A Context-Sensitive Alternative to Hick’s Law of Choice Reaction Times: A Mathematical and Computational Unification of Conceptual Complexity and Choice Behavior

Abstract

Hick’s law describes the time that individuals take to make a preference decision when presented with a set of possible choices. Basically speaking, the law states that decision time is a logarithmic function of the number of choices when the choices are equiprobable. However, the evidence examined here suggests that this, and a variant of the law for non-equiprobable choices based on Shannon entropy, are not effective at predicting decision reaction times involving structured sets of alternatives. The purpose of this report is to communicate a theoretical alternative to Hick’s law that is derived from a mathematical law of invariance for conceptual behavior at the heart of Generalized Invariance Structure Theory (Vigo, 2013, 2015). We argue that such an alternative accounts more precisely for decision reaction times on structured sets. Furthermore, we argue that Hick’s law is a special case of this more general law of choice reaction times for categories with zero degree of invariance.

Keywords

• Hick’s law
• choice law
• invariance structure theory
• computational cognitive model
• choice response times
• categorical invariance