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On the Significance of the Absolute Margin

List, Christian (2002) On the Significance of the Absolute Margin. [Preprint]

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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.


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    Item Type: Preprint
    Keywords: Condorcet jury theorem, Bayes's theorem, voting, epistemic justification, hypothesis testing
    Subjects: General Issues > Confirmation/Induction
    General Issues > Decision Theory
    Specific Sciences > Economics
    Specific Sciences > Probability/Statistics
    Depositing User: Christian List
    Date Deposited: 13 Nov 2002
    Last Modified: 07 Oct 2010 11:11
    Item ID: 879
    URI: http://philsci-archive.pitt.edu/id/eprint/879

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