Variants of the method of triads: Utridimensional Thurstonian models

Abstract

This paper deals with a theory for two variants of the method of triads—Torgerson's and Richardson's methods. For both methods, the relationship between the decision probabilities and the parameters of the momentary psychological magnitudes is derived under the assumption that these magnitudes can be modelled as if they were drawn from normal distributions with particular means and variances. This approach differs from previous theoretical work on the methods of triads, where it has been assumed that distances between momentary psychological magnitudes are normally distributed. Cases where the variances of the distributions of psychological magnitudes are unequal can be handled by the models. It is shown that the duo‐trio and triangular methods are special cases of Torgerson's and Richardson's methods of triads, respectively. Using non‐linear least squares minimization, estimates of the means of the distributions of a sample problem are obtained for random samples of size 200. Decision conflicts, which may occur when using Richardson's method, are discussed.