Decision theory applied to selecting the winners, ranking, and classification

We address the problem of selecting the best of a set of units based on a criterion variable, when its value is recorded for every unit subject to estimation, measurement, or another source of error. The solution is constructed in a decisiontheoretical framework, incorporating the consequences (ramifications) of the various kinds of error that can be committed. The related problems of classifying the units to a small number of groups and ranking them are solved by a similar approach. An application is presented involving retention rates in the undergraduate courses of a university