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Decision Analysis with Incomplete Utility and Probability Information

Author

Listed:
  • Herbert Moskowitz

    (Purdue University, West Lafayette, Indiana)

  • Paul V. Preckel

    (Purdue University, West Lafayette, Indiana)

  • Aynang Yang

    (Purdue University, West Lafayette, Indiana)

Abstract

An approach to the solution of decision analysis problems under uncertainty with imprecise and incomplete information is presented. The methodology is designed for cases in which payoffs (conditional on the state of nature) are known precisely, but only limited or imprecise probability and utility information is available regarding a decision maker's beliefs and tastes. A decision maker provides: conditional payoffs, (optionally) bounds on state probabilities, bounds on the certainty equivalent for a simple lottery, any known relationships between probabilities of states of nature, and a series of strict preferences between pairs of vectors of conditional payoffs. We assume an exponential utility function with unknown parameter. The method proceeds by sequentially eliciting preferences, new bounds on probabilities and/or the certainty equivalent, and new relationships among probabilities until the problem is solved. The methodology is demonstrated through a two-state and a three-state example which illustrate the effects of the progressive elicitation of additional information.

Suggested Citation

  • Herbert Moskowitz & Paul V. Preckel & Aynang Yang, 1993. "Decision Analysis with Incomplete Utility and Probability Information," Operations Research, INFORMS, vol. 41(5), pages 864-879, October.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:5:p:864-879
    DOI: 10.1287/opre.41.5.864
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    Citations

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    Cited by:

    1. Ahn, Byeong Seok & Park, Haechurl, 2014. "Establishing dominance between strategies with interval judgments of state probabilities," Omega, Elsevier, vol. 49(C), pages 53-59.
    2. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
    3. F. Ben Abdelaziz & P. Lang & R. Nadeau, 1999. "Dominance and Efficiency in Multicriteria Decision under Uncertainty," Theory and Decision, Springer, vol. 47(3), pages 191-211, December.
    4. J. C. Moore & H. Raghav Rao & A. B. Whinston, 1997. "Experimental Strategies for Preference Information Acquisition: A Lattice Path Treatment," Group Decision and Negotiation, Springer, vol. 6(2), pages 139-158, March.
    5. Dias, Luis C. & Vetschera, Rudolf, 2019. "On generating utility functions in Stochastic Multicriteria Acceptability Analysis," European Journal of Operational Research, Elsevier, vol. 278(2), pages 672-685.
    6. Liesiö, Juuso & Salo, Ahti, 2012. "Scenario-based portfolio selection of investment projects with incomplete probability and utility information," European Journal of Operational Research, Elsevier, vol. 217(1), pages 162-172.
    7. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti & Ilmola-Sheppard, Leena, 2018. "Scenario-based portfolio model for building robust and proactive strategies," European Journal of Operational Research, Elsevier, vol. 266(1), pages 205-220.
    8. Salvatore Corrente & Salvatore Greco & Roman Słowiński, 2017. "Handling imprecise evaluations in multiple criteria decision aiding and robust ordinal regression by n-point intervals," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 127-157, June.
    9. Tao Huang & J. Eric Bickel, 2019. "Sparse Probability Assessment Heuristic Based on Orthogonal Matching Pursuit," Decision Analysis, INFORMS, vol. 16(4), pages 281-300, December.
    10. Borgonovo, Emanuele & Tonoli, Fabio, 2014. "Decision-network polynomials and the sensitivity of decision-support models," European Journal of Operational Research, Elsevier, vol. 239(2), pages 490-503.
    11. Podinovski, Vladislav V., 2014. "Decision making under uncertainty with unknown utility function and rank-ordered probabilities," European Journal of Operational Research, Elsevier, vol. 239(2), pages 537-541.
    12. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.
    13. Liesiö, Juuso & Kallio, Markku & Argyris, Nikolaos, 2023. "Incomplete risk-preference information in portfolio decision analysis," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1084-1098.

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