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Multiplicative Utilities for Health and Consumption


  • Kenneth C. Lichtendahl

    () (Darden School of Business, University of Virginia, Charlottesville, Virginia 22903)

  • Samuel E. Bodily

    () (Darden School of Business, University of Virginia, Charlottesville, Virginia 22903)


Many challenging medical/financial decisions require a decision maker to express preferences for lifetime streams of health and consumption. To express such preferences, we develop two multiplicative utility forms from basic conditions. These forms have many advantages over the leading additive form and extend the way in which life years are adjusted in the popular quality-adjusted life-year model. Unlike additive forms, a decision maker with one of our multiplicative forms can express correlation aversion in consumption streams. In the special case of constant health and consumption streams, our forms reduce to a double exponential utility in life duration. When the decision maker is correlation averse in consumption streams, this form can express risk aversion, decreasing absolute risk aversion and increasing relative risk aversion in life duration. This reduced form under correlation aversion also has standard gamble probabilities (proportional time trade-offs) that increase (decrease) in life duration. In addition, it has standard gamble probabilities that exceed proportional time trade-offs. The properties of this reduced form under correlation seekingness are also examined and discussed in the context of the empirical evidence on attitudes toward risks in life duration, standard gamble probabilities, and proportional time trade-offs.

Suggested Citation

  • Kenneth C. Lichtendahl & Samuel E. Bodily, 2012. "Multiplicative Utilities for Health and Consumption," Decision Analysis, INFORMS, vol. 9(4), pages 314-328, December.
  • Handle: RePEc:inm:ordeca:v:9:y:2012:i:4:p:314-328

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    References listed on IDEAS

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    Cited by:

    1. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Enrico Diecidue & Robin L. Dillon-Merrill & Raimo P. Hämäläinen & Kenneth C. Lichtendahl & Jason R. W, 2012. "From the Editors ---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus," Decision Analysis, INFORMS, vol. 9(4), pages 297-302, December.
    2. Rakesh K. Sarin, 2013. "From the Editor —Optimal Betting, Reducing Unnecessary Mammography in Breast Cancer Diagnosis, Product Line Design, and Value of Information," Decision Analysis, INFORMS, vol. 10(3), pages 187-188, September.
    3. Yongzhi Cao, 2014. "Reducing Interval-Valued Decision Trees to Conventional Ones: Comments on Decision Trees with Single and Multiple Interval-Valued Objectives," Decision Analysis, INFORMS, vol. 11(3), pages 204-212, September.
    4. Marc St-Pierre, 2017. "Risk-induced discounting," Theory and Decision, Springer, vol. 82(1), pages 13-30, January.
    5. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.


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