On the Use of a Cumulative Distribution as a Utility Function in Educational or Employment Selection

Abstract

Formal decision theory can make important contributions to educational or employment decision-making, provided one can quantify the utilities of different possible outcomes such as test scores and grade-point averages. Because utility is usually a monotonic increasing function of performance score, a cumulative probability function may be convenient for describing one’s utilities. Moreover, calculations of expected utility of a decision are greatly simplified when the utility and the probability function have the same functional form, e.g., both are normal. A least-squares procedure, developed by Lindley and Novick for fitting a utility function, is applied to truncated normal and extended beta distribution functions. The truncated normal and beta distributions avoid the symmetry and infinite range restrictions of the normal distribution and can provide fits in some cases in which the normal functional forms cannot provide a reasonable fit.