  We study repeated independent Blackwell experiments; standard examples
include drawing multiple samples from a population, or performing a measurement
in different locations. In the baseline setting of a binary state of nature, we
compare experiments in terms of their informativeness in large samples.
Addressing a question due to 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.
  We apply our analysis to the problem of measuring the degree of dissimilarity
between distributions by means of divergences. A useful property of Renyi
divergences is their additivity with respect to product distributions. Our
characterization of Blackwell dominance in large samples implies that every
additive divergence that satisfies the data processing inequality is an
integral of Renyi divergences.
