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Decomposing a Utility Function Based on Discrete Distribution Independence

Author

Listed:
  • Ying He

    (Department of Business and Economics, University of Southern Denmark, DK-5230 Odense M, Denmark)

  • James S. Dyer

    (Department of Information, Risk, and Operations Management, McCombs School of Business, University of Texas at Austin, Austin, Texas 78712)

  • John C. Butler

    (Department of Finance, McCombs School of Business, The University of Texas at Austin, Austin, Texas 78712)

Abstract

For two-attribute decision-making problems, the multilinear utility model cannot be applied when the risk aversion on one attribute depends on the level of the other attribute. We propose a family of general preference conditions called n th-degree discrete distribution independence that can accommodate a variety of dependence relationships between two attributes. The special case of second-degree discrete distribution independence is equivalent to the utility independence condition. We focus on third-degree discrete distribution independence that leads to a decomposition formula that contains many other preference models as special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ordeca:v:11:y:2014:i:4:p:233-249
    DOI: 10.1287/deca.2014.0302
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    References listed on IDEAS

    as
    1. David E. Bell, 1979. "Consistent Assessment Procedures Using Conditional Utility Functions," Operations Research, INFORMS, vol. 27(5), pages 1054-1066, October.
    2. Peter C. Fishburn & Ralph L. Keeney, 1975. "Generalized Utility Independence and Some Implications," Operations Research, INFORMS, vol. 23(5), pages 928-940, October.
    3. Ilia Tsetlin & Robert L. Winkler, 2009. "Multiattribute Utility Satisfying a Preference for Combining Good with Bad," Management Science, INFORMS, vol. 55(12), pages 1942-1952, December.
    4. 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.
    5. Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    6. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    7. Peter C. Fishburn, 1974. "von Neumann-Morgenstera Utility Functions on Two Attributes," Operations Research, INFORMS, vol. 22(1), pages 35-45, February.
    8. Peter C. Fishburn, 1977. "Approximations of Two-Attribute Utility Functions," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 30-44, February.
    9. Ali E. Abbas, 2013. "Utility Copula Functions Matching All Boundary Assessments," Operations Research, INFORMS, vol. 61(2), pages 359-371, April.
    10. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    11. Peter C. Fishburn & Peter H. Farquhar, 1982. "Finite-Degree Utility Independence," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 348-353, August.
    12. Beatrice Rey & Jean-Charles Rochet, 2004. "Health and Wealth: How do They Affect Individual Preferences?," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 29(1), pages 43-54, June.
    13. Hiroyuki Tamura & Yutaka Nakamura, 1983. "Decompositions of Multiattribute Utility Functions Based on Convex Dependence," Operations Research, INFORMS, vol. 31(3), pages 488-506, June.
    14. Béatrice Rey & Jean-Charles Rochet, 2004. "Health and Wealth: How do They Affect Individual Preferences?*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 29(1), pages 43-54, June.
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