Decision time grows logarithmically with the number of alternatives
Aliases: Hick's law · choice reaction time
What it is
The Hick-Hyman law describes uncertain choice reactions: as the number of alternatives increases, time to decide which response to make commonly grows with the logarithm of that number. It concerns response selection after alternatives are seen and understood, not the count of elements on a page or the total time to search an unfamiliar menu.
Why it happens
For n equally likely alternatives, uncertainty is roughly log₂n. More equal alternatives require more information to map the present stimulus to the right response. Logarithmic growth means that moving from two to four alternatives adds a burden of similar order to moving from four to eight; doubling choices does not double decision time.
Studying it
Choice-reaction experiments present random stimuli and require mapped key responses, varying alternative count and probability while measuring correct reaction time and error. Interface work should separate selection, visual search, and pointing; familiarised locations or verbal/key responses can isolate motor cost. Fits should account for anticipation, learning, and erroneous outliers.
Where it stops holding
When alternatives differ in probability, label clarity, hierarchy, or user preference, count alone is not effective uncertainty. Real menus add search, reading, and memory costs. For well-practised fixed mappings, responses can be retrieved directly and the relation weakens.
Applying it
- Keep the set of unfamiliar, same-level alternatives that must be compared manageable, and use frequency and task relationship to lower uncertainty.
- In task timing, separate finding, understanding, choosing, and pointing rather than blaming every delay on count.
- Test key choices with realistic probabilities and both novice and experienced users; a rare but high-risk option may need better visibility, not merely a smaller total set.
Related
- Same group: B1.04.2 The premise is equally likely alternatives considered one by one · B1.04.3 Grouping and ordering turn one large decision into several smaller ones · B1.04.4 For skilled users the response is directly retrieved
- Nearby: B1.06 Memory-scanning law · B1.07 Power law of practice
- Search terms:
Hick-Hyman law·choice reaction time·information theory