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On the significance of the absolute margin

List, Christian (2004) On the significance of the absolute margin. The British Journal for the Philosophy of Science, 55 (3). pp. 521-544. ISSN 1464-3537

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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.

Item Type: Article
Official URL: http://bjps.oxfordjournals.org/
Additional Information: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in The British Journal for the Philosophy of Science following peer review. The definitive publisher-authenticated version [The British Journal for the Philosophy of Science 2004 55(3):521-544] is available online at: http://bjps.oxfordjournals.org/. LSE has developed LSE Research Online so that users may access research output of the School. Copyright and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (<http://eprints.lse.ac.uk>) of the LSE Research Online website.
Library of Congress subject classification: J Political Science > JA Political science (General)
Sets: Departments > Government
Research centres and groups > Centre for Philosophy of Natural and Social Science (CPNSS)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 31 Mar 2006
URL: http://eprints.lse.ac.uk/698/

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