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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 R\u00e9nyi divergences.<\/jats:p>\n                  <jats:p>We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of R\u00e9nyi 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 R\u00e9nyi divergences.<\/jats:p>","DOI":"10.3982\/ecta17548","type":"journal-article","created":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T03:05:05Z","timestamp":1610420705000},"page":"475-506","source":"Crossref","is-referenced-by-count":24,"title":["From Blackwell Dominance in Large Samples to R\u00e9nyi Divergences and Back Again"],"prefix":"10.3982","volume":"89","author":[{"given":"Xiaosheng","family":"Mu","sequence":"first","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luciano","family":"Pomatto","sequence":"additional","affiliation":[{"name":"Division of the Humanities and Social Sciences, Caltech"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philipp","family":"Strack","sequence":"additional","affiliation":[{"name":"Department of Economics, Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Omer","family":"Tamuz","sequence":"additional","affiliation":[{"name":"Division of the Humanities and Social Sciences, Caltech"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2021]]},"reference":[{"issue":"1","key":"ecta200239-bib-0001","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s00220-007-0382-4","volume":"278","author":"Aubrun","year":"2008","journal-title":"Communications in Mathematical Physics"},{"issue":"1","key":"ecta200239-bib-0002","doi-asserted-by":"crossref","first-page":"415","DOI":"10.3982\/ECTA11127","volume":"82","author":"Azrieli","year":"2014","journal-title":"Econometrica"},{"key":"ecta200239-bib-0003","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1525\/9780520411586-009","volume-title":"Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability","author":"Blackwell","year":"1951"},{"issue":"2","key":"ecta200239-bib-0004","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1214\/aoms\/1177729032","volume":"24","author":"Blackwell","year":"1953","journal-title":"The Annals of Mathematical Statistics"},{"key":"ecta200239-bib-0005","volume-title":"Theory of Games and Statistical Decisions","author":"Blackwell","year":"1979"},{"key":"ecta200239-bib-0006","unstructured":"Bohnenblust, H. 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