Hick's Law¶

Status: established
Last updated: 2026-06-04
Sources: Hick1952 Rate Of Gain Of Information.Pdf, Lawsofux.Pdf
Tags: [ux-design, design-principles, heuristics, hicks-law, hick-hyman-law, choice-reaction-time, information-theory, decision-making, choice-architecture, progressive-disclosure]

Summary¶

Hick's law holds that the time to choose among alternatives increases with the amount of information the choice carries, rising logarithmically as options are added. Hick (1952) established this experimentally, showing that choice reaction time fits RT = K·log(n + 1) and that the rate of gain of information is, on average, constant at the order of five bits per second within a single perceptual-motor act. In UX design, Yablonski (2024) applies the same relationship to argue for reducing and simplifying choices, breaking complex decisions into steps, and using progressive disclosure. The underlying decision-process science is treated in Decision Making And Decision Support and Selection And Control Of Action; this article records both the original finding and the design heuristic built on it.

Body¶

Context¶

Two sources anchor this article. Hick (1952), in 'On the rate of gain of information' (Quarterly Journal of Experimental Psychology), applies the then-new information theory of Shannon and Wiener to choice-reaction-time data, running experiments with up to ten alternatives and a speed-for-errors variant; it is the primary experimental source for the law. Yablonski (2024), in the Hick's Law chapter of Laws of UX, takes that relationship into interface design and derives guidance for simplifying decision points. Within this knowledge base the article is the design-heuristic counterpart to the response-selection theory in Selection And Control Of Action (where the Hick-Hyman law and choice reaction time appear as motor/cognitive theory) and the choice models in Decision Making And Decision Support. It is paired throughout Yablonski's book with Fitts Law — Hick's contemporary at the same information-theory frontier — and is frequently confused with Millers Law, a confusion Yablonski explicitly warns against.

Key Points¶

Hick (1952) frames the choice as an information-transmission problem. Following Shannon, the information in an event of probability p is −log p, and the expected information (entropy) of a set of alternatives is the probability-weighted sum of those contributions; in a choice-reaction task with n equiprobable signals the input entropy is log n (PDF p. 3, orig. p. 12). The central hypothesis is that the rate of gain of information is, on average, constant with respect to time within the duration of a single perception, which requires reaction time to be proportional to the transmitted information (PDF p. 3, orig. p. 12).

The law takes the form RT = K·log(n + 1). Hick adds one to the number of alternatives because log n alone gives zero reaction time for the simple reaction (n = 1), whereas a simple reaction still carries uncertainty about when the stimulus will occur; treating "no stimulus" as one further equiprobable possibility supplies the missing entropy (PDF p. 4, orig. p. 13). This log(n + 1) form fits the earlier data of Merkel (1885) — replotted from Woodworth (1938) — through the curve RT(seconds) = 0.626·log10(n + 1), and Hick notes it fits better than the alternative A + B·log n, which has the theoretical defect of running to negative infinity at the origin (PDF p. 4, orig. p. 13).

Two experiments support the hypothesis. In Experiment I a single subject reacted to up to ten alternatives with few errors; the mean reaction times fit 0.518·log(n + 1), passing through the origin with a negligible additive constant (PDF pp. 4–5, orig. pp. 13–14). In Experiment II subjects deliberately traded accuracy for speed, making errors at a chosen rate; the residual uncertainty (equivocation) was used to compute an "equivalent degree of choice" n_e, and fast-with-errors runs fell on the same curve as the errorless data, extending the law to partial extraction of information (PDF pp. 5–7, orig. pp. 14–16). For one subject the rate of gain of information averaged 5.6 bits per second (PDF p. 9, orig. p. 18), consistent with the paper's headline value "of the order of five bits per second" (PDF p. 2, orig. p. 11). Hick also reports that the reaction times to individual stimuli and responses correlate with their residual uncertainty (r = 0.80 and 0.95), further evidence that reaction time depends on information in the technical sense (PDF p. 10, orig. p. 19). He considers conceptual models — template-matching by simultaneous, serial, or self-replicating processes, and systematic versus random search — but finds the data cannot decide among them (PDF pp. 11–12, orig. pp. 20–21).

Yablonski (2024) carries this into design. He states the law as: the time it takes to make a decision increases with the number and complexity of choices available, attributing it to Hick and Hyman's 1952 work on stimuli and reaction time (PDF pp. 59–70, orig. pp. 39–50). The design implications are to reduce and structure choice — minimising options where speed matters, breaking complex tasks into smaller steps, and using progressive disclosure so options appear only as they become relevant — while cautioning that hiding too much or oversimplifying can itself harm usability (PDF pp. 59–70, orig. pp. 39–50).

Conclusion¶

Hick (1952) and Yablonski (2024) describe the same relationship at two levels. Hick established it empirically: choice reaction time grows with the logarithm of the number of alternatives, the rate of information gain is roughly constant at about five bits per second, and the relation holds even when speed is traded for errors. Yablonski translates that finding into a design rule, making choice architecture a measurable concern — every added option costs decision time, so interfaces should present the fewest, clearest choices a task needs and stage complexity through disclosure. The two agree on the core logarithmic relationship; Yablonski adds only the practical boundary that simplification has limits. The underlying decision theory is developed in Decision Making And Decision Support.

References¶

Hick, W.E. (1952) 'On the rate of gain of information', Quarterly Journal of Experimental Psychology, 4(1), pp. 11–26. doi: 10.1080/17470215208416600. hick1952rate

Hyman, R. (1953) 'Stimulus information as a determinant of reaction time', Journal of Experimental Psychology, 45(3), pp. 188–196. To be validated.

Merkel, J. (1885) 'Die zeitlichen Verhältnisse der Willensthätigkeit', Philosophische Studien, 2, pp. 73–127. To be validated.

Yablonski, J. (2024) Laws of UX: Using Psychology to Design Better Products & Services. 2nd edn. Sebastopol, CA: O'Reilly Media. yablonski2024lawsux

Open Questions¶

Where is the boundary between helpful choice reduction and harmful oversimplification (Yablonski, 2024)?
How does the logarithmic choice-time relationship interact with the chunking guidance of Millers Law when structuring menus and forms?
Hick (1952) leaves the underlying mechanism undecided among template-matching and search models; which of these (if any) is supported by later choice-reaction-time work, including Hyman (1953)?