A theory of bidirectional judgments

This paper is concerned with a scaling theory for “bidirectional” judgments, for which the order of judgment is reversible, as in fractional and multiple ratio estimation judgments. With the assumption that judgments are mediated by perceived relations of pairs of stimuli, the theory is developed for judgments of comparison stimuli in relation to standards, taking explicit account of the location of the comparison stimulus relative to the standard. The theory of bidirectional judgments, based on a theory of relative judgment by Fagot (1978, 1979), entails a partial nesting of models characterized by a progressive weakening of the constraints placed on the structure of the data. The weakest model, the relative bias/directional standard (RBDS) model, allows each standard to have two biasing effects, depending on the location of the standard above or below the comparison stimulus. Tests of the theory were carried out on the ratio estimation of brightness and weight data of Engen and Levy (1955) and the part-sum estimation data of Goude (1962). Only the RBDS model was found acceptable for all three data sets