Selecting the highest of three binomial probabilities.

A sequential elimination procedure for selecting the highest probability in binomial trials, proposed by Levin and Robbins [Levin, B. & Robbins, H. (1981) Proc. Natl. Acad. Sci. USA 78, 4663-4666], is examined further in the special case of trials involving three probabilities. A conjectured inequality relating ratios of selection probabilities to odds ratios is shown to hold only under certain necessary and sufficient conditions. Weaker conjectured inequalities involving the probability of correct selection are shown to hold without restriction.