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On the Nonexistence of Blackwell's Theorem-Type Results with General Preference Relations

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  • Safra, Zvi
  • Sulganik, Eyal

Abstract

A well-known theorem of Blackwell states that, when quantity of information is properly defined, every expected utility decisionmaker prefers more information to less; for more general preferences, however, the theorem is no longer true. In this article, we investigate the extent to which Blackwell's Theorem does not hold and describe conditions, and situations, under which information is still valuable. We also show that, for many types of additions of information, there exists a decision maker who will reject this information. Copyright 1995 by Kluwer Academic Publishers

Suggested Citation

  • Safra, Zvi & Sulganik, Eyal, 1995. "On the Nonexistence of Blackwell's Theorem-Type Results with General Preference Relations," Journal of Risk and Uncertainty, Springer, vol. 10(3), pages 187-201, May.
    • Handle: RePEc:kap:jrisku:v:10:y:1995:i:3:p:187-201
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    Citations

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    Cited by:

    1. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1998. "Intrinsic Preference for Information," Journal of Economic Theory, Elsevier, vol. 83(2), pages 233-259, December.
    2. B. Bassan & O. Gossner & M. Scarsini & S. Zamir., 1999. "A class of games with positive value of information," THEMA Working Papers 99-32, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Preference for Information and Dynamic Consistency," Theory and Decision, Springer, vol. 48(3), pages 263-286, May.
    4. Feiler, Lauren, 2014. "Testing models of information avoidance with binary choice dictator games," Journal of Economic Psychology, Elsevier, vol. 45(C), pages 253-267.
    5. Rommeswinkel, Hendrik & Chang, Hung-Chi & Hsu, Wen-Tai, 2023. "Preference for Knowledge," Journal of Economic Theory, Elsevier, vol. 214(C).
    6. Roxane Bricet, 2018. "The price for instrumentally valuable information," THEMA Working Papers 2018-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Dillenberger, David, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," MPRA Paper 8342, University Library of Munich, Germany.
    8. Karni, Edi & Safra, Zvi, 2022. "Hybrid decision model and the ranking of experiments," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    9. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2003. "Positive value of information in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 17-31, December.
    10. Mark Whitmeyer, 2023. "Blackwell-Monotone Updating Rules," Papers 2302.13956, arXiv.org, revised Nov 2024.
    11. Eliaz, Kfir & Spiegler, Ran, 2006. "Can anticipatory feelings explain anomalous choices of information sources?," Games and Economic Behavior, Elsevier, vol. 56(1), pages 87-104, July.
    12. David Dillenberger, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," PIER Working Paper Archive 08-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Li, Jian & Zhou, Junjie, 2016. "Blackwell's informativeness ranking with uncertainty-averse preferences," Games and Economic Behavior, Elsevier, vol. 96(C), pages 18-29.

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