Abstract
When a decision maker chooses to form his/her own probability distribution by combining the opinions of a number of experts, it is sometimes recommended that he/she should do so in such a way as to preserve any form of expert agreement regarding the independence of the events of interest. In this paper, we argue against this recommendation. We show that for those probability spaces which contain at least five points, a large class of seemingly reasonable combination methods excludes all independence preserving formulas except those which pick a single expert. In the case where at most four alternatives are present, the same conditions admit a richer variety of non-dictatorial methods which we also characterize. In the discussion, we give our reasons for rejecting independence preservation in expert judgement synthesis.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abou-Zaid, S. H. S.,Functional equations and related measurements. M. Phil. thesis, University of Waterloo, Waterloo, Ontario, 1984.
Bordley, R. F.,A Bayesian model of group polarization. Org. Behav. Hum. Perform.32 (1983), 262–274.
French, S.,Updating of belief in the light of someone else's opinion. J. R. Statist. Soc. Ser. A143 (1980), 43–48.
Genest, C.,A conflict between two axioms for combining subjective distributions. J. R. Statist. Soc. Ser. B46 (1984), 403–405.
Genest, C.,Pooling operators with the marginalization property. Canad. J. Statist.12 (1984), 153–163.
Genest, C., McConway, K. J. andSchervish, M. J.,Characterization of externally Bayesian pooling operators. Ann. Statist.14 (1986), 487–501.
Genest, C. andZidek, J. V.,Combining probability distributions: a critique and an annotated bibliography. Statist. Sci.1 (1986), 114–148.
Kannappan, Pl. andNg, C. T.,On functional equations and measures of information, II. J. Appl. Prob.17 (1980), 271–277.
Laddaga, R.,Lehrer and the consensus proposal. Synthese36 (1977), 473–477.
Lehrer, K. andWagner, C. G.,Probability amalgamation and the independence issue: a reply to Laddaga. Synthese55 (1983), 339–346.
Levi, I.,Consensus as shared agreement and outcome of inquiry. Synthese62 (1985), 3–11.
Lindley, D. V. andSingpurwalla, N. D.,Reliability (and fault tree) analysis using expert opinions. J. Amer. Statist. Assoc.81 (1986), 87–90.
Madansky, A.,Externally Bayesian groups. Rand memo RM-4141-PR, The Rand Corporation, Santa Monica, CA, 1964.
McConway, K. J.,Marginalization and linear opinion pools. J. Amer. Statist. Assoc.76, (1981), 410–414.
Ng, C. T.,Uniqueness theorems for a general class of functional equations. J. Austr. Math. Soc.11 (1970), 362–366.
Raiffa, H.,Decision analysis: introductory lectures on choices under uncertainty. Addison-Wesley, Reading, MA, 1968.
Roberts, A. W. andVarberg, D. E.,Convex functions. Academic Press, New York, 1973.
Wagner, C. G.,Aggregating subjective probabilities: some limitative theorems. Notre Dame J. Formal Logic25 (1984), 233–240.
Winkler, R. L.,Combining probability distributions from dependent information sources. Manag. Sci.27 (1981), 479–488.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Otto Haupt with best wishes on his 100th birthday.
Rights and permissions
About this article
Cite this article
Genest, C., Wagner, C.G. Further evidence against independence preservation in expert judgement synthesis. Aeq. Math. 32, 74–86 (1987). https://doi.org/10.1007/BF02311302
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02311302