Friday, April 6, 2012
Linear utility functions and assessment
When we assess job applicants, or employees, or rank grant applications we typically use a linear utility function. We take things like the number of years in teaching, the number of papers published, the number of talks given, etc., multiply by some weighting number, and sum up to a single numeric score. It is easy to show how poor an approximation such a linear model is likely to be. For a scientist or academic an IQ of 120 would be quite reasonable but an IQ of 60 would surely be hopelessly low. A linear model involving IQ is surely a poor model. A nonlinear model, with IQ raised to some power, would certainly be needed. When we use a linear model we are simply hoping the approximation is good enough.