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Subjective multi-prior probability: A representation of a partial likelihood relation

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  • Alon, Shiri
  • Lehrer, Ehud

Abstract

This paper deals with an incomplete relation over events. Such a relation naturally arises when likelihood estimations are required within environments that involve ambiguity, and in situations which engage multiple assessments and disagreement among individuals' beliefs. The paper characterizes binary relations over events, interpreted as likelihood relations, that can be represented by a unanimity rule applied to a set of prior probabilities. According to this representation an event is at least as likely as another if and only if there is a consensus among all the priors that this is indeed the case. A key axiom employed is a cancellation condition, which is a simple extension of similar conditions that appear in the literature.

Suggested Citation

  • Alon, Shiri & Lehrer, Ehud, 2014. "Subjective multi-prior probability: A representation of a partial likelihood relation," Journal of Economic Theory, Elsevier, vol. 151(C), pages 476-492.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:476-492
    DOI: 10.1016/j.jet.2014.02.005
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    References listed on IDEAS

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    1. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
    2. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
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    6. Blume, Lawrence & Easley, David & Halpern, Joseph Y., 2021. "Constructive decision theory," Journal of Economic Theory, Elsevier, vol. 196(C).
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    Cited by:

    1. Wesley H. Holliday, 2024. "A partial-state space model of unawareness," Papers 2412.00897, arXiv.org, revised Dec 2024.
    2. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    3. Blume, Lawrence & Easley, David & Halpern, Joseph Y., 2021. "Constructive decision theory," Journal of Economic Theory, Elsevier, vol. 196(C).
    4. Matthew Harrison-Trainor & Wesley H. Holliday & Thomas F. Icard, 2016. "A note on cancellation axioms for comparative probability," Theory and Decision, Springer, vol. 80(1), pages 159-166, January.
    5. Borie, Dino, 2023. "Purely subjective revealed ambiguity," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    6. Holliday, Wesley H., 2025. "A partial-state space model of unawareness," Journal of Mathematical Economics, Elsevier, vol. 116(C).
    7. Shiri Alon & Aviad Heifetz, 2014. "The logic of Knightian games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 161-182, October.
    8. Harrison-Trainor, Matthew & Holliday, Wesley H. & Icard, Thomas F., 2018. "Inferring probability comparisons," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 62-70.
    9. Soo Hong Chew & Jacob S. Sagi & Wenqian Wang, 2025. "An exchangeability-based finite-state axiomatization of subjective probability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(3), pages 685-702, November.
    10. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).

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    JEL classification:

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

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