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Probabilistic sophistication without completeness

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  • Karni, Edi

Abstract

This is a study of probabilistically sophisticated choice behavior when the preference relation is incomplete. Invoking the analytical framework of Anscombe and Aumann (1963) and building on the work of Machina and Schmeidler (1995), the paper provides an axiomatic characterization of the general multi-prior multi-utility probabilistically sophisticated representation. In addition, the paper examines the axiomatic foundations for two special cases: complete beliefs and complete tastes. In the former case, the incompleteness is due to ambiguous tastes and in latter case it is due to ambiguous beliefs.

Suggested Citation

  • Karni, Edi, 2020. "Probabilistic sophistication without completeness," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 8-13.
    • Handle: RePEc:eee:mateco:v:89:y:2020:i:c:p:8-13
    DOI: 10.1016/j.jmateco.2020.04.002
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    References listed on IDEAS

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    1. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
    2. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    3. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    4. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    5. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    6. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-189, January.
    7. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, January.
    8. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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    Cited by:

    1. Pierre Bardier & Bach Dong-Xuan & Van-Quy Nguyen, 2024. "Unanimity of two selves in decision making," Papers 2406.11166, arXiv.org.
    2. Karni, Edi & Vierø, Marie-Louise, 2023. "Comparative incompleteness: Measurement, behavioral manifestations and elicitation," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 423-442.
    3. Edi Karni, 2024. "Irresolute choice behavior," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(1), pages 70-87, March.

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