Sufficiency in Blackwell's theorem
نویسنده
چکیده
If one information service is more informative than the other, then any agent values it more. In fact, the opposite implication (sufficiency) is also true, and this characterization is the celebrated Blackwell’s theorem. We present here a short proof of sufficiency. Actually, we show a stronger result: it is enough to check whether the value of the service is greater than the value of the other for any fixed positive a priori probabilities and a set of terminal actions that has only two elements. 2003 Elsevier Science B.V. All rights reserved.
منابع مشابه
Sufficiency and Fuzziness in Random Experiments*
In previous papers, the consequences of the "presence of fuzziness" in the experimental information on which statistical inferences are based were discussed. Thus, the intuitive assertion ((fuzziness entails a loss of information)) was formalized, by comparing the information in the "exact case" with that in the "fuzzy case". This comparison was carried out through different criteria to compare...
متن کاملLecture : Blackwell's Approachability Theorem . Blackwell's Approachability Theorem
Counter-example to (.): If S = {(p,q) : p = q} and r(p,q) = (p,q), one can trivially, for all q, choose p(q) = q to guarantee that r(p(q),q) ∈ S. It is however not possible to find a p which works for all q, indeed the only p which works for a given q is p = q. However, the duality statement (.) holds when S is a half-space {x | v ·x ≥ c}. To see this, define a zero-sum game with scalar p...
متن کاملBirkhoff's Theorem from a geometric perspective: A simple example
From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometr...
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملZero - Sum Games with Vector - Valued Payoffs
In this lecture we formulate and prove the celebrated approachability theorem of Blackwell, which extends von Neumann's minimax theorem to zero-sum games with vector-valued payoffs [1]. (The proof here is based on the presentation in [2]; a similar presentation was given by Foster and Vohra [3].) This theorem is powerful in its own right, but also has significant implications for regret minimiz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical Social Sciences
دوره 46 شماره
صفحات -
تاریخ انتشار 2003