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Coherent Decision Analysis with Inseparable Probabilities and Utilities

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  • Nau, Robert F

Abstract

This article explores the extent to which a decisionmaker's probabilities can be measured separately from his/her utilities by observing his/her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partitioned into a set of "belief gambles," which reveals probabilities distorted by marginal utilities for money, and a set of "preference gambles," which reveals utilities reciprocally distorted by marginal utilities for money. However, the information in these gambles still enables us to solve the decisionmaker's problem: his/her utility-maximizing decision is the one that avoids arbitrage (i.e., incoherence or Dutch books). Copyright 1995 by Kluwer Academic Publishers

Suggested Citation

  • Nau, Robert F, 1995. "Coherent Decision Analysis with Inseparable Probabilities and Utilities," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 71-91, January.
    • Handle: RePEc:kap:jrisku:v:10:y:1995:i:1:p:71-91
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    Citations

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    Cited by:

    1. Crocker, Thomas D. & Shogren, Jason F. & Turner, Paul R., 1998. "Incomplete beliefs and nonmarket valuation," Resource and Energy Economics, Elsevier, vol. 20(2), pages 139-162, June.
    2. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    3. Enrico Diecidue & Peter Wakker & Marcel Zeelenberg, 2007. "Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 179-199, June.
    4. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    5. David M. Pennock & Michael P. Wellman, 2013. "Compact Securities Markets for Pareto Optimal Reallocation of Risk," Papers 1301.3886, arXiv.org.
    6. Enrico Diecidue & Dolchai La-ornual, 2009. "Reconciling support theory and the book-making principle," Journal of Risk and Uncertainty, Springer, vol. 38(3), pages 173-190, June.
    7. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    8. Christian Gollier, 2007. "Whom should we believe? Aggregation of heterogeneous beliefs," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 107-127, October.
    9. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    10. Edi Karni, 2011. "Subjective Probabilities on a State Space," American Economic Journal: Microeconomics, American Economic Association, vol. 3(4), pages 172-185, November.
    11. Edi Karni, 2013. "Bayesian decision theory with action-dependent probabilities and risk attitudes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 335-356, June.
    12. Edi Karni, 2007. "Bayesian Decision Theory and the Representation of Beliefs," Discussion Paper Series dp444, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    13. MacLaren, D., 1995. "Uncertainty AVersion and Technical Barriers to Trade: An Australian Example," Department of Economics - Working Papers Series 498, The University of Melbourne.
    14. Edi Karni, 2009. "A Theory of Bayesian Decision Making," EIEF Working Papers Series 0904, Einaudi Institute for Economics and Finance (EIEF), revised May 2009.
    15. David M. Pennock & Michael P. Wellman, 2005. "Graphical Models for Groups: Belief Aggregation and Risk Sharing," Decision Analysis, INFORMS, vol. 2(3), pages 148-164, September.
    16. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Jul 2023.
    17. Robert F. Nau, 2003. "A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility," Management Science, INFORMS, vol. 49(8), pages 1089-1104, August.
    18. Grant, Andrew & Johnstone, David & Kwon, Oh Kang, 2019. "The cost of capital in a prediction market," International Journal of Forecasting, Elsevier, vol. 35(1), pages 313-320.
    19. Peter P. Wakker & Sylvia J. T. Jansen & Anne M. Stiggelbout, 2004. "Anchor Levels as a New Tool for the Theory and Measurement of Multiattribute Utility," Decision Analysis, INFORMS, vol. 1(4), pages 217-234, December.

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