Equivalent Comparisons of Experiments

Sherman 8 and Stein 9 have shown that a method given by the author 1 for comparing two experiments is equivalent, for experiments with a finite number of outcomes, to the original method introduced by Bohnenblust, Shapley, and Sherman 4. 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.