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Proximal Decision Analysis

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  • Ronald A. Howard

    (Stanford University)

Abstract

This paper presents simplified techniques for analyzing the effect of uncertainty in large decision problems. Starting with the development of approximate expressions for the moments of a value lottery, we show that the probabilistic assessments of jointly related random variables necessary for these approximations are quite reasonable in number. The concepts of risk aversion, certain equivalent, and exponential utility function then permit writing useful approximations for the certain equivalent of the value lottery. Deterministic sensitivity analyses are described first for the case when the decision variables are fixed and then for the case when they can be changed to compensate for variations in state variables. The approximate effect and value of clairvoyance (revelation of ultimate values of uncertain variables) is derived from the original probabilistic assessment and the results of the deterministic sensitivity analysis. We next determine the approximate value of wizardry (changing uncertain variables into decision variables). The amount by which decision variables must be adjusted to account for risk aversion is established from earlier results. The final portion of the paper discusses a simple economic example that illustrates the application of the development.

Suggested Citation

  • Ronald A. Howard, 1971. "Proximal Decision Analysis," Management Science, INFORMS, vol. 17(9), pages 507-541, May.
    • Handle: RePEc:inm:ormnsc:v:17:y:1971:i:9:p:507-541
    DOI: 10.1287/mnsc.17.9.507
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    Citations

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    Cited by:

    1. Abbas, 2004. "Utility Probability Duality," General Economics and Teaching 0403001, University Library of Munich, Germany.
    2. Logan, Douglas M., 1990. "5.4. Decision analysis in engineering-economic modeling," Energy, Elsevier, vol. 15(7), pages 677-696.
    3. Pelin G. Canbolat & Uriel G. Rothblum, 2019. "Constant risk aversion in stochastic contests with exponential completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 4-14, February.
    4. Ali E. Abbas & James E. Matheson & Robert F. Bordley, 2009. "Effective utility functions induced by organizational target-based incentives," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(4), pages 235-251.
    5. J. Eric Bickel, 2008. "The Relationship Between Perfect and Imperfect Information in a Two-Action Risk-Sensitive Problem," Decision Analysis, INFORMS, vol. 5(3), pages 116-128, September.
    6. Jens Gudmundsson & Jens Leth Hougaard, 2020. "Enabling reciprocity through blockchain design," IFRO Working Paper 2020/14, University of Copenhagen, Department of Food and Resource Economics, revised 09 Feb 2021.
    7. LaValle, Irving H. & Fishburn, Peter C., 1996. "On the varieties of matrix probabilities in nonarchimedean decision theory," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 33-54.
    8. Philippe Delquié, 2008. "Interpretation of the Risk Tolerance Coefficient in Terms of Maximum Acceptable Loss," Decision Analysis, INFORMS, vol. 5(1), pages 5-9, March.
    9. Christopher Raphael, 2003. "Bayesian Networks with Degenerate Gaussian Distributions," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 235-263, June.
    10. John M. Charnes & Prakash P. Shenoy, 2004. "Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation," Management Science, INFORMS, vol. 50(3), pages 405-418, March.
    11. Yijing Li & Prakash P. Shenoy, 2012. "A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions," Decision Analysis, INFORMS, vol. 9(1), pages 55-75, March.
    12. Ali Abbas, 2010. "Invariant multiattribute utility functions," Theory and Decision, Springer, vol. 68(1), pages 69-99, February.
    13. Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, November.

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