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Risk, Ambiguity, and the Rank-Dependence Axioms

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  • Mark J. Machina

Abstract

Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent ("Choquet expected utility") preferences over subjective gambles might be subject to the same difficulties that Ellsberg's earlier examples posed for subjective expected utility. These difficulties stem from event-separability properties that rank-dependent preferences partially retain from expected utility, and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes. (JEL D81)

Suggested Citation

  • Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-392, March.
  • Handle: RePEc:aea:aecrev:v:99:y:2009:i:1:p:385-92
    Note: DOI: 10.1257/aer.99.1.385
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    References listed on IDEAS

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    1. repec:ebl:ecbull:v:4:y:2008:i:19:p:1-6 is not listed on IDEAS
    2. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    3. A. Marley & R. Luce, 2005. "Independence Properties Vis-À-Vis Several Utility Representations," Theory and Decision, Springer, vol. 58(1), pages 77-143, February.
    4. Laetitia Placido & Olivier L'Haridon, 2008. "An allais paradox for generalized expected utility theories?," Economics Bulletin, AccessEcon, vol. 4(19), pages 1-6.
    5. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    6. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
    7. Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 39-60, July.
    8. Fennema, Hein & Wakker, Peter, 1996. "A Test of Rank-Dependent Utility in the Context of Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 13(1), pages 19-35, July.
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    Citations

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    Cited by:

    1. André Lapied & Pascal Toquebeuf, 2011. "Dynamically consistent CEU preferences," Working Papers halshs-00856193, HAL.
    2. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    3. Roee Teper, 2015. "Subjective Independence and Concave Expected Utility," Working Paper 5865, Department of Economics, University of Pittsburgh.
    4. David B. BROWN & Enrico G. DE GIORGI & Melvyn SIM, "undated". "A Satiscing Alternative to Prospect Theory," Swiss Finance Institute Research Paper Series 09-19, Swiss Finance Institute.
    5. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
    6. repec:eee:jetheo:v:171:y:2017:i:c:p:213-267 is not listed on IDEAS
    7. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    8. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    9. Blavatskyy, Pavlo R., 2013. "Two examples of ambiguity aversion," Economics Letters, Elsevier, vol. 118(1), pages 206-208.
    10. Grant, S. & Kline, J. & Meneghel, I. & Quiggin, J. & Tourky, R., 2016. "A theory of robust experiments for choice under uncertainty," Journal of Economic Theory, Elsevier, vol. 165(C), pages 124-151.
    11. Chambers, Robert G. & Grant, Simon & Polak, Ben & Quiggin, John, 2014. "A two-parameter model of dispersion aversion," Journal of Economic Theory, Elsevier, vol. 150(C), pages 611-641.
    12. Enrico G. De Giorgi & David B. Brown & Melvyn Sim, 2010. "Dual representation of choice and aspirational preferences," University of St. Gallen Department of Economics working paper series 2010 2010-07, Department of Economics, University of St. Gallen.
    13. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    14. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    15. Bommier, Antoine, 2017. "A dual approach to ambiguity aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 104-118.
    16. repec:kap:jrisku:v:54:y:2017:i:3:d:10.1007_s11166-017-9260-4 is not listed on IDEAS
    17. Laure Cabantous & Denis Hilton & Howard Kunreuther & Erwann Michel-Kerjan, 2011. "Is imprecise knowledge better than conflicting expertise? Evidence from insurers’ decisions in the United States," Journal of Risk and Uncertainty, Springer, vol. 42(3), pages 211-232, June.
    18. Lehrer, Ehud & Teper, Roee, 2015. "Subjective independence and concave expected utility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 33-53.
    19. Peysakhovich, Alexander & Naecker, Jeffrey, 2017. "Using methods from machine learning to evaluate behavioral models of choice under risk and ambiguity," Journal of Economic Behavior & Organization, Elsevier, vol. 133(C), pages 373-384.
    20. Abhinash Borah & Christopher Kops, 2016. "The Anscombe–Aumann representation and the independence axiom: a reconsideration," Theory and Decision, Springer, vol. 80(2), pages 211-226, February.
    21. Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.
    22. Özgür Evren, 2017. "Cautious and Globally Ambiguity Averse," Working Papers w0236, Center for Economic and Financial Research (CEFIR).

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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