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The Discursive Dilemma and Probabilistic Judgement Aggregation

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Pivato, Marcus

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

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Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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  1. John Geanakoplos & (**), Moshe Y. Vardi & Joseph Y. Halpern & Ronald Fagin, 1999. "The hierarchical approach to modeling knowledge and common knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 331-365. [Downloadable!] (restricted)
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  2. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April. [Downloadable!] (restricted)
  3. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation, Yale University. [Downloadable!]
  4. Franz Dietrich & Christian List, 2005. "Arrow's Theorem in Judgement Aggregation," Public Economics 0504007, EconWPA, revised 10 Sep 2005. [Downloadable!]
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  5. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October. [Downloadable!] (restricted)
  6. Ménager, Lucie, 2008. "Consensus and common knowledge of an aggregate of decisions," Games and Economic Behavior, Elsevier, vol. 62(2), pages 722-731, March. [Downloadable!] (restricted)
  7. 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, vol. 160(3), pages 785-802, February. [Downloadable!] (restricted)
  8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June. [Downloadable!] (restricted)
  9. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June. [Downloadable!] (restricted)
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  10. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-36, November. [Downloadable!] (restricted)
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