IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v113y2019icp285-305.html
   My bibliography  Save this article

Truth-revealing voting rules for large populations

Author

Listed:
  • Núñez, Matías
  • Pivato, Marcus

Abstract

We propose a new solution to the problem of strategic voting for large electorates. For any deterministic voting rule, we design a stochastic rule that asymptotically approximates it in the following sense: for a sufficiently large population of voters, the stochastic voting rule (i) incentivizes every voter to reveal her true preferences and (ii) produces the same outcome as the deterministic rule, with arbitrarily high probability. We then apply these results to obtain an implementation in Bayesian Nash equilibrium.

Suggested Citation

  • Núñez, Matías & Pivato, Marcus, 2019. "Truth-revealing voting rules for large populations," Games and Economic Behavior, Elsevier, vol. 113(C), pages 285-305.
  • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:285-305
    DOI: 10.1016/j.geb.2018.09.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825618301519
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2018.09.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jean-François Laslier, 2009. "The Leader Rule," Journal of Theoretical Politics, , vol. 21(1), pages 113-136, January.
    2. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
    3. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    4. Kei Kawai & Yasutora Watanabe, 2013. "Inferring Strategic Voting," American Economic Review, American Economic Association, vol. 103(2), pages 624-662, April.
    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Acharya, Avidit & Meirowitz, Adam, 2017. "Sincere voting in large elections," Games and Economic Behavior, Elsevier, vol. 101(C), pages 121-131.
    7. McLennan, Andrew, 2011. "Manipulation in elections with uncertain preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 370-375.
    8. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    9. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    10. Bouton, Laurent & Llorente-Saguer, Aniol & Malherbe, Frédéric, 2017. "Unanimous rules in the laboratory," Games and Economic Behavior, Elsevier, vol. 102(C), pages 179-198.
    11. Matías Núñez & Jean Laslier, 2014. "Preference intensity representation: strategic overstating in large elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 313-340, February.
    12. repec:dau:papers:123456789/12477 is not listed on IDEAS
    13. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    14. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    15. Barbera, Salvador, 1977. "The Manipulation of Social Choice Mechanisms That Do Not Leave "Too Much" to Chance," Econometrica, Econometric Society, vol. 45(7), pages 1573-1588, October.
    16. Régis Renault & Alain Trannoy, 2011. "Assessing the extent of strategic manipulation: the average vote example," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 497-513, December.
    17. Jean-François Laslier, 2009. "The Leader rule: a model of strategic approval voting in a large electorate," Post-Print hal-00363218, HAL.
    18. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    19. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    20. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    21. Prasanta K. Pattanaik, 1975. "Strategic Voting Without Collusion Under Binary and Democratic Group Decision Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 93-103.
    22. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    23. Fristrup, Peter & Kleiding, Hans, 1989. "A note on asymptotical strategy-proofness," Economics Letters, Elsevier, vol. 31(4), pages 307-312, December.
    24. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-424, June.
    25. Chamberlain, Gary & Rothschild, Michael, 1981. "A note on the probability of casting a decisive vote," Journal of Economic Theory, Elsevier, vol. 25(1), pages 152-162, August.
    26. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-1288, June.
    27. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    28. Arkadii Slinko, 2002. "On asymptotic strategy-proofness of the plurality and the run-off rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 313-324.
    29. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    30. Ilia Tsetlin & Michel Regenwetter & Bernard Grofman, 2003. "The impartial culture maximizes the probability of majority cycles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 387-398, December.
    31. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    32. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    33. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2004. "Threshold strategy-proofness: on manipulability in large voting problems," Games and Economic Behavior, Elsevier, vol. 49(1), pages 103-116, October.
    34. Austen-Smith, David & Banks, Jeffrey S., 1996. "Information Aggregation, Rationality, and the Condorcet Jury Theorem," American Political Science Review, Cambridge University Press, vol. 90(1), pages 34-45, March.
    35. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    36. Jörg L. Spenkuch, 2015. "Please Don't Vote for Me: Voting in a Natural Experiment with Perverse Incentives," Economic Journal, Royal Economic Society, vol. 125(585), pages 1025-1052, June.
    37. Merrill, Samuel & Nagel, Jack, 1987. "The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules," American Political Science Review, Cambridge University Press, vol. 81(2), pages 509-524, June.
    38. Elisha A. Pazner & Eugene Wesley, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 85-91.
    39. Gilat Levy & Ronny Razin, 2015. "Correlation Neglect, Voting Behavior, and Information Aggregation," American Economic Review, American Economic Association, vol. 105(4), pages 1634-1645, April.
    40. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    41. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    42. Arkadii Slinko, 2006. "How the size of a coalition affects its chances to influence an election," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 143-153, January.
    43. Jean‐François Laslier & Jörgen W. Weibull, 2013. "An Incentive‐Compatible Condorcet Jury Theorem," Scandinavian Journal of Economics, Wiley Blackwell, vol. 115(1), pages 84-108, January.
    44. Acharya, Avidit, 2016. "Information aggregation failure in a model of social mobility," Games and Economic Behavior, Elsevier, vol. 100(C), pages 257-272.
    45. Sourav Bhattacharya, 2013. "Preference Monotonicity and Information Aggregation in Elections," Econometrica, Econometric Society, vol. 81(3), pages 1229-1247, May.
    46. Arkadii Slinko, 2002. "On Asymptotic Strategy-Proofness of Classical Social Choice Rules," Theory and Decision, Springer, vol. 52(4), pages 389-398, June.
    47. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    48. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    49. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
    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. Lirong Xia, 2020. "How Likely Are Large Elections Tied?," Papers 2011.03791, arXiv.org, revised Jul 2021.
    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. Kirneva Margarita & N'u~nez Mat'ias, 2023. "Legitimacy of collective decisions: a mechanism design approach," Papers 2302.09548, arXiv.org, revised Oct 2023.

