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Coherent combination of probabilistic outputs for group decision making: an algebraic approach

Author

Listed:
  • Manuele Leonelli

    (IE University)

  • Eva Riccomagno

    (Università degli Studi di Genova)

  • Jim Q. Smith

    (University of Warwick)

Abstract

Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational power to produce the scores necessary to rank the available policies. Recently, integrating decision support systems have been introduced to enable a formal Bayesian multi-agent decision analysis to be distributed and consequently efficient. In such systems, where different panels of experts independently oversee disjoint but correlated vectors of variables, each expert group needs to deliver only certain summaries of the variables under their jurisdiction, derived from a conditional independence structure common to all panels, to properly derive an overall score for the available policies. Here we present an algebraic approach that makes this methodology feasible for a wide range of modelling contexts and that enables us to identify the summaries needed for such a combination of judgements. We are also able to demonstrate that coherence, in a sense we formalize here, is still guaranteed when panels only share a partial specification of their model with other panel members. We illustrate this algebraic approach by applying it to a specific class of Bayesian networks and demonstrate how we can use it to derive closed form formulae for the computations of the joint moments of variables that determine the score of different policies.

Suggested Citation

  • Manuele Leonelli & Eva Riccomagno & Jim Q. Smith, 2020. "Coherent combination of probabilistic outputs for group decision making: an algebraic approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 499-528, June.
  • Handle: RePEc:spr:orspec:v:42:y:2020:i:2:d:10.1007_s00291-020-00588-8
    DOI: 10.1007/s00291-020-00588-8
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    References listed on IDEAS

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    1. Manuele Leonelli & Jim Q. Smith, 2017. "Directed Expected Utility Networks," Decision Analysis, INFORMS, vol. 14(2), pages 108-125, June.
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    3. Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
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    5. Freeman, G. & Smith, J.Q., 2011. "Bayesian MAP model selection of chain event graphs," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1152-1165, August.
    6. Muller, Sigrid M. & Machina, Mark J., 1987. "Moment preferences and polynomial utility," Economics Letters, Elsevier, vol. 23(4), pages 349-353.
    7. Manuele Leonelli & James Smith, 2015. "Bayesian decision support for complex systems with many distributed experts," Annals of Operations Research, Springer, vol. 235(1), pages 517-542, December.
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