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METHODS---One-Switch Conditions for Multiattribute Utility Functions

Author

Listed:
  • Ali E. Abbas

    (University of Illinois at Urbana--Champaign, Urbana, Illinois 61820)

  • David E. Bell

    (Harvard Business School, Boston, Massachusetts 02163)

Abstract

We introduce a variety of new independence conditions for multiattribute utility functions that permit preference dependencies among the attributes of a decision problem. The hierarchy of new conditions varies in the degree to which it specifies the functional form, ranging from more general solutions with weaker constraints, to more specific solutions with stronger constraints. This formulation provides a wealth of new functional forms that a decision maker may use in a multiattribute decision problem. In addition, it may be used to tailor the utility elicitation process to the comfort level of the decision maker. The new conditions, and the corresponding functional forms, are based on the idea of limiting the number of switches that a decision maker may make between two decision alternatives as a parameter of the problem varies. We show how this formulation also relates many widely used concepts in single and multiattribute utility theory.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1199-1212
    DOI: 10.1287/opre.1120.1088
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    References listed on IDEAS

    as
    1. Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    2. Peter C. Fishburn, 1974. "von Neumann-Morgenstera Utility Functions on Two Attributes," Operations Research, INFORMS, vol. 22(1), pages 35-45, February.
    3. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    4. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    5. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    6. Ali E. Abbas & János Aczél, 2010. "The Role of Some Functional Equations in Decision Analysis," Decision Analysis, INFORMS, vol. 7(2), pages 215-228, June.
    7. Peter C. Fishburn, 1977. "Approximations of Two-Attribute Utility Functions," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 30-44, February.
    8. Ilia Tsetlin & Robert L. Winkler, 2012. "Multiattribute One-Switch Utility," Management Science, INFORMS, vol. 58(3), pages 602-605, March.
    9. David E. Bell, 1979. "Consistent Assessment Procedures Using Conditional Utility Functions," Operations Research, INFORMS, vol. 27(5), pages 1054-1066, October.
    10. David E. Bell, 1986. "Double-Exponential Utility Functions," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 351-361, May.
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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, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    3. 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.
    4. 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.
    5. Ali E. Abbas & David E. Bell, 2015. "Ordinal One-Switch Utility Functions," Operations Research, INFORMS, vol. 63(6), pages 1411-1419, December.

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