    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. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    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. 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.
    4. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    5. Martin Gregor, 2013. "The Optimal Ballot Structure for Double-Member Districts," CERGE-EI Working Papers wp493, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    6. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    7. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    8. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2019. "Strongly sincere best responses under approval voting and arbitrary preferences," Games and Economic Behavior, Elsevier, vol. 117(C), pages 388-401.
    9. François Maniquet & Massimo Morelli, 2015. "Approval quorums dominate participation quorums," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 1-27, June.
    10. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2017. "Multicandidate elections: Aggregate uncertainty in the laboratory," Games and Economic Behavior, Elsevier, vol. 101(C), pages 132-150.
    11. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    12. Spenkuch, Jörg, 2013. "On the Extent of Strategic Voting," MPRA Paper 50198, University Library of Munich, Germany.
    13. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    14. Gerardi, Dino & McLean, Richard & Postlewaite, Andrew, 2009. "Aggregation of expert opinions," Games and Economic Behavior, Elsevier, vol. 65(2), pages 339-371, March.
    15. Igerseim, Herrade & Baujard, Antoinette & Laslier, Jean-François, 2016. "La question du vote. Expérimentations en laboratoire et In Situ," L'Actualité Economique, Société Canadienne de Science Economique, vol. 92(1-2), pages 151-189, Mars-Juin.
    16. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    17. Laurent Bouto & Aniol Llorente-Saguer & Fédéric Malherbe, 2014. "Get Rid of Unanimity: The Superiority of Majority Rule with Veto Power," Working Papers 722, Queen Mary University of London, School of Economics and Finance.
    18. Hirofumi Yamamura & Ryo Kawasaki, 2013. "Generalized average rules as stable Nash mechanisms to implement generalized median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 815-832, March.
    19. Acharya, Avidit, 2016. "Information aggregation failure in a model of social mobility," Games and Economic Behavior, Elsevier, vol. 100(C), pages 257-272.
    20. Laurent Bouto & Aniol Llorente-Saguer & Fédéric Malherbe, 2014. "Get Rid of Unanimity: The Superiority of Majority Rule with Veto Power," Working Papers 722, Queen Mary University of London, School of Economics and Finance.

    More about this item

    Keywords

    Large elections; Strategic voting; Truth-revelation; Stochastic voting rule; Bayesian Nash implementation;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:eee:gamebe:v:113:y:2019:i:c:p:285-305. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.