A random multiplicative model of Piéron’s law and choice reaction times

Abstract

We present a random multiplicative model with additive noise of human reaction/response times based on the power-law function, Piéron’s law. We study the role of weak additive noise in two different scenarios: in the first case, the multiplicative model describes the differences between simple, and two-choice reaction times in Piéron’s law. In the second case, we investigate how choice reaction times depend on the transfer of information in neurons. A transition is found at 0.5 bits due to weak additive noise. Reaction times follow an U-shaped function that lead to both anti-Hick’s and Hick’s effects. We discuss the implications of random multiplicative processes, and minimum transfer of information in decision making, and neural control.