IDEAS home Printed from https://ideas.repec.org/p/tor/tecipa/tecipa-493.html
   My bibliography  Save this paper

Optimal Voting Rules

Author

Listed:
  • Alex Gershkov
  • Benny Moldovanu
  • Xianwen Shi

Abstract

We study dominant strategy incentive compatible (DIC) and deterministic mechanisms in a social choice setting with several alternatives. The agents are privately informed about their preferences, and have single-crossing utility functions. Monetary transfers are not feasible. We use an equivalence between deterministic, DIC mechanisms and generalized median voter schemes to construct the constrained-efficient, optimal mechanism for an utilitarian planner. Optimal schemes for other welfare criteria such as, say, a Rawlsian maximin can be analogously obtained.

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Voting Rules," Working Papers tecipa-493, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-493
    as

    Download full text from publisher

    File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-493.pdf
    File Function: Main Text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    2. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    3. Eddie Dekel & Michele Piccione, 2000. "Sequential Voting Procedures in Symmetric Binary Elections," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 34-55, February.
    4. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    5. 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.
    6. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    7. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    8. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    9. 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.
    10. Paul Gompers & Joy Ishii & Andrew Metrick, 2003. "Corporate Governance and Equity Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(1), pages 107-156.
    11. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    12. S. Ali & Navin Kartik, 2012. "Herding with collective preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 601-626, November.
    13. Romer, Thomas, 1975. "Individual welfare, majority voting, and the properties of a linear income tax," Journal of Public Economics, Elsevier, vol. 4(2), pages 163-185, February.
    14. Steven Callander, 2007. "Bandwagons and Momentum in Sequential Voting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 653-684.
    15. Chakravarty, Surajeet & Kaplan, Todd R., 2013. "Optimal allocation without transfer payments," Games and Economic Behavior, Elsevier, vol. 77(1), pages 1-20.
    16. Moritz Drexl & Andreas Kleiner, 2018. "Why Voting? A Welfare Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 253-271, August.
    17. 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.
    18. Kovác, Eugen & Mylovanov, Tymofiy, 2009. "Stochastic mechanisms in settings without monetary transfers: The regular case," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1373-1395, July.
    19. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    20. repec:dau:papers:123456789/7683 is not listed on IDEAS
    21. Howard R. Bowen, 1943. "The Interpretation of Voting in the Allocation of Economic Resources," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 58(1), pages 27-48.
    22. Apesteguia, Jose & Ballester, Miguel A. & Masatlioglu, Yusufcan, 2014. "A foundation for strategic agenda voting," Games and Economic Behavior, Elsevier, vol. 87(C), pages 91-99.
    23. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    24. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    25. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    26. Lucian Bebchuk & Alma Cohen & Allen Ferrell, 2009. "What Matters in Corporate Governance?," The Review of Financial Studies, Society for Financial Studies, vol. 22(2), pages 783-827, February.
    27. Alessandro Riboni & Francisco J. Ruge-Murcia, 2010. "Monetary Policy by Committee: Consensus, Chairman Dominance, or Simple Majority?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(1), pages 363-416.
    28. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    29. Ledyard, John O. & Palfrey, Thomas R., 2002. "The approximation of efficient public good mechanisms by simple voting schemes," Journal of Public Economics, Elsevier, vol. 83(2), pages 153-171, February.
    30. 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.
    31. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    32. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
    33. Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
    34. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    35. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    36. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
    37. Jose Apesteguia & Miguel A. Ballester & Rosa Ferrer, 2011. "On the Justice of Decision Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 1-16.
    38. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    39. Meltzer, Allan H & Richard, Scott F, 1981. "A Rational Theory of the Size of Government," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 914-927, October.
    40. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    41. 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.
    42. Condorelli, Daniele, 2012. "What money canʼt buy: Efficient mechanism design with costly signals," Games and Economic Behavior, Elsevier, vol. 75(2), pages 613-624.
    43. Matthew O Jackson & Hugo F Sonnenschein, 2007. "Overcoming Incentive Constraints by Linking Decisions -super-1," Econometrica, Econometric Society, vol. 75(1), pages 241-257, January.
    44. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    45. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    Full references (including those not matched with items on IDEAS)

    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. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
    2. Tobias Rachidi, 2020. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214, University of Bonn and University of Mannheim, Germany.
    3. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    4. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    5. Kwiek, Maksymilian, 2014. "Efficient voting with penalties," Discussion Paper Series In Economics And Econometrics 1419, Economics Division, School of Social Sciences, University of Southampton.
    6. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    7. Kwiek, Maksymilian, 2017. "Efficient voting with penalties," Games and Economic Behavior, Elsevier, vol. 104(C), pages 468-485.
    8. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    9. Moritz Drexl & Andreas Kleiner, 2018. "Why Voting? A Welfare Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 253-271, August.
    10. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    11. Bierbrauer, Felix & Winkelmann, Justus, 2020. "All or nothing: State capacity and optimal public goods provision," Journal of Economic Theory, Elsevier, vol. 185(C).
    12. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    13. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    14. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    15. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    16. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    17. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    18. Alejandro Saporiti, 2006. "Strategic voting on single-crossing domains," Economics Discussion Paper Series 0617, Economics, The University of Manchester.
    19. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    20. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.

    More about this item

    Keywords

    Mechanism Design; Voting; Dominant Strategy; Utilitarian;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:tor:tecipa:tecipa-493. 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: RePEc Maintainer (email available below). General contact details of provider: .

    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.