New characterization of Blackwell's order for subsets of information structures*

We provide a new characterization of Blackwell's order for two subsets of stochastic information structures with meaningful economic interpretations. First, we show that one doubly stochastic information structure is strictly more informative than another, if and only if the convex hull of the former and all of its permutations, which are equally informative, contains that of the latter. We further present another subset of stochastic information structures for which we show that Blackwell's order is complete.