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Analysis of Decisions with Incomplete Knowledge of Probabilities

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  • Peter C. Fishburn

    (Research Analysis Corporation, McLean, Virginia)

Abstract

This paper discusses the application of personalistic decision theory in a typical setting of decision making under uncertainty. The criterion for choice of strategy is maximization of expected utility. In this setting it is often difficult to obtain very precise measurements of the decision maker's probabilities on the states of nature. We therefore pay particular attention to several “imprecise” measures of probability, including sets of inequalities and bounds, and see how this information may be used in trying to determine an ordering or partial ordering of the expected utilities of the alternative strategies. At the end of the paper we note how, in practice, one may try to obtain the measures of probability presented herein.

Suggested Citation

  • Peter C. Fishburn, 1965. "Analysis of Decisions with Incomplete Knowledge of Probabilities," Operations Research, INFORMS, vol. 13(2), pages 217-237, April.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:2:p:217-237
    DOI: 10.1287/opre.13.2.217
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    Cited by:

    1. Meimei Xia & Jian Chen & Xiao-Jun Zeng, 2018. "Decision Analysis on Choquet Integral-Based Multi-Criteria Decision-Making with Imprecise Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 677-704, March.
    2. Han, Chang Hee & Kim, Jae Kyeong & Choi, Sang Hyun, 2004. "Prioritizing engineering characteristics in quality function deployment with incomplete information: A linear partial ordering approach," International Journal of Production Economics, Elsevier, vol. 91(3), pages 235-249, October.
    3. Daniel R. Georgiadis & Thomas A. Mazzuchi & Shahram Sarkani, 2013. "Using multi criteria decision making in analysis of alternatives for selection of enabling technology," Systems Engineering, John Wiley & Sons, vol. 16(3), pages 287-303, September.
    4. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
    5. C M Yates, 2007. "A positive approach to estimating the weights for quadratic multiple objective programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1332-1340, October.
    6. Robert G. Chambers & Tigran Melkonyan & John Quiggin, 2022. "Incomplete preferences, willingness to pay, and willingness to accept," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 727-761, October.
    7. Park, Kyung Sam & Kim, Soung Hie, 1997. "Tools for interactive multiattribute decisionmaking with incompletely identified information," European Journal of Operational Research, Elsevier, vol. 98(1), pages 111-123, April.
    8. Kim, Soung Hie & Han, Chang Hee, 2000. "Establishing dominance between alternatives with incomplete information in a hierarchically structured attribute tree," European Journal of Operational Research, Elsevier, vol. 122(1), pages 79-90, April.
    9. Ahn, Byeong Seok & Park, Haechurl, 2014. "Establishing dominance between strategies with interval judgments of state probabilities," Omega, Elsevier, vol. 49(C), pages 53-59.
    10. K S Park & I Jeong, 2011. "How to treat strict preference information in multicriteria decision analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1771-1783, October.
    11. Jiménez, Antonio & Mateos, Alfonso & Ríos-Insua, Sixto, 2009. "Missing consequences in multiattribute utility theory," Omega, Elsevier, vol. 37(2), pages 395-410, April.
    12. Jiamin Wang, 2012. "Robust optimization analysis for multiple attribute decision making problems with imprecise information," Annals of Operations Research, Springer, vol. 197(1), pages 109-122, August.
    13. Kim, Soung Hie & Choi, Sang Hyun & Kim, Jae Kyeong, 1999. "An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach," European Journal of Operational Research, Elsevier, vol. 118(1), pages 139-152, October.
    14. Azondekon, Sebastien H. & Martel, Jean-Marc, 1999. ""Value" of additional information in multicriterion analysis under uncertainty," European Journal of Operational Research, Elsevier, vol. 117(1), pages 45-62, August.
    15. Johannes G. Jaspersen & Gilberto Montibeller, 2015. "Probability Elicitation Under Severe Time Pressure: A Rank‐Based Method," Risk Analysis, John Wiley & Sons, vol. 35(7), pages 1317-1335, July.
    16. Ahn, Byeong Seok, 2011. "Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach," European Journal of Operational Research, Elsevier, vol. 212(3), pages 552-559, August.
    17. F. Hutton Barron & Charles P. Schmidt, 1988. "Entropy‐based selection with multiple objectives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 643-654, December.
    18. Kaddani, Sami & Vanderpooten, Daniel & Vanpeperstraete, Jean-Michel & Aissi, Hassene, 2017. "Weighted sum model with partial preference information: Application to multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 665-679.
    19. Sam Park, Kyung & Sang Lee, Kyung & Seong Eum, Yun & Park, Kwangtae, 2001. "Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information," European Journal of Operational Research, Elsevier, vol. 134(3), pages 557-563, November.
    20. 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.
    21. A Mateos & S Ríos-Insua & A Jiménez, 2007. "Dominance, potential optimality and alternative ranking in imprecise multi-attribute decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 326-336, March.

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