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von Neumann-Morgenstera Utility Functions on Two Attributes

Author

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  • Peter C. Fishburn

    (The Pennsylvania State University, University Park, Pennsylvania)

Abstract

Five special forms for a von Neumann-Morgenstern utility function u on a product set A × X are examined. Each expresses u as a combination of functions defined on the separate factors A and X . The five forms include the additive and multiplicative forms, u = u 1 + u 2 and u = f 1 f 2 , respectively, and the additive form with independent product expressed by u = u 1 + u 2 + f 1 f 2 . Necessary and sufficient preference conditions are identified for each form, along with admissible transformations on the single-argument functions.

Suggested Citation

  • Peter C. Fishburn, 1974. "von Neumann-Morgenstera Utility Functions on Two Attributes," Operations Research, INFORMS, vol. 22(1), pages 35-45, February.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:1:p:35-45
    DOI: 10.1287/opre.22.1.35
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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. Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    3. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.
    4. 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.
    5. 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.
    6. 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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