Hick’s Law Automatic translate

The effort required to make a decision increases with the number of options. The more options you offer, the more difficult it is for customers to decide.

Hick’s Law (also known as the Hick-Hyman Law) is a psychological principle that states that the time it takes a person to make a decision when choosing between several alternatives increases logarithmically with the number of alternatives. The law describes not just the subjective perception of difficulty in choosing, but a measurable relationship between the number of options and reaction time, which is why it is widely used in cognitive psychology, ergonomics, and interface design.

History of discovery

Background: Merkel and early observations

The first experimental data on the relationship between the number of alternatives and reaction time were obtained in 1885 by the German psychologist Josef Merkel. He demonstrated that subjects respond more slowly to stimuli when the number of possible signals is large. Merkel’s work remained within the purview of a small circle of researchers and was not widely known, but it laid the empirical foundation that scientists turned to in the mid-20th century.

At the same time, related observations in physiology and psychophysics were accumulating. Researchers noted that as the number of stimuli requiring various motor responses increased, reaction speed invariably decreased. However, the nature of this relationship — whether linear or logarithmic — remained unclear until the 1950s.

William Edmund Hick: The 1952 Experiment

In 1952, British psychologist William Edmund Hick conducted a series of experiments in which subjects were required to respond by pressing keys to flashing lights, the number of which varied from one to ten. The results showed that reaction time increased proportionally to the base-2 logarithm of the number of options, rather than linearly. Hick formulated his law as a dependence of reaction speed on "information acquisition rate" — a term directly borrowed from Claude Shannon’s information theory, published just a few years earlier.

Hick’s article "On the Rate of Gain of Information" was published in 1952 in the Quarterly Journal of Experimental Psychology. It described subjects’ responses in units of information — bits — which was fundamentally new for psychology at the time. It was the application of information theory to a psychological experiment that made Hick’s work a scientific milestone, not just a mere accumulation of data.

Ray Hyman and the Clarification of the Law

In 1953, American psychologist Ray Hyman conducted his own series of experiments, exploring the relationship between reaction time and the average number of options presented. Hyman used a matrix of eight light bulbs, each assigned a name: the subject was asked to pronounce the name of the illuminated bulb as quickly as possible.

Hyman varied not only the number of lamps but also the probability of each one appearing, which allowed him to distinguish between the influence of the number of stimuli and their information uncertainty. He confirmed the logarithmic relationship identified by Hick and expanded on it: reaction time is linearly related to the amount of information transmitted in bits. The combined contributions of both researchers were codified in the term "Hick-Hyman law," although the abbreviation "Hick’s law" is more commonly used in popular and applied literature.

Mathematical description

Formula and its components

The basic formula of the law is:

T = a + b × log ₂ (n + 1)

Where T is the average reaction time; n is the number of equally probable alternatives; a and b are constants reflecting the base reaction time and information processing speed, respectively. Unity is added to n to account for the "no stimulus" option as an independent information situation.

The b -factor numerically expresses the speed of information processing in the brain: it is measured in milliseconds per bit. In most studies, this value ranges from 150 to 200 ms/bit, although it varies significantly depending on the task, the subject’s training, and the nature of the stimuli.

Logarithmic rather than linear dependence

The logarithmic nature of reaction time growth means that doubling the number of options does not double the decision-making time. When moving from two options to four, the time increases by one bit; when moving from four to eight, it increases by one bit again. This is a practically important property: adding the first few alternatives is expensive, while adding each subsequent one, as the number of options increases, leads to progressively smaller increases in time.

In practice, this means that the difference between two and three options is much more noticeable to the user than the difference between twenty and twenty-one options. The law thus captures the diminishing, but not zero, influence of each additional option.

Generalized Hyman formula

Hyman expanded the formula by abandoning the assumption of equal incentive probability. In its generalized form, the law takes into account the information entropy of the set of alternatives, as defined by Shannon:

T = b × H

where H = ∑ ⁿ _i=1 × p _i × log ₂ × 1/ p _i is the entropy of the probability distribution of stimuli. If some options appear significantly more frequently than others, the total uncertainty is lower and reaction time is shorter than would be predicted by a simple formula with n. This observation has direct implications for design: selecting the most likely action reduces cognitive load even while maintaining the total number of options.

