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The Consensus of Subjective Probability Distributions


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  • Robert L. Winkler

    (Indiana University)

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    "`But we can't agree whether A or B is correct,' he concluded, `and so we're collecting expert opinions, weighting them appropriately, and programming WESCAC to arbitrate the whole question.'" (John Barth, Giles Goat-Boy, p. 664.) In the Bayesian framework, quantified judgments about uncertainty are an indispensable input to methods of statistical inference and decision. If a decision maker has little knowledge with regard to the parameters of interest, he may decide to consult a number of experts and obtain their quantified judgments in the form of subjective probability distributions. If this is the case, the decision maker must somehow combine the distributions assessed by the experts and form a single distribution to be used as an input to a formal Bayesian analysis. Several methods for combining the distributions are suggested, some involving mathematical formulae and some involving feedback and/or group discussion. These methods are compared under certain assumptions regarding the form of the distributions and also under experimental conditions.

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 15 (1968)
    Issue (Month): 2 (October)
    Pages: B61-B75

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    Handle: RePEc:inm:ormnsc:v:15:y:1968:i:2:p:b61-b75

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    Cited by:
    1. Cho, Sungbin, 2009. "A linear Bayesian stochastic approximation to update project duration estimates," European Journal of Operational Research, Elsevier, vol. 196(2), pages 585-593, July.
    2. Robert Inman, 1981. "On setting the agenda for Pennsylvania school finance reform: An exercise in giving policy advice," Public Choice, Springer, vol. 36(3), pages 449-474, January.
    3. Patrizio Frederic & Mario Di Bacco & Frank Lad, 2012. "Combining expert probabilities using the product of odds," Theory and Decision, Springer, vol. 73(4), pages 605-619, October.
    4. Joseph Kadane & Javier Girón & Daniel Peña & Peter Fishburn & Simon French & D. Lindley & Giovanni Parmigiani & Robert Winkler, 1993. "Several Bayesians: A review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 2(1), pages 1-32, December.
    5. Palfrey, Thomas R. & Wang, Stephanie W., . "On eliciting beliefs in strategic games," Working Papers 1271, California Institute of Technology, Division of the Humanities and Social Sciences.
    6. Wang, W., 1997. "Subjective estimation of the delay time distribution in maintenance modelling," European Journal of Operational Research, Elsevier, vol. 99(3), pages 516-529, June.
    7. Irene Valsecchi, 2008. "Learning from Experts," Working Papers 2008.35, Fondazione Eni Enrico Mattei.
    8. Greig, I.D., 1981. "Agricultural Research Management and the Ex Ante Evaluation of Research Proposals : A Review," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 49(02), August.
    9. Marcello Basili & Luca Pratelli, 2013. "Aggregation of not necessarily independent opinions," Department of Economics University of Siena 677, Department of Economics, University of Siena.
    10. Timo Henckel & Shaun Vahey & Liz Wakerly, 2011. "Probabilistic Interest Rate Setting With A Shadow Board: A Description Of The Pilot Project," CAMA Working Papers 2011-27, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    11. Anderson, Jock R. & Hardaker, J. Brian, 1972. "An Appreciation of Decision Analysis in Management," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 40(04), December.
    12. Hurley, W. J. & Lior, D. U., 2002. "Combining expert judgment: On the performance of trimmed mean vote aggregation procedures in the presence of strategic voting," European Journal of Operational Research, Elsevier, vol. 140(1), pages 142-147, July.


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