On the Significance of the Absolute Margin

Christian List

Public Economics from University Library of Munich, Germany

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.

Keywords: Condorcet jury theorem; Bayes's theorem; voting; epistemic justification; hypothesis testing (search for similar items in EconPapers)
JEL-codes: D71 D72 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2002-11-18
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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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwppe:0211004

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