Before revision:  In the context of statistical experiments, we answer a long-standing open question posed by Blackwell (1951) : we show that generically, an experiment is more informative than another in large samples if and only if it has higher Renyi divergences  .
After revision:  In the context of statistical experiments, we answer a long-standing open question posed by Blackwell (1951) : we show that generically, an experiment is more informative than another in large samples if and only if it has higher Renyi divergences . As an application of our techniques we in addition provide a novel characterization of kth-order stochastic dominance as second-order stochastic dominance of large i.i.d. sums .