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Probabilistic opinion pooling generalized. Part two: the premise-based approach

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  • Dietrich, Franz
  • List, Christian

Abstract

How can several individuals’ probability functions on a given σσ -algebra of events be aggregated into a collective probability function? Classic approaches to this problem usually require ‘event-wise independence’: the collective probability for each event should depend only on the individuals’ probabilities for that event. In practice, however, some events may be ‘basic’ and others ‘derivative’, so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize this idea by introducing a ‘premise-based’ approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the ‘premises’.

Suggested Citation

  • Dietrich, Franz & List, Christian, 2017. "Probabilistic opinion pooling generalized. Part two: the premise-based approach," LSE Research Online Documents on Economics 73519, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:73519
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    File URL: http://eprints.lse.ac.uk/73519/
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    References listed on IDEAS

    as
    1. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    2. Franz Dietrich, 2010. "Bayesian group belief," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 595-626, October.
    3. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    4. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    5. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
    6. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    7. Weymark, John A., 1997. "Aggregating Ordinal Probabilities on Finite Sets," Journal of Economic Theory, Elsevier, vol. 75(2), pages 407-432, August.
    8. repec:wly:riskan:v:19:y:1999:i:2:p:187-203 is not listed on IDEAS
    9. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    10. Christopher Chambers, 2007. "An ordinal characterization of the linear opinion pool," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 457-474, December.
    11. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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