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Multiattribute Utility Functions Satisfying Mutual Preferential Independence

Author

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  • Ali E. Abbas

    (Epstein Department of Industrial and Systems Engineering and Department of Public Policy, Viterbi School of Engineering, and Price School of Public Policy, University of Southern California, Los Angeles, California, 90089)

  • Zhengwei Sun

    (Department of Management Science and Engineering, East China University of Science and Technology, Shanghai 200237, China)

Abstract

The construction of a multiattribute utility function is an important step in decision analysis. One of the most widely used conditions for constructing the utility function is the assumption of mutual preferential independence where trade-offs among any subset of the attributes do not depend on the instantiations of the remaining attributes. Mutual preferential independence asserts that ordinal preferences can be represented by an additive function of the attributes. This paper derives the most general form of a multiattribute utility function that (i) exhibits mutual preferential independence and (ii) is strictly increasing with each argument at the maximum value of the complement attributes. We show that a multiattribute utility function satisfies these two conditions if and only if it is an Archimedean combination of univariate utility assessments. This result enables the construction of multiattribute utility functions that satisfy additive ordinal preferences using univariate utility assessments and a single generating function. We also provide a nonparametric approach for estimating the generating function of the Archimedean form by iteration.

Suggested Citation

  • Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:2:p:378-393
    DOI: 10.1287/opre.2015.1350
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    References listed on IDEAS

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    2. Michel Grabisch & Christophe Labreuche, 2015. "On the decomposition of Generalized Additive Independence models," Documents de travail du Centre d'Economie de la Sorbonne 15064, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Mauricio Lopez-Mendez & Rowan Iskandar & Eric Jutkowitz, 2023. "Individual and Dyadic Health-Related Quality of Life of People Living with Dementia and their Caregivers," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 18(4), pages 1673-1692, August.
    4. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    5. Ali E. Abbas & Zhengwei Sun, 2019. "Archimedean Utility Copulas with Polynomial Generating Functions," Decision Analysis, INFORMS, vol. 16(3), pages 218-237, September.
    6. William B. Haskell & Wenjie Huang & Huifu Xu, 2018. "Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions," Papers 1805.06632, arXiv.org.
    7. William B. Haskell & J. George Shanthikumar & Z. Max Shen, 2017. "Aspects of optimization with stochastic dominance," Annals of Operations Research, Springer, vol. 253(1), pages 247-273, June.

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