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Ordinal One-Switch Utility Functions

Author

Listed:
  • Ali E. Abbas

    (University of Southern California, Los Angeles, California 90089)

  • David E. Bell

    (Harvard Business School, Boston, Massachusetts 02163)

Abstract

We study the problem of finding ordinal utility functions to rank the outcomes of a decision when preference independence between the attributes is not present. We propose that the next level of complexity is to assume that preferences over one attribute can switch at most once as another attribute varies from low to high. We refer to this property as ordinal one-switch independence. We present both necessary and sufficient conditions for this ordinal property to hold and provide families of functions that satisfy this new property.

Suggested Citation

  • Ali E. Abbas & David E. Bell, 2015. "Ordinal One-Switch Utility Functions," Operations Research, INFORMS, vol. 63(6), pages 1411-1419, December.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:6:p:1411-1419
    DOI: 10.1287/opre.2015.1426
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    References listed on IDEAS

    as
    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. 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.
    3. Ali E. Abbas, 2007. "Invariant Utility Functions and Certain Equivalent Transformations," Decision Analysis, INFORMS, vol. 4(1), pages 17-31, March.
    4. Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    5. Peter C. Fishburn, 1974. "von Neumann-Morgenstera Utility Functions on Two Attributes," Operations Research, INFORMS, vol. 22(1), pages 35-45, February.
    6. Peter C. Fishburn, 1977. "Approximations of Two-Attribute Utility Functions," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 30-44, February.
    7. Peter H. Farquhar, 1975. "A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 23(5), pages 941-967, October.
    8. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    9. David E. Bell, 1979. "Multiattribute Utility Functions: Decompositions Using Interpolation," Management Science, INFORMS, vol. 25(8), pages 744-753, August.
    10. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
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    Citations

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    Cited by:

    1. Nina Anchugina, 2017. "One-Switch Discount Functions," Papers 1702.02254, arXiv.org.
    2. Ali E. Abbas & Zhengwei Sun, 2019. "Archimedean Utility Copulas with Polynomial Generating Functions," Decision Analysis, INFORMS, vol. 16(3), pages 218-237, September.

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    Keywords

    utility theory; dependence;

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