An Expected Utility Model for “Optimal” Selection

Abstract

The Threshold Utility Model for culture-fair selection introduced by Gross and Su (1975) and byPetersen (1974) is defined here for both quota-free and for restricted selection. In addition, a full Bayesian solution based on posterior predictive distributions is provided. By providing a mechanism for coherently combining probabilities and utilities, this model makes it possible to determine an optimal selection strategy in all situations in which a threshold utility function is applicable. This paper studies the mathematical properties of the solution in detail in the case of quota-free selection. In the more complex restricted selection case, the study lacks some detail but is more complete than that given by Gross and Su and should be adequate for most practical purposes. Several data analyses highlight the strengths and weaknesses of the model.