A choice model for paired comparison data based on imperfectly nested sets

A ratio scale of subjective magnitude is developed from paired-comparison data. The model attempts to combine arguments of Restle, Ekman, and Luce relating data obtained from paired comparisons and corresponding data from direct psychophysical scaling methods at the ratio level. The basic set-theoretical model involves the use of imperfectly nested sets. A numerical example illustrates the application of the theory.This research was supported by the Swedish Social Science Research Council and by the Swedish Board of Computing Machinery. I am indebted to Mr. U. Forsberg for computational assistance.