Cognitive mechanisms

Information load and working memory

Hick’s Law describes a phenomenon commonly associated in modern cognitive psychology with working memory load. Human working memory has a limited capacity: according to George Miller, it can hold approximately 7 ± 2 units of information at a time. Each additional choice takes up some of this capacity, slowing down processing.

With each new option, the brain is forced to perform an additional discrimination step: comparing the new alternative with those already considered, assessing its significance, and updating its internal "ranking" of options. This is why the law is logarithmic rather than stepwise — processing each additional option is less expensive than the previous one, but not free.

Stimulus-response compatibility

According to Hick’s law, reaction time is influenced by so-called stimulus-response compatibility. When the proposed action is "similar" to the stimulus itself — for example, turning the steering wheel in the same direction the car needs to turn — reaction time decreases regardless of the number of alternatives. Incompatible stimulus-response combinations increase reaction time beyond that predicted by the basic formula.

This aspect is especially important in ergonomics: the layout of controls must match the operator’s intuitive expectations. An unclear correspondence between a control and its function adds cognitive load on top of that already created by multiple variations.

The role of familiarity and training

It’s well known that experienced users react significantly faster to choice situations than novices. Training reduces the coefficient b in the formula: the brain begins to process familiar alternatives as unified "chunks" — condensed semantic units that require fewer resources. A professional pianist choosing from musical symbols acts faster than a student, even though both are faced with the same number of alternatives.

This leads to a practical conclusion: Hick’s Law is more restrictive for new users or those working with an unfamiliar interface. For experts, too many options are less harmful, although they don’t completely eliminate the harm.

Criticisms and limitations

Conditions of applicability

Research in the second half of the 20th century identified a number of conditions under which Hick’s law is not strictly observed or not observed at all. A number of experiments have demonstrated deviations from linearity in atypical tasks — for example, with very high uncertainty (more than 3 bits). Furthermore, some types of rapid automatic reactions, such as saccades (eye movements), show virtually no slowing as the number of options increases.

Another limitation stems from the confounding of stimulus and response numbers in the original experiments. Hick and Hyman used tasks in which each stimulus had a unique response, making it impossible to distinguish between the influence of stimulus uncertainty and response uncertainty. Later studies — notably, Whyfall et al.’s 2015 study — attempted to disentangle these two contributions and found that both are significant, but their relative weighting depends on the specific experimental conditions.

Choice paralysis as a separate phenomenon

Hick’s law describes a slowing of reaction time, but it doesn’t describe the complete loss of choice — a phenomenon commonly referred to in psychology as "choice paralysis" or "choice overload." This is a crucial distinction: the Hick-Hyman law quantitatively describes the increase in reaction time, whereas choice paralysis occurs when the psychological costs of choice exceed the perceived value of any option.

This is where the law intersects with a broader class of phenomena studied in consumer psychology. Choice overload can lead not only to slowing down, but also to a refusal to make a decision altogether.

Meta-analysis and reproducibility

The law’s reliability in practical contexts remains a matter of debate. The classic "jam experiment" conducted by Sheena Iyengar and Mark Lepper in 2000 showed that shoppers were significantly more likely to purchase jam when offered six varieties than when offered 24. While the 24-variety display attracted more attention, it converted that attention into a purchase less effectively — approximately 10 times less frequently.

However, subsequent meta-analyses yielded less definitive results. Some experiments failed to reproduce a significant overload effect, and the degree of slowing depended on the subject area, the number of options offered, and the subjects’ familiarity with the products. Therefore, Hick’s law should be viewed as a consistent trend rather than a universal formula with fixed coefficients.

Related concepts

The Paradox of Choice by Barry Schwartz

In his book "The Paradox of Choice" (2004), psychologist Barry Schwartz developed ideas related to Hick’s Law on a social and philosophical level. Schwartz demonstrated that an excess of options not only slows down decision-making but also reduces subsequent satisfaction with it: a person who chooses one of twenty options is more likely to regret missed options than someone who chooses from three.

