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One-Switch Independence 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

Assessment of multiattribute utility functions is significantly simplified if it is possible to decompose the function into more manageable pieces. Utility independence is a powerful property that serves well for this purpose, but if it is not appropriate in a given situation, what options does the analyst have? We review some possibilities and propose a new independence assumption based on the one-switch property. We argue that it is a natural generalization of utility independence and show how it leads to tractable multiattribute utility functions.

Suggested Citation

  • Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:764-771
    DOI: 10.1287/opre.1100.0911
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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. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    3. Peter C. Fishburn, 1974. "von Neumann-Morgenstera Utility Functions on Two Attributes," Operations Research, INFORMS, vol. 22(1), pages 35-45, February.
    4. Peter C. Fishburn, 1977. "Approximations of Two-Attribute Utility Functions," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 30-44, February.
    5. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    6. Craig W. Kirkwood, 1976. "Parametrically Dependent Preferences for Multiattributed Consequences," Operations Research, INFORMS, vol. 24(1), pages 92-103, February.
    7. Ralph L. Keeney & Robin S. Gregory, 2005. "Selecting Attributes to Measure the Achievement of Objectives," Operations Research, INFORMS, vol. 53(1), pages 1-11, February.
    8. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. 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.
    2. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    3. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    4. Jiehua Xie & Zhengyong Zhou, 2022. "Patchwork Constructions of Multiattribute Utility Functions," Decision Analysis, INFORMS, vol. 19(2), pages 141-169, June.
    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. Ilia Tsetlin & Robert L. Winkler, 2012. "Multiattribute One-Switch Utility," Management Science, INFORMS, vol. 58(3), pages 602-605, March.
    7. Ali E. Abbas, 2011. "The Multiattribute Utility Tree," Decision Analysis, INFORMS, vol. 8(3), pages 180-205, September.
    8. 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.
    9. Chen Wang & Vicki M. Bier, 2013. "Expert Elicitation of Adversary Preferences Using Ordinal Judgments," Operations Research, INFORMS, vol. 61(2), pages 372-385, April.
    10. Nina Anchugina, 2017. "One-Switch Discount Functions," Papers 1702.02254, arXiv.org.
    11. Kenneth C. Lichtendahl & Raul O. Chao & Samuel E. Bodily, 2012. "Habit Formation from Correlation Aversion," Operations Research, INFORMS, vol. 60(3), pages 625-637, June.
    12. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    13. Navin Kartik & SangMok Lee & Daniel Rappoport, 2022. "Single-Crossing Differences in Convex Environments," Papers 2212.12009, arXiv.org, revised Jun 2023.
    14. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    15. Ali E. Abbas & David E. Bell, 2015. "Ordinal One-Switch Utility Functions," Operations Research, INFORMS, vol. 63(6), pages 1411-1419, December.
    16. 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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