IDEAS home Printed from https://ideas.repec.org/p/ema/worpap/2014-17.html
   My bibliography  Save this paper

Condorcet Meets Bentham

Author

Listed:
  • Marcus Pivato

    (Université de Cergy-Pontoise, THEMA and Department of Mathematics, Trent University, Canada)

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. In particular, it will be the subgame-perfect equilibrium outcome of several voting games.

Suggested Citation

  • Marcus Pivato, 2014. "Condorcet Meets Bentham," THEMA Working Papers 2014-17, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2014-17
    as

    Download full text from publisher

    File URL: http://thema.u-cergy.fr/IMG/documents/2014-17.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nitzan,Shmuel, 2009. "Collective Preference and Choice," Cambridge Books, Cambridge University Press, number 9780521722131, October.
    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. 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.
    7. 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.
    8. 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.
    9. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Pivato, Marcus & Soh, Arnold, 2020. "Weighted representative democracy," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 52-63.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    4. Bierbrauer, Felix & Winkelmann, Justus, 2020. "All or nothing: State capacity and optimal public goods provision," Journal of Economic Theory, Elsevier, vol. 185(C).
    5. Hans Peter Grüner & Thomas Tröger, 2019. "Linear Voting Rules," Econometrica, Econometric Society, vol. 87(6), pages 2037-2077, November.
    6. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    7. Moritz Drexl & Andreas Kleiner, 2018. "Why Voting? A Welfare Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 253-271, August.
    8. Kwiek, Maksymilian, 2014. "Efficient voting with penalties," Discussion Paper Series In Economics And Econometrics 1419, Economics Division, School of Social Sciences, University of Southampton.
    9. Erlanson, Albin & Kleiner, Andreas, 2020. "Costly verification in collective decisions," Theoretical Economics, Econometric Society, vol. 15(3), July.
    10. NAKADA, Satoshi & NITZAN, Shmuel & UI, Takashi & 宇井, 貴志, 2017. "Robust Voting under Uncertainty," Discussion paper series HIAS-E-60, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    11. Michel Breton & Karine Straeten, 2015. "Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula," Public Choice, Springer, vol. 165(1), pages 103-122, October.
    12. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    13. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
    14. Kwiek, Maksymilian, 2017. "Efficient voting with penalties," Games and Economic Behavior, Elsevier, vol. 104(C), pages 468-485.
    15. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    16. Azrieli, Yaron & Kim, Semin, 2016. "On the self-(in)stability of weighted majority rules," Games and Economic Behavior, Elsevier, vol. 100(C), pages 376-389.
    17. Irem Bozbay, 2019. "Truth-tracking judgment aggregation over interconnected issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 337-370, August.
    18. Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Post-Print halshs-00142479, HAL.
    19. 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.
    20. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ema:worpap:2014-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Stefania Marcassa (email available below). General contact details of provider: https://edirc.repec.org/data/themafr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.