IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v68y2014icp31-52.html
   My bibliography  Save this article

Equilibrium and effectiveness of two-parameter scoring rules

Author

Listed:
  • Giles, Adam
  • Postl, Peter

Abstract

We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.

Suggested Citation

  • Giles, Adam & Postl, Peter, 2014. "Equilibrium and effectiveness of two-parameter scoring rules," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 31-52.
  • Handle: RePEc:eee:matsoc:v:68:y:2014:i:c:p:31-52
    DOI: 10.1016/j.mathsocsci.2013.12.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016548961300108X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.mathsocsci.2013.12.003?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Rafael Hortala-Vallve, 2010. "Inefficiencies on linking decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 471-486, March.
    2. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 329-352, February.
    3. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    4. Myerson, Roger B. & Weber, Robert J., 1993. "A Theory of Voting Equilibria," American Political Science Review, Cambridge University Press, vol. 87(1), pages 102-114, March.
    5. Miralles, Antonio, 2012. "Cardinal Bayesian allocation mechanisms without transfers," Journal of Economic Theory, Elsevier, vol. 147(1), pages 179-206.
    6. Robert J. Weber, 1978. "Comparison of Public Choice Systems," Cowles Foundation Discussion Papers 498, Cowles Foundation for Research in Economics, Yale University.
    7. Ahn, David S. & Oliveros, Santiago, 2016. "Approval voting and scoring rules with common values," Journal of Economic Theory, Elsevier, vol. 166(C), pages 304-310.
    8. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    9. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    10. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    11. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    12. repec:esx:essedp:732 is not listed on IDEAS
    13. 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.
    14. André Blais, 2002. "Why Is there So Little Strategic Voting in Canadian Plurality Rule Elections?," Political Studies, Political Studies Association, vol. 50(3), pages 445-454, August.
    15. Postl Peter, 2011. "Strategy-Proof Compromises," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-37, October.
    16. Postl Peter, 2011. "Strategy-Proof Compromises," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-37, October.
    17. Jose Apesteguia & Miguel A. Ballester & Rosa Ferrer, 2011. "On the Justice of Decision Rules," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 1-16.
    18. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
    19. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
    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. Ahn, David S. & Oliveros, Santiago, 2016. "Approval voting and scoring rules with common values," Journal of Economic Theory, Elsevier, vol. 166(C), pages 304-310.
    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. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    4. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," GLO Discussion Paper Series 185, Global Labor Organization (GLO).
    5. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which “Almost” Rule is Optimal?," Group Decision and Negotiation, Springer, vol. 27(1), pages 129-151, February.
    6. 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.
    7. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which "Almost" Rule is Optimal?," CESifo Working Paper Series 6851, CESifo.
    8. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," IZA Discussion Papers 11287, Institute of Labor Economics (IZA).
    9. Kim, Semin, 2017. "Ordinal versus cardinal voting rules: A mechanism design approach," Games and Economic Behavior, Elsevier, vol. 104(C), pages 350-371.
    10. Postl, Peter, 2017. "Évaluation et comparaison des règles de vote derrière le voile de l’ignorance : Tour d'horizon sélectif et analyse des règles de scores à deux paramètres," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 249-290, Mars-Juin.

    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. Postl, Peter, 2017. "Évaluation et comparaison des règles de vote derrière le voile de l’ignorance : Tour d'horizon sélectif et analyse des règles de scores à deux paramètres," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 249-290, Mars-Juin.
    2. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    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. Ehlers, Lars & Majumdar, Dipjyoti & Mishra, Debasis & Sen, Arunava, 2020. "Continuity and incentive compatibility in cardinal mechanisms," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 31-41.
    5. Lars EHLERS & Dipjyoti MAJUMDAR & Debasis MISHRA & Arunava SEN, 2016. "Continuity and Incentive Compatibility in Cardinal Voting Mechanisms," Cahiers de recherche 04-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    7. Rafael Hortala-Vallve, 2012. "Qualitative voting," Journal of Theoretical Politics, , vol. 24(4), pages 526-554, October.
    8. Kim, Semin, 2017. "Ordinal versus cardinal voting rules: A mechanism design approach," Games and Economic Behavior, Elsevier, vol. 104(C), pages 350-371.
    9. 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.
    10. 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(4), pages 1067-1088, November.
    11. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    12. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
    13. Rafael Hortalà-Vallvé, 2010. "Qualitative Voting," Cuadernos de Economía - Spanish Journal of Economics and Finance, Asociación Cuadernos de Economía, vol. 33(92), pages 5-44, Mayo-Sept.
    14. François Durand & Antonin Macé & Matias Nunez, 2019. "Analysis of Approval Voting in Poisson Games," Working Papers halshs-02049865, HAL.
    15. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    16. Kei Kawai & Yasutora Watanabe, 2013. "Inferring Strategic Voting," American Economic Review, American Economic Association, vol. 103(2), pages 624-662, April.
    17. Sebastien Courtin & Matias Nunez, 2013. "A Map of Approval Voting Equilibria Outcomes," Working Papers hal-00914887, HAL.
    18. Laurent Bouton & Aniol Llorente-Saguer & Frédéric Malherbe, 2014. "Get Rid of Unanimity: The Superiority of Majority Rule with Veto Power," NBER Working Papers 20417, National Bureau of Economic Research, Inc.
    19. Kwiek, Maksymilian, 2014. "Efficient voting with penalties," Discussion Paper Series In Economics And Econometrics 1419, Economics Division, School of Social Sciences, University of Southampton.
    20. Miguel Ballester & Pedro Rey-Biel, 2009. "Does uncertainty lead to sincerity? Simple and complex voting mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 477-494, September.

    More about this item

    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:matsoc:v:68:y:2014:i:c:p:31-52. 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/505565 .

    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.