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On the Significance of the Absolute Margin

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  • Christian List

    (Nuffield College, Oxford)

Abstract

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.

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File URL: http://128.118.178.162/eps/pe/papers/0211/0211004.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Public Economics with number 0211004.

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Length: 22 pages
Date of creation: 18 Nov 2002
Date of revision:
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 http://www.nuff.ox.ac.uk/Politics/papers/
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Web page: http://128.118.178.162

Related research

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

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References

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  1. Shmuel Nitzan & Jacob Paroush, 1984. "Are qualified majority rules special?," Public Choice, Springer, vol. 42(3), pages 257-272, January.
  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 175-86, February.
  3. 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.
  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.
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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.

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