We establish laws of large numbers for comparing sums of i.i.d. random variables in terms of stochastic dominance. Our results shed new light on a classic question, raised first by Samuelson (1963), on the relation between expected utility, risk aversion, and the aggregation of independent risks . 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  .
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 . 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 .
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establish laws of large numbers for comparing sums of i.i.d. random variables in terms of stochastic dominance. Our results shed new light on a classic question, raised first by Samuelson (1963), on the relation between expected utility, risk aversion, and the aggregation of independent risks
study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations
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context of statistical experiments, we answer a long-standing open question posed by
baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to
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. 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