From binary evaluations of triads and quadruples, perceptual scales have been generated using maximum likelihood estimation (MLE). The approach was based on Thurstone’s notion of a stochastic perception process, in which the perceived strength of two stimuli differs from each other to represent a stimulus’ perceived difference. The phenomenon known as diminishing returns may cause the perception of a suprathreshold difference to be overstated when smaller differences are added. 

The existing method for creating a perceptual scale using MLE did not consider the phenomena. For a study, researchers provided a method for modeling the perception of differences using Thurstone’s theory and MLE, modified to take the prospect of diminishing returns into account. The approach could accurately model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns in situations where a perceptual scale is known as well as situations where the true perceived strengths of the stimuli are unknown. 

It was validated using Monte Carlo simulated responses to experimental triads. The approach was also used on empirical data sets to assess its viability for perception research. In the end, it was discovered that the study permitted a more thorough modeling of suprathreshold difference judgments, a fuller comprehension of the perceptual mechanisms driving comparisons, and an assessment of Thurstone’s theory of different judgments.