A comparison of two procedures to select the best binomial population with sequential elimination of inferior populations

We compare the selection procedure of Levin and Robbins [1981. Selecting the highest probability in binomial or multinomial trials. Proc. Nat. Acad. Sci. USA 78, 4663-4666.] with the procedure of Paulson [1994. Sequential procedures for selecting the best one of k Koopman-Darmois populations. Sequential Analysis 13, 207-220.] to identify the best of several binomial populations with sequential elimination of unlikely candidates. We point out situations in which the Levin-Robbins procedure dominates the Paulson procedure in terms of the duration of the experiment, the expected total number of observations, and the expected number of failures. Because the Levin-Robbins procedure is also easier to implement than Paulson's procedure and gives a tighter guarantee for the probability of correct selection, we conclude that it holds a competitive edge over Paulson's procedure.