Models proposed by Cleary, Thorndike, Cole, Linn, Einhorn and Bass, Darlington, and Gross and Su for analyzing bias in the use of tests in a selection strategy are surveyed. Several additional models are also introduced. The purpose is to describe, compare, contrast, and evaluate these models while extracting such useful ideas as may be found in these approaches. The models of Thorndike, Cole, and Linn are judged to contain operational contradictions because of their use of the wrong conditional probability within the context of the probabilistic structure. These models, deriving from a concept of group parity, are also shown to have highly objectionable practical implications. It is suggested that the use of any of these models is contraindicated and that, indeed, the very concept of culture-fair selection is unworkable. It is then suggested that the necessary level of compensatory treatment for disadvantaged persons can be guaranteed only through the formal use of an appropriate model based on the Von Neumann-Morgenstern theory of maximizing expected utility. The models of Cleary, Einhorn and Bass, Gross and Su are based on what we judge to be the correct conditional probability and are special cases of the Expected Utility Model, but each has limited applicability. (Author/RC)