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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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References

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  1. Christian List, 2007. "Group deliberation and the transformation ofjudgments: an impossibility result," STICERD - Political Economy and Public Policy Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 26, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Franz Dietrich & Christian List, 2005. "Arrow’s theorem in judgment aggregation," Levine's Bibliography 784828000000000546, UCLA Department of Economics.
  3. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 639, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, Springer, vol. 28(4), pages 529-565, June.
  6. Ronald Fagin & John Geanakoplos & Joseph Y. Halpern & Moshe Y. Vardi, 1999. "The Hierarchical Approach to Modeling Knowledge and Common Knowledge," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1213, Cowles Foundation for Research in Economics, Yale University.
  7. Mongin, Ph., 1991. "Harsanyi's aggregation theorem: multi-profile version and unsettled questions," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1991036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(2), pages 170-190, June.
  9. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 63, pages 309.
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  11. Nielsen, Lars Tyge, 1984. "Common knowledge, communication, and convergence of beliefs," Mathematical Social Sciences, Elsevier, Elsevier, vol. 8(1), pages 1-14, August.
  12. Konieczny, Sebastien & Pino Perez, Ramon, 2005. "Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory," European Journal of Operational Research, Elsevier, Elsevier, vol. 160(3), pages 785-802, February.
  13. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, Econometric Society, vol. 47(6), pages 1321-36, November.
  14. Ménager, Lucie, 2008. "Consensus and common knowledge of an aggregate of decisions," Games and Economic Behavior, Elsevier, Elsevier, vol. 62(2), pages 722-731, March.
  15. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, Elsevier, vol. 91(2), pages 127-179, April.
  16. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
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  18. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496 Elsevier.
  19. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, Elsevier, vol. 28(1), pages 192-200, October.
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Cited by:
  1. Christian List, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 27596, London School of Economics and Political Science, LSE Library.
  2. Franz Dietrich, 2010. "Bayesian group belief," Social Choice and Welfare, Springer, Springer, vol. 35(4), pages 595-626, October.

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