Piéron's Law is not just an artifact of the response mechanism

Piéron's Law, the power relation between mean RT and stimulus intensity or discriminability, has historically been understood to reflect a non-linear scaling between objective intensity and perception. More recently, Piéron's Law was demonstrated to arise out of the architecture of rise-to-threshold decision-making models (Stafford and Gurney, 2004). Here we explicitly tested whether such an explanation would suffice to fit human data, or whether additional assumptions about the nature of perceptual processing are required. We fitted a simple rise-to-threshold model to full RT distributions and choice probabilities from three data sets that show Piéron's Law. The model assumed that accumulation rate was linearly related to perceptual processing, leaving only the architecture of the model to produce Piéron's Law. For two data sets, this linear rate model is unable to account for the data, suggesting that Piéron's Law sometimes reflects additional perceptual scaling information. For the third data set, however, Piéron's Law does appear to simply arise out of the rise-to-threshold architecture of decision-making models. Our results suggest that it is important to fit models to data in order to draw inference about the causes underlying Piéron's Law.