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Incomplete preferences and confidence

Author

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  • Hill, Brian
Abstract
A theory of incomplete preferences under uncertainty is proposed, according to which a decision maker’s preferences are indeterminate if and only if her confidence in the relevant beliefs does not match up to the stakes involved in the decision. We use the representation of confidence in beliefs introduced in Hill (2013), and axiomatise a class of models, differing from each other in the appropriate notion of stakes. The theory naturally suggests two distinct strategies for completing preferences, and hence for choosing in the presence of incompleteness: one that relies only on beliefs in which the decision maker is sufficiently confident, and one that mobilises all beliefs, no matter how little confidence she may have in them. Axiomatic characterisations are given for completion procedures following each of the strategies. Finally, in a market setting, the incorporation of confidence is shown to add an extra friction, beyond the standard implications of non-expected utility models for Pareto optima.

Suggested Citation

  • Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    • Handle: RePEc:eee:mateco:v:65:y:2016:i:c:p:83-103
    DOI: 10.1016/j.jmateco.2016.05.007
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    References listed on IDEAS

    as
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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. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    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.
    4. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," SIRE Discussion Papers 2015-17, Scottish Institute for Research in Economics (SIRE).
    5. Echenique, Federico & Miyashita, Masaki & Nakamura, Yuta & Pomatto, Luciano & Vinson, Jamie, 2022. "Twofold multiprior preferences and failures of contingent reasoning," Journal of Economic Theory, Elsevier, vol. 202(C).
    6. Minardi, Stefania & Savochkin, Andrei, 2015. "Preferences with grades of indecisiveness," Journal of Economic Theory, Elsevier, vol. 155(C), pages 300-331.
    7. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," SIRE Discussion Papers 2015-17, Scottish Institute for Research in Economics (SIRE).
    8. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-17, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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    More about this item

    Keywords

    Incomplete preferences; Confidence; Multiple priors; Choice under incomplete preferences; Absence of trade;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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