Sherman  and Stein  have shown that a method given by the author  for comparing two experiments is equivalent, for experiments with a finite number of outcomes, to the original method introduced by Bohnenblust, Shapley, and Sherman . A new proof of this result is given, and the restriction to experiments with a finite number of outcomes is removed. A class of weaker comparisons--comparison in $k$-decision problems--is introduced, in three equivalent forms. For dichotomies, all methods are equivalent, and can be described in terms of errors of the first and second kinds.
"Equivalent Comparisons of Experiments." Ann. Math. Statist. 24 (2) 265 - 272, June, 1953. https://doi.org/10.1214/aoms/1177729032