Value systems for comparing three or more independent multinomial trials

SUMMARY Gail (1974) defined a value system as any real function on the outcome space of a multinomial random variable, and he showed how the mean value of this function can be used as a figure of merit for comparing two multinomial populations. This note generalizes those results to the comparison of three or more independent multinomial trials. Methods are given for finding that value system, an eigenvector, which maximizes the differences in figure of merit among several multinomials.