Journal of Risk and Uncertainty

, Volume 10, Issue 3, pp 187–201 | Cite as

On the nonexistence of Blackwell's theorem-type results with general preference relations

  • Zvi Safra
  • Eyal Sulganik
Article

Abstract

A well-known theorem of Blackwell states that, when quantity of information is properly defined, every expected utility decision maker 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.

Key words

Blackwell's Theorem value of information nonexpected utility preferences 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blackwell, D. (1953). “Equivalent Comparison of Experiments,”Annals of Mathematics and Statistics 24, 265–272.Google Scholar
  2. Border, K., and U. Segal. (1994). “Dynamic Consistency implies approximately Expected Utility,”Journal of Economic Theory 63, 170–188.Google Scholar
  3. Chew, S. H., and L. G. Epstein. (1989). “The Structure of Preferences and Attitudes Towards the Timing of the Resolution of Uncertainty, “International Economic Review 30, 103–117.Google Scholar
  4. Debreu, G. (1972). “Smooth Preferences,”Econometrica 40, 603–615.Google Scholar
  5. Epstein, L. G. (1990). “Behavior under Risk: Recent Developments in Theory and Applications.” InAdvances in Economic Theory, J.J. Laffont (ed.), Cambridge Univ. Press.Google Scholar
  6. Fishburn, P. C. (1988).Nonlinear Preferences and Utility Theory. Baltimore. Johns Hopkins University Press.Google Scholar
  7. Green, J. R., and N. L. Stokey. (1980). “A Two-person Game of Information Transmission.” H.I.E.R. Discussion Paper No. 751.Google Scholar
  8. Hilton, R. W. (1990). “Failure of Blackwell's Theorem under Machina's Generalization of Expected-Utility Analysis without the Independence Axiom,”Journal of Economic Behavior and Organization 13, 233–244.Google Scholar
  9. Karni, E., and Z. Safra. (1989). “Ascending Bid Auctions with Behaviorally Consistent Bidders,”Annals of Operations Research 19, 435–446.Google Scholar
  10. Karni, E., and Z. Safra. (1990). “Behaviorally Consistent Optimal Stopping Rules,”Journal of Economic Theory 51, 391–402.Google Scholar
  11. Kami, E., and D. Schmeidler. (1990). “Utility Theory and Uncertainty.” In W. Hildenbrand and H. Sonnenschein (eds.),Handbook of Mathematical Economics IV, North Holland Publishing Company.Google Scholar
  12. Machina, M. (1987). “Choice under Uncertainty: Problems Solved and Unsolved,”Journal of Economic Perspectives 1, 121–154.Google Scholar
  13. Machina, M. (1989). “Dynamic Consistency and Non-Expected Utility Models of Choice under Uncertainty,”Journal of Economic Literature 4, 1622–1668.Google Scholar
  14. McClennen, E. F. (1990).Rationality and Dynamic Choice. Cambridge University Press.Google Scholar
  15. Newman, D. P. (1980). “Prospect Theory: Implications for Information Evaluation,”Accounting Organizations and Society 5, 217–230.Google Scholar
  16. Quiggin, J. (1982). “A Theory of Anticipated Utility,”Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
  17. Schlee, E. (1990). “The Value of Information in Anticipated Utility Theory,”Journal of Risk and Uncertainty 3, 83–92.Google Scholar
  18. Schlee, E. (1991). “The Value of Perfect Information in Nonlinear Utility Theory,”Theory and Decision 30, 127–131.Google Scholar
  19. Segal, U. (1987). “The Eisberg Paradox and Risk Aversion: An Anticipated Utility Approach,”International Economic Review 28, 175–202.Google Scholar
  20. Segal, U. (1990). “Two-stage Lotteries without the Reduction Axiom,”Econometrica 58, 349–377.Google Scholar
  21. Wakker, P. (1988). “Nonexpected Utility as Aversion of Information,”Journal of Behavioral Decision Making 1, 169–175.Google Scholar
  22. Weymark, J. A. (1981). “Generalized Gini Inequality Indices,”Mathematical Social Sciences 1, 409–430.Google Scholar
  23. Yaari, M. E. (1987). “The Dual Theory of Choice Under Risk,”Econometrica 55, 95–105.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Zvi Safra
    • 1
  • Eyal Sulganik
    • 2
  1. 1.Faculty of ManagementTel Aviv UniversityRamat-AvivIsrael
  2. 2.Department of EconomicsTel Aviv UniversityRamat-AvivIsrael

Personalised recommendations