The mechanism here is different from Hick’s law: it’s not about reaction speed, but about the cognitive processing of alternatives after a decision has been made. But both phenomena describe the same underlying fact: the brain is forced to pay a mental "price" for each alternative offered.

Cognitive load

Cognitive load theory, developed by John Sweller in the late 1980s, provides a theoretical framework for understanding the mechanisms behind Hick’s law. Sweller distinguished between intrinsic load (caused by the complexity of the material itself), extraneous load (caused by irrelevant elements of the task), and productive load (associated with the formation of new schemas). An excess of choice options primarily qualifies as extraneous load: it does not enrich comprehension but merely drains processing resources.

Decision fatigue

The phenomenon of decision fatigue was described by social psychologist Roy Baumeister in the context of his theory of "ego depletion." The idea is that the resource for volitional regulation and conscious choice is limited: each decision expends some of this resource, and by the end of a long series of choices, people tend to make more impulsive or formulaic decisions.

Hick’s Law describes a situation where a single choice is present, while decision fatigue is the cumulative effect of a long series of choices. But both phenomena point to the same thing: human cognitive bandwidth when making decisions is finite, and this must be taken into account whenever options are presented.

Application in UX and interface design

Navigation and information architecture

In digital product design, Hick’s Law is one of the most frequently cited theoretical principles. Applied to navigation menus, it states: the more items a menu has at a single level, the longer it takes the user to decide which section to select. This doesn’t mean the menu should be minimalist at the expense of completeness; rather, it means organizing information in such a way that the number of perceived alternatives at each level is small.

Dividing navigation into categories and subcategories is a direct consequence of Hick’s Law. Instead of presenting the user with twenty equally valuable links, the designer groups them into four or five categories with five links each. The perceived number of alternatives is determined by the number of top-level categories, not the total number of links.

Progressive disclosure

Progressive disclosure is a method whereby advanced or rarely used features are hidden on initial screens and become available as the user progresses through the flow. This allows for a small number of visible options without sacrificing functionality.

A clear example is step-by-step order forms: instead of one long page with dozens of fields, the user is presented with several short steps in sequence. Each step requires only one or two decisions, and the sum of these decisions is easier to bear than having to face them all at once.

Call to action buttons

Hick’s Law also applies to call-to-action buttons. When several equally important buttons compete on a single screen, the user reacts more slowly to any of them. Emphasizing one primary action and downgrading the visual status of others is an effective way to reduce reaction time.

This is precisely the logic behind subscription pages on many streaming services: several tariff plans are presented as three or four cards, one of which is visually highlighted as "recommended." This highlighting reduces subjective uncertainty by shifting the probability distribution toward one option, which, according to Hyman’s generalized formula, reduces entropy and speeds up the selection process.

Search and filter interfaces

In interfaces with large product or content catalogs, Hick’s Law explains why overloaded filters with dozens of parameters slow down decision-making, despite formally offering the user more options. Displaying filters in descending order of frequency of use and hiding less frequently used parameters behind a "More" button is a practical consequence of this principle.

Application in marketing and sales

Product range structure

Hick’s Law directly applies to the issue of product assortment depth. Data from the "jam experiment" showed that a display with six varieties converted casual observers into buyers 10 times more effectively than a display with 24 varieties, despite the latter attracting more initial attention. This clearly demonstrates the gap between the appeal of a variety of choices and its practical value in completing a purchase.

At the product strategy level, this leads to a recommendation to limit the number of price plans, product configurations, or service packages. Three options instead of seven is standard practice in the software, phone plan, and banking product markets.

The Decoy Effect and Attention Management

A marketing tool related to Hick’s Law is the decoy effect: the introduction of an asymmetrically dominated alternative into a set of options, making the target option more attractive. Within the generalized formula of Hick’s Law, this "red pencil" effect works by reducing subjective uncertainty: one option begins to be perceived as clearly preferable, which reduces the entropy of the set and speeds up decision making.

A product highlighted visually or positioned as "most popular" highlights the probabilistic asymmetry of the options. The user processes it as a nearly obvious answer, not as another element of comparison.

