A paired comparison of pair comparisons

Abstract

The theory of choice developed by Luce and the paired comparison theory due to Thurstone are restated so as to permit direct comparison. It is shown that the theories differ in general, but coincide for certain sets of stimuli. The class of stimuli on which they coincide is described, and it is proved that they can coincide on no stimuli outside of the class. The problem of finding a class of stimuli which gives maximal discrepancy between the theories can be posed in a number of ways. For one statement of the problem, solutions are found. Unfortunately, the nature of the solutions makes it very difficult to design an experiment for deciding between the theories. The general problem of an experimental decision is discussed briefly, and some pair comparison data are analyzed. The sets of data conform somewhat more closely to the Thurstone than to the Luce model, but superiority is by no means definitive.