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The Discursive Dilemma and Probabilistic Judgement Aggregation

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  • Pivato, Marcus

Abstract

Let S be a set of logically related propositions, and suppose a jury must decide the truth/falsehood of each member of S. A `judgement aggregation rule' (JAR) is a rule for combining the truth valuations on S from each juror into a collective truth valuation on S. Recent work has shown that there is no reasonable JAR which always yields a logically consistent collective truth valuation; this is referred to as the `Doctrinal Paradox' or the `Discursive Dilemma'. In this paper we will consider JARs which aggregate the subjective probability estimates of the jurors (rather than Boolean truth valuations) to produce a collective probability estimate for each proposition in S. We find that to properly aggregate these probability estimates, the JAR must also utilize information about the private information from which each juror generates her own probability estimate.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8412.

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Date of creation: 23 Apr 2008
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Handle: RePEc:pra:mprapa:8412

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Keywords: discursive dilemma; doctrinal paradox; judgement aggregation; statistical opinion pool; interactive epistemology; common knowledge; epistemic democracy; deliberative democracy;

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  1. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  2. Mongin, Ph., 1991. "Harsanyi's aggregation theorem: multi-profile version and unsettled questions," CORE Discussion Papers 1991036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  6. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  7. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, December.
  8. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
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  13. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  14. Christian List, 2007. "Group deliberation and the transformation ofjudgments: an impossibility result," STICERD - Political Economy and Public Policy Paper Series 26, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  15. G Rdenfors, Peter, 2006. "A Representation Theorem For Voting With Logical Consequences," Economics and Philosophy, Cambridge University Press, vol. 22(02), pages 181-190, July.
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Cited by:
  1. Dietrich, Franz, 2008. "Bayesian Group Belief," Research Memorandum 046, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Christian List, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics 27596, London School of Economics and Political Science, LSE Library.

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