Institute for Mathematical Behavioral Sciences

Two examples of behavioral measurement are explored — utility theory and global psychophysical theory of intensity — that closely parallel classical physical measurement in several ways. First, the attribute in question can be manipulated in two independent ways. Second, each method of manipulation is axiomatized and each leads to a measure of the attribute that because they are order preserving must be strictly monotonically related. Third, a law-like constraint, somewhat akin to the distribution property of, e.g., mass measurement, link the two types of manipulation. Fourth, given the measures that result from each manipulation, the linking law between them can be recast as a functional equation that establishes the connection between the two measures of the same attribute. Fifth, a major difference from physics is that the resulting measures are themselves mathematical functions of underlying physical variables — of money and probability in the utility case and of physical intensity and numerical proportions in the psychophysical case. Axiomatizing these functions, although still problematic, appears to lead to interesting results and to limit the degrees of freedom in the representations.