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Maximum Entropy Aggregation of Expert Predictions

Author

Listed:
  • In Jae Myung

    (Department of Psychology, The Ohio State University, 1885 Neil Avenue Mall, Columbus, Ohio 43210-1222)

  • Sridhar Ramamoorti

    (University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

  • Andrew D. Bailey, Jr.

    (University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

Abstract

This paper presents a maximum entropy framework for the aggregation of expert opinions where the expert opinions concern the prediction of the outcome of an uncertain event. The event to be predicted and individual predictions rendered are assumed to be discrete random variables. A measure of expert competence is defined using a distance metric between the actual outcome of the event and each expert's predicted outcome. Following Levy and Delic (Levy, W. B., H. Delic. 1994. Maximum entropy aggregation of individual opinions. IEEE Trans. Sys. Man & Cybernetics 24 606--613.), we use Shannon's information measure (Shannon [Shannon, C. E. 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27 379--423.], Jaynes [Jaynes, E. T. 1957. Information theory and statistical mechanics. Phys. Rev. 106 Part I: 620--630, 108 Part II: 171--190.]) to derive aggregation rules for combining two or more expert predictions into a single aggregated prediction that appropriately calibrates different degrees of expert competence and reflects any dependence that may exist among the expert predictions. The resulting maximum entropy aggregated prediction is least prejudiced in the sense that it utilizes all information available but remains maximally non committal with regard to information not available. Numerical examples to illuminate the implications of maximum entropy aggregation are also presented.

Suggested Citation

  • In Jae Myung & Sridhar Ramamoorti & Andrew D. Bailey, Jr., 1996. "Maximum Entropy Aggregation of Expert Predictions," Management Science, INFORMS, vol. 42(10), pages 1420-1436, October.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:10:p:1420-1436
    DOI: 10.1287/mnsc.42.10.1420
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    Cited by:

    1. Marcello Basili & Silvia Ferrini & Emanuele Montomoli, 2012. "Swine influenza and vaccines: an alternative approach for decision making about pandemic prevention," Department of Economics University of Siena 647, Department of Economics, University of Siena.
    2. Janet K. Tandy & Leon Shilton, 1999. "Risk Assessment Steeplechase: Hurdles to Becoming a Target Market," Journal of Real Estate Research, American Real Estate Society, vol. 17(2), pages 127-150.
    3. David M. Pennock & Michael P. Wellman, 2005. "Graphical Models for Groups: Belief Aggregation and Risk Sharing," Decision Analysis, INFORMS, vol. 2(3), pages 148-164, September.
    4. Sridhar Ramamoorti & Andrew D. Bailey Jr & Richard O. Traver, 1999. "Risk assessment in internal auditing: a neural network approach," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 8(3), pages 159-180, September.
    5. Francesco Cesarone & Justo Puerto, 2024. "New approximate stochastic dominance approaches for Enhanced Indexation models," Papers 2401.12669, arXiv.org.
    6. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.

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