Modeling human perception Could Stevens´ Power Law be an emergent feature?

Stevens´ power law links the magnitude of a physical stimulus to its perceived internal intensity via a psychophysical power function. Because of the law´s sensitivity to the procedure used to collect its data, its failure to manifest itself at the individual level, its manifestation in non-sensory modalities, and the difficulty associated with rating stimuli on a ratio scale, many have speculated that the power law is a product of the experimental procedure Stevens used. This work tested this hypothesis by reproducing one of Stevens´ original power law experiments (using different pressure levels of a 1 kHz tone) in which 52 data series were generated from a computerized process that simulated Stevens´ experimental procedure. However, instead of generating ratio data for each magnitude estimate, random ordinal data were generated. When a power function was fitted to these data using the same procedure utilized by Stevens, it fit with an adjusted R² of 0.997, while generating the same psychophysical model. This indicates that Stevens´ assumption that participants make magnitude estimates on a ratio scale is not necessary to collect power law data. Thus, Stevens´ power law is likely a product of Stevens´ experimental procedure.