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We study repeated independent Blackwell experiments; standard examplesinclude drawing multiple samples from a population, or performing a measurementin different locations. In the baseline setting of a binary state of nature, wecompare experiments in terms of their informativeness in large samples.Addressing a question due to Blackwell (1951), we show that generically anexperiment is more informative than another in large samples if and only if ithas higher Renyi divergences.  We apply our analysis to the problem of measuring the degree of dissimilaritybetween distributions by means of divergences. A useful property of Renyidivergences is their additivity with respect to product distributions. Ourcharacterization of Blackwell dominance in large samples implies that everyadditive divergence that satisfies the data processing inequality is anintegral of Renyi divergences.

From Blackwell Dominance in Large Samples to Renyi Divergences and Back Again