The common approach to studies of predictive bias is analyzed within the context of a conceptual model in which predictors and criterion measures are viewed as fallible indicators of idealized qualifications. Selection on the basis of idealized qualifications depends on acceptance of a meritocratic principle, a principle which is itself subject to debate. Even with acceptance of this principle, however, it is shown that there will generally be a wide range of uncertainty as the result of the fallible nature of the indicators. Only when boundary conditions defined by Birnbaum (1979) are exceeded will the results be unambiguous. An example of such a case is presented. It is argued, however, that such instances are probably somewhat rare.