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Decision theory, linear partial information and statistical dominance

Author

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  • Kmietowicz, ZW
  • Pearman, AD

Abstract

The paper deals with decision making under conditions of linear partial information, i.e. when probabilities of states of nature are not known precisely, but are subject to linear constraints. Conditions ensuring strict and weak statistical dominance of one strategy over another are derived. It is also shown that weak dominance in terms of payoffs is equivalent to weak dominance in terms of regrets. The new results are more general than those obtained by Fishburn and by Kmietowicz and Pearman for weak and strict ranking of probabilities, and include them as special cases. The new results can be employed in practical decision making in several ways.

Suggested Citation

  • Kmietowicz, ZW & Pearman, AD, 1984. "Decision theory, linear partial information and statistical dominance," Omega, Elsevier, vol. 12(4), pages 391-399.
    • Handle: RePEc:eee:jomega:v:12:y:1984:i:4:p:391-399
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    Citations

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    Cited by:

    1. 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.
    2. Vetschera, Rudolf, 2017. "Deriving rankings from incomplete preference information: A comparison of different approaches," European Journal of Operational Research, Elsevier, vol. 258(1), pages 244-253.
    3. Park, Kyung Sam & Kim, Soung Hie & Yoon, Wan Chul, 1997. "Establishing strict dominance between alternatives with special type of incomplete information," European Journal of Operational Research, Elsevier, vol. 96(2), pages 398-406, January.
    4. 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.
    5. Helena Gaspars-Wieloch, 2017. "Newsvendor problem under complete uncertainty: a case of innovative products," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 561-585, September.
    6. 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.
    7. Ahn, Byeong Seok, 2017. "Approximate weighting method for multiattribute decision problems with imprecise parameters," Omega, Elsevier, vol. 72(C), pages 87-95.
    8. C H Han & B S Ahn, 2005. "Interactive group decision-making procedure using weak strength of preference," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1204-1212, October.
    9. 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.
    10. 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.
    11. John R. Doyle, 1999. "Elicitation and Context Effects in Judgments: Fixed Sum Versus Fixed Scale Frames," Management Science, INFORMS, vol. 45(7), pages 972-979, July.
    12. 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.
    13. 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.
    14. Kim, Soung Hie & Ahn, Byeong Seok, 1999. "Interactive group decision making procedure under incomplete information," European Journal of Operational Research, Elsevier, vol. 116(3), pages 498-507, August.
    15. Helena Gaspars-Wieloch, 2018. "The Impact of the Structure of the Payoff Matrix on the Final Decision made Under Uncertainty," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-27, February.
    16. Helena Gaspars-Wieloch, 2015. "On a decision rule supported by a forecasting stage based on the decision maker’s coefficient of optimism," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 579-594, September.
    17. Ahn, Byeong Seok & Sam Park, Kyung & Hee Han, Chang & Kyeong Kim, Jae, 2000. "Multi-attribute decision aid under incomplete information and hierarchical structure," European Journal of Operational Research, Elsevier, vol. 125(2), pages 431-439, September.
    18. 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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