IDEAS home Printed from https://ideas.repec.org/p/biu/wpaper/2010-20.html
   My bibliography  Save this paper

Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

Author

Listed:
  • Eyal Baharad

    () (Department of Economics, Bar Ilan University)

  • Jacob Goldberger

    (Bar-Ilan University)

  • Moshe Koppel

    (Bar-Ilan University)

  • Shmuel Nitzan

    (Department of Economics,Bar-Ilan University)

Abstract

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-maker's capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This paper presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters' past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of the decision-maker's capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers.

Suggested Citation

  • Eyal Baharad & Jacob Goldberger & Moshe Koppel & Shmuel Nitzan, 2010. "Beyond Condorcet: Optimal Aggregation Rules Using Voting Records," Working Papers 2010-20, Bar-Ilan University, Department of Economics.
  • Handle: RePEc:biu:wpaper:2010-20
    as

    Download full text from publisher

    File URL: https://www2.biu.ac.il/soc/ec/wp/2010-20.pdf
    File Function: Working paper
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Young, Andrew T. & Higgins, Matthew J. & Levy, Daniel, 2008. "Sigma Convergence versus Beta Convergence: Evidence from U.S. County-Level Data," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 1083-1093.
    2. 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.
    3. Steven J. Brams & Peter C. Fishburn, 2010. "Going from Theory to Practice: The Mixed Success of Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 19-37, Springer.
    4. Chen, Haipeng (Allan) & Levy, Daniel & Ray, Sourav & Bergen, Mark, 2008. "Asymmetric Price Adjustment in the Small," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 728-737.
    5. Ben-Yashar, Ruth C & Nitzan, Shmuel I, 1997. "The Optimal Decision Rule for Fixed-Size Committees in Dichotomous Choice Situations: The General Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 175-186, February.
    6. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    7. Ray, Sourav & Chen, Haipeng (Allan) & Bergen, Mark & Levy, Daniel, 2006. "Asymmetric Wholesale Pricing: Theory and Evidence," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 109-201.
    8. Ronen Bar-El & Teresa García-Muñoz & Shoshana Neuman & Yossef Tobol, 2013. "The evolution of secularization: cultural transmission, religion and fertility—theory, simulations and evidence," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(3), pages 1129-1174, July.
    9. Ruth Ben-Yashar & Igal Milchtaich, 2007. "First and second best voting rules in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 453-486, October.
    10. Owen, Guillermo & Grofman, Bernard & Feld, Scott L., 1989. "Proving a distribution-free generalization of the Condorcet Jury Theorem," Mathematical Social Sciences, Elsevier, vol. 17(1), pages 1-16, February.
    11. Daniel Berend & Luba Sapir, 2005. "Monotonicity in Condorcet Jury Theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 83-92, August.
    12. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    13. Feddersen, Timothy & Pesendorfer, Wolfgang, 1998. "Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts under Strategic Voting," American Political Science Review, Cambridge University Press, vol. 92(1), pages 23-35, March.
    14. McLennan, Andrew, 1998. "Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents," American Political Science Review, Cambridge University Press, vol. 92(2), pages 413-418, June.
    15. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
    16. Leonid V. Azarnert, 2008. "Involuntary Integration in Public Education, Fertility and Human Capital," Working Papers 2008-07, Bar-Ilan University, Department of Economics.
    17. Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
    18. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    19. Coughlan, Peter J., 2000. "In Defense of Unanimous Jury Verdicts: Mistrials, Communication, and Strategic Voting," American Political Science Review, Cambridge University Press, vol. 94(2), pages 375-393, June.
    20. Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 481-488.
    21. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    22. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-297, June.
    23. Karotkin, Drora, 1994. "Effect of the size of the bench on the correctness of court judgments: The case of Israel," International Review of Law and Economics, Elsevier, vol. 14(3), pages 371-375, September.
    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. Alpern, Steve & Chen, Bo, 2017. "The importance of voting order for jury decisions by sequential majority voting," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1072-1081.
    2. Steve Alpern & Bo Chen, 2020. "Optimizing Voting Order on Sequential Juries: A Median Voter Theorem," Papers 2006.14045, arXiv.org.
    3. Steve Alpern & Bo Chen, 2017. "Who should cast the casting vote? Using sequential voting to amalgamate information," Theory and Decision, Springer, vol. 83(2), pages 259-282, August.

    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. Ruth Ben-Yashar & Shmuel Nitzan, 2014. "On the significance of the prior of a correct decision in committees," Theory and Decision, Springer, vol. 76(3), pages 317-327, March.
    2. Ruth Ben-Yashar & Leif Danziger, 2015. "When is voting optimal?," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 341-356, October.
    3. 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.
    4. Hummel, Patrick, 2011. "Information aggregation in multicandidate elections under plurality rule and runoff voting," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 1-6, July.
    5. Ruth Ben-Yashar, 2014. "The generalized homogeneity assumption and the Condorcet jury theorem," Theory and Decision, Springer, vol. 77(2), pages 237-241, August.
    6. Ruth Ben-Yashar & Igal Milchtaich, 2003. "First and Second Best Voting Rules in Committees," Working Papers 2003-08, Bar-Ilan University, Department of Economics.
    7. Buechel, Berno & Mechtenberg, Lydia, 2019. "The swing voter's curse in social networks," Games and Economic Behavior, Elsevier, vol. 118(C), pages 241-268.
    8. Ruth Ben-Yashar & Shmuel Nitzan, 2017. "Is diversity in capabilities desirable when adding decision makers?," Theory and Decision, Springer, vol. 82(3), pages 395-402, March.
    9. Gil S. Epstein & Alessandra Venturini, 2011. "The Impact of Worker Effort on Public Sentiment Towards Temporary Migrants," Development Working Papers 310, Centro Studi Luca d'Agliano, University of Milano, revised 09 May 2011.
    10. Young, Andrew T. & Levy, Daniel, 2014. "Explicit Evidence of an Implicit Contract," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 804-832.
    11. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    12. Adi Schnytzer & Janez Sustersic, 2011. "The Regression Tournament: A Novel Approach To Prediction Model Assessment," Journal of Prediction Markets, University of Buckingham Press, vol. 5(2), pages 32-43.
    13. Adi Schnytzer & Sara Westreich, 2011. "Information and Attitudes to Risk at the Track," Working Papers 2011-16, Bar-Ilan University, Department of Economics.
    14. Stephen E. Spear & Warren Young, 2011. "MD Dialog on: Optimum Savings and Optimal Growth: the Cass-Malinvaud-Koopmans Nexus," Working Papers 2011-22, Bar-Ilan University, Department of Economics.
    15. Ben-Yashar, Ruth & Danziger, Leif, 2011. "Symmetric and asymmetric committees," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 440-447.
    16. Baharad, Eyal & Ben-Yashar, Ruth & Patal, Tal, 2020. "On the merit of non-specialization in the context of majority voting," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 128-133.
    17. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    18. Poindron, Alexis, 2021. "A general model of binary opinions updating," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 52-76.
    19. Adi Schnytzer & Yisrael Schnytzer, 2011. "Animal Modeling of Earthquakes and Prediction Market," Working Papers 2011-20, Bar-Ilan University, Department of Economics.
    20. BEN-YASHAR, Ruth & NITZAN, Shmuel, 2016. "Is Diversity in Capabilities Desirable When Adding Decision Makers?," Discussion paper series HIAS-E-21, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.

    More about this item

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    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:biu:wpaper:2010-20. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Department of Economics). General contact details of provider: https://edirc.repec.org/data/debaril.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.