In the mathematical subjects of information theory and decision theory, Blackwell's informativeness theorem is an important result related to the ranking of information structures, or experiments. It states that there is an equivalence between three possible rankings of information structures: one based in expected utility, one based in informativeness, and one based in feasibility. This ranking defines a partial order over information structures known as the Blackwell order, or Blackwell's criterion.[1][2]
The theorem states equivalent conditions under which any expected utility maximizing decision maker prefers information structure over , for any decision problem. The result was first proven by David Blackwell in 1951, and generalized in 1953.[3][4]
- ^ de Oliveira, Henrique (2018). "Blackwell's informativeness theorem using diagrams". Games and Economic Behavior. 109: 126–131. doi:10.1016/j.geb.2017.12.008.
- ^ Kosenko, Andre (2021). "Algebraic Properties of Blackwell's Order and A Cardinal Measure of Informativeness". arXiv:2110.11399 [econ.TH].
- ^ Blackwell, David (1951). "Comparison of Experiments". Second Berkeley Symposium on Mathematical Statistics and Probability: 2.
- ^ Blackwell, David (1953). "Equivalent comparison of experiments". The Annals of Mathematical Statistics. 24 (2): 265–272. doi:10.1214/aoms/1177729032.