Peaked Preferences

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  • Martin F. Hellwig

    (Max Planck Institute for Research on Collective Goods)

Abstract

Anonymous social choice function for a large atomless population maps cross-section distributions of preferences into outcomes. Because any one individual is too insignificant to a¤ect these distributions, every anonymous social choice function is individually strategy-proof. However, not every anonymous social choice function is group strategy-proof. If the set of outcomes is linearly ordered and participants have single-peaked preferences, an anonymous social choice function is group strategy-proof if and only if it can be implemented by a mechanism involving binary votes between neighbouring outcomes with nondecreasing thresholds for "moving higher up". Such a mechanism can be interpreted as a version of Moulin's (1980) generalized median-voter mechanism for a large population.

Suggested Citation

  • Martin F. Hellwig, 2021. "Social Choice in Large Populations with Single-Peaked Preferences," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2021_18, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2021_18
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    References listed on IDEAS

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    1. Hellwig, Martin, 2004. "Optimal Income Taxation, Public-Goods Provision," Sonderforschungsbereich 504 Publications 04-42, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    2. Marco Battaglini & Stephen Coate, 2008. "A Dynamic Theory of Public Spending, Taxation, and Debt," American Economic Review, American Economic Association, vol. 98(1), pages 201-236, March.
    3. Felix Bierbrauer & Aleh Tsyvinski & Nicolas Werquin, 2021. "Taxes and Turnout: When the Decisive Voter Stays at Home," ECONtribute Discussion Papers Series 071, University of Bonn and University of Cologne, Germany.
    4. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    5. Boadway, Robin & Keen, Michael, 1993. "Public Goods, Self-Selection and Optimal Income Taxation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 463-478, August.
    6. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    7. Ledyard, John O., 1978. "Incentive compatibility and incomplete information," Journal of Economic Theory, Elsevier, vol. 18(1), pages 171-189, June.
    8. Hellwig, Martin, 2004. "Optimal income taxation, public-goods provision and public-sector pricing : a contribution to the foundations of public economics," Papers 04-42, Sonderforschungsbreich 504.
    9. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    10. Felix Bierbrauer & Aleh Tsyvinski & Nicolas D. Werquin, 2017. "Taxes and Turnout," NBER Working Papers 24123, National Bureau of Economic Research, Inc.
    11. Barro, Robert J, 1990. "Government Spending in a Simple Model of Endogenous Growth," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 103-126, October.
    12. Bierbrauer, Felix & Tsyvinski, Aleh & Werquin, Nicolas, 2021. "Taxes and Turnout: When the decisive voter stays at home," CEPR Discussion Papers 15928, C.E.P.R. Discussion Papers.
    13. Martin F. Hellwig, 2003. "Public-Good Provision with Many Participants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 589-614.
    14. Felix J. Bierbrauer, 2014. "Optimal Tax and Expenditure Policy with Aggregate Uncertainty," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 205-257, February.
    15. Jonathan Heathcote & Kjetil Storesletten & Giovanni L Violante, 0. "How Should Tax Progressivity Respond to Rising Income Inequality?," Journal of the European Economic Association, European Economic Association, vol. 18(6), pages 2715-2754.
    16. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2020. "How Should Tax Progressivity Respond to Rising Income Inequality?," NBER Working Papers 28006, National Bureau of Economic Research, Inc.
    17. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    18. Goeree, Jacob K. & Zhang, Jingjing, 2017. "One man, one bid," Games and Economic Behavior, Elsevier, vol. 101(C), pages 151-171.
    19. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, December.
    20. Felix Bierbrauer & Aleh Tsyvinski & Nicolas Werquin, 2021. "Taxes and Turnout: When the Decisive Voter Stays at Home," CESifo Working Paper Series 8954, CESifo.
    21. Jonathan Heathcote & Kjetil Storesletten & Giovanni L Violante, 2020. "Presidential Address 2019: How Should Tax Progressivity Respond to Rising Income Inequality?," Journal of the European Economic Association, European Economic Association, vol. 18(6), pages 2715-2754.
    22. Felix J. Bierbrauer & Martin F. Hellwig, 2016. "Robustly Coalition-Proof Incentive Mechanisms for Public Good Provision are Voting Mechanisms and Vice Versa," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1440-1464.
    23. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
    24. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    25. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    26. Gaube, Thomas, 2000. "When do distortionary taxes reduce the optimal supply of public goods?," Journal of Public Economics, Elsevier, vol. 76(2), pages 151-180, May.
    27. Bierbrauer, Felix, 2009. "A note on optimal income taxation, public goods provision and robust mechanism design," Journal of Public Economics, Elsevier, vol. 93(5-6), pages 667-670, June.
    28. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
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    Keywords

    Social choice; large populations; strategy proofness; group strategy proofness; single-peaked preferences;
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