Louis Leon Thurstone's Law of Comparative Judgment (1927) is one of the foundational achievements of mathematical psychology. It provides a rigorous method for constructing psychological scales from the seemingly simple data of paired comparisons — asking observers which of two stimuli is greater on some attribute.
The Model
Thurstone assumed that each stimulus evokes a distribution of values on an internal psychological continuum (the "discriminal process"). When comparing two stimuli, the observer selects the one that happens to have the higher value on that trial. The probability of choosing stimulus j over stimulus k depends on the difference between their mean scale values and the variability of the discriminal processes.
Under the assumption of equal and uncorrelated discriminal dispersions,
the scale difference equals the z-score of the comparison proportion.
Legacy
Thurstonian scaling demonstrated that rigorous interval measurement was possible in psychology, provided the right mathematical framework. It influenced the development of signal detection theory (which extends Thurstone's distributional assumptions) and modern choice models. Thurstone's approach remains widely used in psychometrics, marketing research, and any field where subjective preferences must be placed on a quantitative scale.