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Probabilistic Opinion Pooling

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  • Dietrich, Franz
  • List, Christian

Abstract

This review article introduces and evaluates various ways to aggregate probabilistic opinions of different individuals. For each of these three ways, an axiomatic characterization result is presented (a new one in the case of multiplicative pooling). The three ways satisfy different axioms and are justifiable under different conditions. Linear pooling may be justified on procedural grounds, but not on epistemic grounds. Geometric and multiplicative pooling may be justified on epistemic grounds, but which of the two is appropriate depends not just on the opinion profiles to be aggregated but also on the information on which they are based. Geometric pooling can be justified if all individuals' opinions are based on the same information, while multiplicative pooling can be justified if every individual's opinions are based solely on private information, except for some shared background information held by everyone.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 54806.

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Date of creation: Mar 2014
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Handle: RePEc:pra:mprapa:54806

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Keywords: subjective probability; aggregation; linear pooling; geometric pooling; multiplicative pooling; Bayesianism; informational symmetry; informational asymmetry;

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  1. Franz Dietrich & Christian List, 2005. "Arrow's Theorem in Judgement Aggregation," Public Economics, EconWPA 0504007, EconWPA, revised 10 Sep 2005.
  2. 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.
  3. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(2), pages 793-805.
  5. Franz Dietrich, 2010. "Bayesian group belief," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 29573, London School of Economics and Political Science, LSE Library.
  6. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, Springer, vol. 28(4), pages 529-565, June.
  7. Christopher Chambers, 2007. "An ordinal characterization of the linear opinion pool," Economic Theory, Springer, Springer, vol. 33(3), pages 457-474, December.
  8. Weymark, John A., 1997. "Aggregating Ordinal Probabilities on Finite Sets," Journal of Economic Theory, Elsevier, Elsevier, vol. 75(2), pages 407-432, August.
  9. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 495-511, March.
  10. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 544-561, March.
  11. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, INFORMS, vol. 20(9), pages 1233-1241, May.
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