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Condorcet meets Bentham

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  • Pivato, Marcus

Abstract

We show that if the statistical distribution of utility functions in a population satisfies a certain condition, then a Condorcet winner will not only exist, but will also maximize the utilitarian social welfare function. We also show that, if people’s utility functions are generated according to certain plausible random processes, then in a large population, this condition will be satisfied with very high probability. Thus, in a large population, the utilitarian outcome will be selected by any Condorcet consistent voting rule.

Suggested Citation

  • Pivato, Marcus, 2015. "Condorcet meets Bentham," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 58-65.
  • Handle: RePEc:eee:mateco:v:59:y:2015:i:c:p:58-65
    DOI: 10.1016/j.jmateco.2015.04.006
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    1. Nitzan,Shmuel, 2009. "Collective Preference and Choice," Cambridge Books, Cambridge University Press, number 9780521722131, December.
    2. Marcus Pivato, 2016. "Asymptotic utilitarianism in scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 431-458, August.
    3. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    4. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    5. Vijay Krishna & John Morgan, 2011. "Overcoming Ideological Bias in Elections," Journal of Political Economy, University of Chicago Press, vol. 119(2), pages 183-211.
    6. Annick Laruelle & Federico Valenciano, 2010. "Egalitarianism and utilitarianism in committees of representatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 221-243, July.
    7. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    8. A. S. Tangian, 2000. "Unlikelihood of Condorcet's paradox in a large society," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 337-365.
    9. Marcus Pivato, 2016. "Statistical Utilitarianism," Studies in Political Economy, in: Maria Gallego & Norman Schofield (ed.), The Political Economy of Social Choices, pages 187-204, Springer.
    10. Robert Bordley, 1985. "Using factions to estimate preference intensity: Improving upon one person/one vote," Public Choice, Springer, vol. 45(3), pages 257-268, January.
    11. Aki Lehtinen, 2007. "The Welfare Consequences of Strategic Voting in Two Commonly Used Parliamentary Agendas," Theory and Decision, Springer, vol. 63(1), pages 1-40, August.
    12. Gelman, Andrew & Katz, Jonathan N. & Bafumi, Joseph, 2004. "Standard Voting Power Indexes Do Not Work: An Empirical Analysis," British Journal of Political Science, Cambridge University Press, vol. 34(4), pages 657-674, October.
    13. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    14. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
    15. Bag, Parimal Kanti & Sabourian, Hamid & Winter, Eyal, 2009. "Multi-stage voting, sequential elimination and Condorcet consistency," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1278-1299, May.
    16. Aki Lehtinen, 2015. "Strategic Voting and the Degree of Path-Dependence," Group Decision and Negotiation, Springer, vol. 24(1), pages 97-114, January.
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    Cited by:

    1. Keshab Bhattarai, 2016. "Growth and Income Distributions in Four EU Economies," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 22(3), pages 263-277, August.
    2. Marcus Pivato, 2016. "Asymptotic utilitarianism in scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 431-458, August.
    3. Pivato, Marcus & Soh, Arnold, 2020. "Weighted representative democracy," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 52-63.

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