On the significance of the absolute Margin

Abstract
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 Condorcet's formula, 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. Introduction The classical Condorcet jury model and the Condorcet jury theorem The significance of the absolute margin for the degree of belief we attach to the hypothesis given the evidence The significance of the absolute margin for the degree of support the evidence gives to the hypothesis An implication for the definition of special majority voting 5.1 Making positive decisions if and only if the truth of the hypothesis is beyond any reasonable doubt 5.2 Tracking the truth in the limit 5.3 Summary The jury model without the assumption of symmetrical competence Concluding remarks.
Keywords Condorcet's jury theorem
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