An empirical relation in human information processing stating that choice reaction time increases approximately with the logarithm of the number of equally probable alternatives; commonly expressed as T = a + b log2(n + 1), where T is decision time, n the number of choices, and a,b are empirically determined constants.

Principle

Decision latency grows with the information (in bits) required to select among alternatives; doubling the effective choice information increases time by a constant amount determined by b, linking information-theoretic entropy to response time in simple choice tasks.

Demonstration

Illustrative scenario → A user must select one icon from menus containing 2, 4, 8 and 16 equally probable items. Recognition → Measured reaction times for the same user show roughly linear increase when plotted against log2(n+1). Action → Fit T = a + b log2(n+1) to the data to estimate a and b. Consequence → The relation predicts that increasing menu breadth increases average selection time approximately logarithmically, informing menu grouping or hierarchical design.

Misapplication

Applying the law without regard to stimulus–response compatibility, unequal choice probabilities, learning effects, or when the task requires visual search or motor precision; assuming the constants a and b are universal across devices, populations or tasks.

Consequence

Appropriate application quantifies the tradeoff between number of choices and decision latency, guiding interface simplification and hierarchical organization; inappropriate use may lead designers to misattribute delays to choice count rather than to perceptual, cognitive or motor factors.

Reversal

When choices are practiced to automaticity, when choices have different probabilities, or when perceptual search dominates, the logarithmic relationship breaks down and decision time may be better predicted by entropy (T = a + bH) or by alternative models that include search or motor components.

Boundary

Clearly within: a laboratory choice‑reaction task with discrete, equally likely responses and minimal perceptual search. Boundary case: a menu with visually similar items differing slightly in salience or probability. Clearly outside: continuous decision tasks, visually guided search tasks dominated by perceptual scanning, or tasks in which motor execution time dominates.

Semantic Tension

Hick’s Law ↔ Fitts’s Law — Hick addresses cognitive choice time as a function of alternatives; Fitts addresses motor movement time as a function of distance and target size; interactive tasks often require combining both cognitive and motor models.

Synthesis

Hick’s Law provides a compact, information‑theoretic baseline for expected choice latency in simple tasks, but it must be integrated with perceptual, motor and learning factors to predict performance in real interfaces.