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On the Significance of the Absolute Margin


  • Christian List

    (Nuffield College, Oxford)


Consider the hypothesis H that a defendant is guilty (a patient has condition C), and the evidence E that a majority of h out of n independent jurors (diagnostic tests) have voted for H and a minority of k:=n-h against H. How likely is the majority verdict to be correct? By a formula of Condorcet, the probability that H is true given E depends only on each juror’s competence and on the absolute margin between the majority and the minority h-k, but neither on the number n, nor on the proportion h/n. This paper reassesses that result and explores its implications. First, using the classical Condorcet jury model, I derive a more general version of Condorcet’s formula, confirming the significance of the absolute margin, but showing that the probability that H is true given E depends also on an additional parameter: the prior probability that H is true. Second, I show that a related result holds when we consider not the degree of belief we attach to H given E, but the degree of support E gives to H. Third, I address the implications for the definition of special majority voting, a procedure used to capture the asymmetry between false positive and false negative decisions. I argue that the standard definition of special majority voting in terms of a required proportion of the jury is epistemically questionable, and that the classical Condorcet jury model leads to an alternative definition in terms of a required absolute margin between the majority and the minority. Finally, I show that the results on the significance of the absolute margin can be resisted if the so-called assumption of symmetrical juror competence is relaxed.

Suggested Citation

  • Christian List, 2002. "On the Significance of the Absolute Margin," Public Economics 0211004, EconWPA.
  • Handle: RePEc:wpa:wuwppe:0211004
    Note: Type of Document - PDF; prepared on Windows; pages: 22. This paper is included in the Nuffield College Working Paper Series in Politics at

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    References listed on IDEAS

    1. 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.
    2. repec:cup:apsrev:v:94:y:2000:i:02:p:407-423_22 is not listed on IDEAS
    3. repec:cup:apsrev:v:92:y:1998:i:01:p:23-35_20 is not listed on IDEAS
    4. Franz Dietrich & Christian List, 2002. "A Model of Jury Decisions Where All Jurors Have the Same Evidence," Economics Papers 2002-W23, Economics Group, Nuffield College, University of Oxford.
    5. 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.
    6. repec:cup:apsrev:v:94:y:2000:i:02:p:395-406_22 is not listed on IDEAS
    7. repec:cup:apsrev:v:94:y:2000:i:02:p:375-393_22 is not listed on IDEAS
    8. Shmuel Nitzan & Jacob Paroush, 1984. "Are qualified majority rules special?," Public Choice, Springer, vol. 42(3), pages 257-272, January.
    9. 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.
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    Cited by:

    1. 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, EconWPA.

    More about this item


    Condorcet jury theorem; Bayes's theorem; voting; epistemic justification; hypothesis testing;

    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

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