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Hoping for the best while preparing for the worst in the face of uncertainty: a new type of incomplete preferences

Author

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  • Bardier, Pierre

    (Center for Mathematical Economics, Bielefeld University)

  • Dong-Xuan, Bach

    (Center for Mathematical Economics, Bielefeld University)

  • Nguyen, Van-Quy

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We propose and axiomatize a new model of incomplete preferences under uncertainty, which we call *hope-and-prepare preferences*. An act is considered more desirable than another when, and only when, both an optimistic evaluation, computed as the welfare level attained in a best-case scenario, and a pessimistic one, computed as the welfare level attained in a worst-case scenario, rank the former above the latter. Our comparison criterion involves multiple priors, as best and worst cases are determined among sets of probability distributions. We make the case that, compared to existing incomplete criteria under ambiguity, hope-and-prepare preferences address the trade-off between conviction and decisiveness in a new way, which is more favorable to decisiveness.

Suggested Citation

  • Bardier, Pierre & Dong-Xuan, Bach & Nguyen, Van-Quy, 2025. "Hoping for the best while preparing for the worst in the face of uncertainty: a new type of incomplete preferences," Center for Mathematical Economics Working Papers 701, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:701
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    File URL: https://pub.uni-bielefeld.de/download/3000922/3000923
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    References listed on IDEAS

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    1. David K. Levine & Drew Fudenberg, 2006. "A Dual-Self Model of Impulse Control," American Economic Review, American Economic Association, vol. 96(5), pages 1449-1476, December.
    2. Jianming Xia, 2020. "Decision Making under Uncertainty: A Game of Two Selves," Papers 2012.07509, arXiv.org.
    3. Thaler, Richard H & Shefrin, H M, 1981. "An Economic Theory of Self-Control," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 392-406, April.
    4. Nascimento, Leandro & Riella, Gil, 2011. "A class of incomplete and ambiguity averse preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 728-750, March.
    5. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    6. Hartmann, Lorenz, 2023. "Strength of preference over complementary pairs axiomatizes alpha-MEU preferences," Journal of Economic Theory, Elsevier, vol. 213(C).
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    Cited by:

    1. Kensei Nakamura & Shohei Yanagita, 2025. "Partially rational preferences under ambiguity," Papers 2509.11660, arXiv.org.

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