Journal of Applied Probability

Two remarks on Blackwell's theorem

Ehud Lehrer and Eran Shmaya

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In a decision problem with uncertainty a decision maker receives partial information about the actual state via an information structure. After receiving a signal, he is allowed to withdraw and gets zero profit. We say that one structure is better than another when a withdrawal option exists if it may never happen that one structure guarantees a positive profit while the other structure guarantees only zero profit. This order between information structures is characterized in terms that are different from those used by Blackwell's comparison of experiments. We also treat the case of a malevolent nature that chooses a state in an adverse manner. It turns out that Blackwell's classical characterization also holds in this case.

Article information

J. Appl. Probab. Volume 45, Number 2 (2008), 580-586.

First available: 1 July 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46N10: Applications in optimization, convex analysis, mathematical programming, economics 62C10: Bayesian problems; characterization of Bayes procedures 62C20: Minimax procedures 91B06: Decision theory [See also 62Cxx, 90B50, 91A35] 91B08: Individual preferences

Blackwell's comparison of experiments withdrawal option Bayesian decision problem minimax


Lehrer, Ehud; Shmaya, Eran. Two remarks on Blackwell's theorem. Journal of Applied Probability 45 (2008), no. 2, 580--586. doi:10.1239/jap/1214950370.

Export citation


  • Blackwell, D. (1953). Equivalent comparisons of experiments. Ann. Math. Statist. 24, 265--272.
  • Le Cam, L. (1996). Comparison of experiments---a short review. In Statistics, Probability and Game Theory (IMS Lecture Notes Monogr. Ser. 30), eds T. Ferguson and L. Shapley, Institute of Mathematical Statistics, Hayward, CA, pp. 127--138.
  • Torgersen, E. N. (1991). Comparison of Statistical Experiments. Cambridge University Press.
  • Tversky A. and Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science 211, 453--458.