Hick's Law of Choice Time
The time required to make a decision increases logarithmically with the number of equally-probable options presented (Hick-Hyman Law).
Why This Is an Axiom
This is an empirical axiom representing a quantified psychophysical law discovered through extensive experimentation. Hick's Law (1952) and Hyman's refinement (1953) established that reaction time RT = a + b·log₂(n+1), where n is the number of choices. This relationship cannot be derived from more fundamental principles of psychology—it represents an observed regularity in human information processing that must be taken as foundational for understanding choice behavior.
Evidence and Reasoning
Decades of experimental research across varied domains (visual choice, menu selection, button pressing, linguistic decisions) consistently demonstrate the logarithmic relationship. The pattern holds remarkably well for homogeneous choices of roughly equal probability. The logarithmic form reflects the binary search-like process humans use to narrow option spaces—each mental comparison roughly halves the remaining candidates. Important constraints: the law applies primarily to simple, practiced choices between distinct alternatives; it breaks down when options have vastly different probabilities, when choices are highly practiced (approaching automaticity), or when semantic processing dominates. The law quantifies the irreducible cognitive cost of discriminating among alternatives.
Curriculum Connection
This axiom grounds the curriculum's analysis of menu design, navigation structures, and choice architecture. It explains why presenting 10 options isn't proportionally harder than presenting 5, but provides a specific quantifiable prediction. Understanding this axiom enables designers to optimize interface layouts, predict user performance, and recognize when to break large option sets into hierarchical structures that leverage the logarithmic relationship across multiple levels.