Equal probability of correct selection for bernoulli selection procedures

The problem of selecting the Bernoulli population which has the highest “success” probability is considered. It has been noted in several articles that the probability of a correct selection is the same, uniformly in the Bernoulli p-vector (p₁, p₂., p_k), for two or more different selection procedures. We give a general theorem which explains this phenomenon. An application of particular interest arises when “strong” curtailment of a single-stage procedure (as introduced by Bechhofer and Kulkarni (1982a)) is employed; the corresponding result for “weak” curtailment of a single-stage procedure needs no proof. The use of strong curtailment in place of weak curtailment requires no more (and usually many less) observations to achieve the same probability of a correct selection. Similar general results hold for the analogous multinomial selection problems.