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Multiattribute Utility Copulas

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  • Ali E. Abbas

    (Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

Abstract

We introduce the notion of a multiattribute utility copula that expresses any (i) continuous; (ii) bounded multiattribute utility function that is (iii) nondecreasing with each of its arguments, and (iv) strictly increasing with each argument for at least one reference value of the complement attributes, in terms of single-attribute utility assessments. This formulation provides a wealth of new functional forms that can be used to model preferences over utility-dependent attributes and enables sensitivity analyses to some of the widely used functional forms of utility independence. We introduce a class of utility copulas, called Archimedean utility copulas, and discuss the conditions under which it yields the additive and multiplicative forms. We also discuss linear and composite transformations of utility copulas that construct utility functions with partial utility independence. We conclude with the risk aversion functions that are induced by utility copula formulations and work through several examples to illustrate the approach.

Suggested Citation

  • Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:6:p:1367-1383
    DOI: 10.1287/opre.1080.0687
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    References listed on IDEAS

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    1. James S. Dyer & Rakesh K. Sarin, 1982. "Relative Risk Aversion," Management Science, INFORMS, vol. 28(8), pages 875-886, August.
    2. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    3. Alsina, Claudi & Nelsen, Roger B. & Schweizer, Berthold, 1993. "On the characterization of a class of binary operations on distribution functions," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 85-89, May.
    4. Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    5. Woojune Yi & Vicki M. Bier, 1998. "An Application of Copulas to Accident Precursor Analysis," Management Science, INFORMS, vol. 44(12-Part-2), pages 257-270, December.
    6. Peter H. Farquhar, 1975. "A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 23(5), pages 941-967, October.
    7. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    8. Ralph L. Keeney, 1979. "Evaluation of Proposed Storage Sites," Operations Research, INFORMS, vol. 27(1), pages 48-64, February.
    9. Craig W. Kirkwood, 1976. "Parametrically Dependent Preferences for Multiattributed Consequences," Operations Research, INFORMS, vol. 24(1), pages 92-103, February.
    10. Ralph L. Keeney, 1981. "Analysis of Preference Dependencies among Objectives," Operations Research, INFORMS, vol. 29(6), pages 1105-1120, December.
    11. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
    12. David E. Bell, 1979. "Multiattribute Utility Functions: Decompositions Using Interpolation," Management Science, INFORMS, vol. 25(8), pages 744-753, August.
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    Citations

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    Cited by:

    1. Dogucan Mazicioglu & Jason R. W. Merrick, 2018. "Behavioral Modeling of Adversaries with Multiple Objectives in Counterterrorism," Risk Analysis, John Wiley & Sons, vol. 38(5), pages 962-977, May.
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    3. Ali E. Abbas & David E. Bell, 2012. "METHODS---One-Switch Conditions for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 60(5), pages 1199-1212, October.
    4. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    5. 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.
    6. 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.
    7. Michel Denuit & Louis Eeckhoudt, 2010. "Bivariate Stochastic Dominance and Substitute Risk-(In)dependent Utilities," Decision Analysis, INFORMS, vol. 7(3), pages 302-312, September.
    8. Jiehua Xie & Zhengyong Zhou, 2022. "Patchwork Constructions of Multiattribute Utility Functions," Decision Analysis, INFORMS, vol. 19(2), pages 141-169, June.
    9. Ali E. Abbas & Zhengwei Sun, 2019. "Archimedean Utility Copulas with Polynomial Generating Functions," Decision Analysis, INFORMS, vol. 16(3), pages 218-237, September.
    10. 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.
    11. 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.
    12. Ali E. Abbas, 2011. "The Multiattribute Utility Tree," Decision Analysis, INFORMS, vol. 8(3), pages 180-205, September.
    13. Ying He & James S. Dyer & John C. Butler, 2014. "Decomposing a Utility Function Based on Discrete Distribution Independence," Decision Analysis, INFORMS, vol. 11(4), pages 233-249, December.
    14. Samuel Kotz & Johan René van Dorp, 2010. "Generalized Diagonal Band Copulas with Two-Sided Generating Densities," Decision Analysis, INFORMS, vol. 7(2), pages 196-214, June.
    15. Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    16. Tim Bedford & Alireza Daneshkhah & Kevin J. Wilson, 2016. "Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 792-815, April.
    17. Francesca Beccacece & Emanuele Borgonovo & Greg Buzzard & Alessandra Cillo & Stanley Zionts, 2013. "Elicitation of Multiattribute Value Functions through High Dimensional Model Representations," Working Papers 495, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    18. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    19. Roger J. Jiao & Feng Zhou & Chih-Hsing Chu, 2017. "Decision theoretic modeling of affective and cognitive needs for product experience engineering: key issues and a conceptual framework," Journal of Intelligent Manufacturing, Springer, vol. 28(7), pages 1755-1767, October.
    20. Liesiö, Juuso & Kee, Taeyoung & Malo, Pekka, 2024. "Modeling project interactions in multiattribute portfolio decision analysis: Axiomatic foundations and practical implications," European Journal of Operational Research, Elsevier, vol. 316(3), pages 988-1000.
    21. Ali E. Abbas & David E. Bell, 2015. "Ordinal One-Switch Utility Functions," Operations Research, INFORMS, vol. 63(6), pages 1411-1419, December.
    22. Luis V. Montiel & J. Eric Bickel, 2014. "A Generalized Sampling Approach for Multilinear Utility Functions Given Partial Preference Information," Decision Analysis, INFORMS, vol. 11(3), pages 147-170, September.
    23. Ali E. Abbas, 2013. "Utility Copula Functions Matching All Boundary Assessments," Operations Research, INFORMS, vol. 61(2), pages 359-371, April.

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