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The probability of inconsistencies in complex collective decisions

List, Christian (2005) The probability of inconsistencies in complex collective decisions. Social Choice and Welfare, 24 (1). 3 -32. ISSN 1432-217X

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Abstract

Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the paradox converges to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz (2001, 2003), I use the model to assess the “truth-tracking” performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcet’s paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions.

Item Type: Article
Official URL: http://link.springer.de/link/service/journals/0035...
Additional Information: Published 2005 © Springer. The original publication is available at www.springerlink.com. 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: 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: 10 Mar 2006
URL: http://eprints.lse.ac.uk/664/

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