A compensatory approach to optimal selection with mastery scores

A Bayesian approach for simultaneous optimization of test-based decisions is presented using the example of a selection decision for a treatment followed by a mastery decision. A distinction is made between weak and strong rules where, as opposed to strong rules, weak rules use prior test scores as collateral data. Conditions for monotonicity of optimal weak and strong rules are presented. It is shown that under mild conditions on the test score distributions and utility functions, weak rules are always compensatory by nature. The authors are indebted to Wilbert Kallenberg for his valuable comments and to Jan Gulmans for providing the data for the empirical example. The names of the authors are alphabetical; they are equally responsible for the contents of this paper.