British Journal for the Philosophy of Science 55 (3):521-544 (2004)
|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|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Christian List, Some Remarks on the Probability of Cycles - Appendix 3 to 'Epistemic Democracy: Generalizing the Condorcet Jury Theorem'.
Jan-Willem Romeijn & David Atkinson (2011). Learning Juror Competence: A Generalized Condorcet Jury Theorem. Politics, Philosophy and Economics 10 (3):237-262.
Franz Dietrich & Christian List (2004). A Model of Jury Decisions Where All Jurors Have the Same Evidence. Synthese 142 (2):175 - 202.
Franz Dietrich (2008). The Premises of Condorcet's Jury Theorem Are Not Simultaneously Justified. Episteme 5 (1):56-73.
Robert E. Goodin & David Estlund (2004). The Persuasiveness of Democratic Majorities. Politics, Philosophy and Economics 3 (2):131-142.
James Hawthorne, Voting in Search of the Public Good: The Probabilistic Logic of Majority Judgments.
Added to index2009-01-28
Total downloads6 ( #154,676 of 722,826 )
Recent downloads (6 months)1 ( #60,541 of 722,826 )
How can I increase my downloads?