IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwppe/0304004.html
   My bibliography  Save this paper

What is special about the proportion? A research report on special majority voting and the classical Condorcet jury theorem

Author

Listed:
  • Christian List

    (Nuffield College, Oxford)

Abstract

It is known that, in Condorcet’s classical model of jury decisions, the proportion of jurors supporting a decision is not a significant indicator of that decision’s reliability: the probability that a particular majority decision is correct given the size of the majority depends only on the absolute margin between the majority and the minority, and is invariant under changes of the proportion in the majority if the absolute margin is held fixed. Here I show that, if we relax the assumption that juror competence is independent of the jury’s size, the proportion can be made significant: there are then conditions in which the probability that a given majority decision is correct depends only on the proportion of jurors supporting that decision, and is invariant under changes of the jury size. The proportion is significant in this way if and only if juror competence is a particular decreasing function of the jury size. However, the required condition on juror competence is not only highly special – thereby casting doubt on the significance of the proportion in realistic conditions – but it also has an adverse implication for the Condorcet jury theorem. If the proportion is significant, then the Condorcet jury theorem fails to hold; and if the Condorcet jury theorem holds, the proportion is not significant. I discuss the implications of these results for defining and justifying special majority voting from the perspective of an epistemic account of voting.

Suggested Citation

  • Christian List, 2003. "What is special about the proportion? A research report on special majority voting and the classical Condorcet jury theorem," Public Economics 0304004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwppe:0304004
    Note: Type of Document - PDF; prepared on Windows; pages: 26; figures: included
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/pe/papers/0304/0304004.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christian List, 2002. "On the Significance of the Absolute Margin," Public Economics 0211004, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. Kanazawa, Satoshi, 1998. "A brief note on a further refinement of the Condorcet Jury Theorem for heterogeneous groups," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 69-73, January.
    5. 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.
    6. 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.
    7. Shmuel Nitzan & Jacob Paroush, 1984. "Are qualified majority rules special?," Public Choice, Springer, vol. 42(3), pages 257-272, January.
    8. Timothy Feddersen & Wolfgang Pesendorfer, 1996. "Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts," Discussion Papers 1170, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Christian List, 2002. "On the Significance of the Absolute Margin," Public Economics 0211004, University Library of Munich, Germany.
    2. Roland Kirstein, "undated". "The Condorcet Jury-Theorem with Two Independent Error-Probabilities," German Working Papers in Law and Economics 2006-1-1154, Berkeley Electronic Press.
    3. Eyal Baharad & Jacob Goldberger & Moshe Koppel & Shmuel Nitzan, 2012. "Beyond Condorcet: optimal aggregation rules using voting records," Theory and Decision, Springer, vol. 72(1), pages 113-130, January.
    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 & 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.
    6. Sapir, Luba, 2005. "Generalized means of jurors' competencies and marginal changes of jury's size," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 83-101, July.
    7. Jan Marc Berk & Beata K. Bierut, 2005. "On the Optimality of Decisions made by Hub-and-Spokes Monetary Policy Committees," DNB Working Papers 027, Netherlands Central Bank, Research Department.
    8. Ben-Yashar, Ruth & Khuller, Samir & Kraus, Sarit, 2001. "Optimal collective dichotomous choice under partial order constraints," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 349-364, May.
    9. Ruth Ben-Yashar, 2006. "Information is important to Condorcet jurors," Public Choice, Springer, vol. 127(3), pages 305-319, June.
    10. 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.
    11. Stephen Hansen & Michael McMahon, 2016. "First Impressions Matter: Signalling as a Source of Policy Dynamics," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1645-1672.
    12. Albrecht, James & Anderson, Axel & Vroman, Susan, 2010. "Search by committee," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1386-1407, July.
    13. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    14. Kata Bognar & Lones Smith, 2004. "We Can't Argue Forever," CERS-IE WORKING PAPERS 0415, Institute of Economics, Centre for Economic and Regional Studies.
    15. Elisabeth Schulte, 2010. "Information aggregation and preference heterogeneity in committees," Theory and Decision, Springer, vol. 69(1), pages 97-118, July.
    16. Gilat Levy, 2007. "Decision Making in Committees: Transparency, Reputation, and Voting Rules," American Economic Review, American Economic Association, vol. 97(1), pages 150-168, March.
    17. Dino Gerardi & Leeat Yariv, 2003. "Committee Design in the Presence of Communication," Cowles Foundation Discussion Papers 1411, Cowles Foundation for Research in Economics, Yale University.
    18. Ruth Ben-Yashar & Igal Milchtaich, 2003. "First and Second Best Voting Rules in Committees," Working Papers 2003-08, Bar-Ilan University, Department of Economics.
    19. Jacob K. Goeree & Leeat Yariv, 2009. "An experimental study of jury deliberation," IEW - Working Papers 438, Institute for Empirical Research in Economics - University of Zurich.
    20. 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.

    More about this item

    Keywords

    Condorcet jury theorem; special majority voting; proportion; decreasing juror competence;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:wpa:wuwppe:0304004. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.