Online Commerce and Conversion

The application of Hick’s Law to e-commerce concerns not only the number of products in the catalog but also the structure of checkout pages. Long forms with numerous fields, cart pages with related product offers, and active promotions all increase the number of perceived options and slow down or interrupt the purchase process.

Amazon, with its "Buy in 1-Click" button, is a textbook example of Hick’s Law applied to product architecture. Stored payment information and shipping address transform the final purchasing step into a single decision ("buy now" or "not"), dramatically reducing cognitive overhead.

Application in ergonomics and industrial design

Control panels

Hick’s Law has a long history of application in industrial ergonomics, long before the advent of digital interfaces. The design of control panels — for nuclear power plants, aircraft cockpits, and medical equipment — is based, among other things, on minimizing the number of actions simultaneously visible to operators.

In aviation, the principle of minimizing the number of options in critical situations is directly related to Hick’s Law: in emergency situations, every second counts, and any unnecessary decision can cost lives. Therefore, emergency procedures are built on the principle of rigid decision trees with a minimum number of alternatives at each step.

Remote controls for household appliances

At the level of household appliances, Hick’s Law explains why washing machines or multicookers overloaded with buttons are perceived as difficult to use, even if each individual function is simple. Users tend to select the few most familiar modes, ignoring the others — this behavior is well described by Hyman’s generalized formula: when some options have a near-zero subjective probability of use, they are largely inactive in choosing, but still create an overload when first encountering the device.

Road signs and navigation

Transport ergonomics uses Hick’s law when designing road markings and signs. At an intersection with multiple exits, drivers must make decisions in seconds; if there are too many information stimuli, reaction time increases, as does the likelihood of error. This is why international road marking standards require limiting the number of signs on a single pole and providing advance notice — this distributes the cognitive load over time.

Applications in healthcare and medicine

Decision making in emergency medicine

Hick’s Law is actively discussed in the context of clinical decision making. In emergency and intensive care settings, physicians are forced to choose from numerous diagnostic and treatment alternatives under severe time pressure. Research shows that structured protocols with a limited number of branches significantly reduce decision delays and reduce errors.

The creation of clinical protocols and checklists in medicine is a direct engineering response to Hick’s Law. The World Health Organization’s surgical checklist, proposed by Atul Gawande, is built on the principle of reducing each step to a binary "pass/fail" decision, thereby minimizing uncertainty.

Pharmaceuticals and pharmacy products

The number of similarly acting medications on pharmacy shelves is a classic problem related to Hick’s Law. A patient standing in front of a shelf with twenty brands of ibuprofen spends significantly more time choosing than when faced with three or four options. OTC (over-the-counter) drug manufacturers actively use the "recommended" option — analogous to the decoy effect — to reduce consumer uncertainty.

Application in education

Didactics and structure of tasks

In pedagogy, Hick’s Law describes a phenomenon well known to teachers: a student presented with several topics for an independent presentation often spends a disproportionate amount of time choosing a topic rather than actually studying it. Limiting the number of options in an assignment reduces the administrative burden and allows for greater focus on the substantive work.

The flipped classroom approach and other modern pedagogical formats often imply rigid structuring of task selection for precisely this reason: a small number of well-formulated alternatives is more motivating than a wide menu of possibilities.

Multiple choice testing

The number of answer options in test items is a separate subject of research. The classic recommendation by test designers to include four to five answer options is partly based on Hick’s Law: increasing the number of distractors (incorrect options) slows response time and increases cognitive load, which impacts the validity of the measurement. At the same time, reducing the number of options below three dramatically reduces the psychometric discriminability of the question.

Application in law and law enforcement

Making decisions under stress

Hick’s Law is considered in law enforcement training in the context of threat response. Research shows that an officer who must choose from multiple options in a critical situation reacts more slowly and makes more mistakes than one who has narrowed their repertoire down to a few well-practiced strategies.

The practical conclusion is that practicing typical scenarios to the point of automatism reduces the effective n in the formula: a well-trained response is perceived by the brain as almost the only option, rather than one of many. This allows for faster response even in objectively challenging situations.

Hick’s Law and Neuroscience

Neurobiological basis

Neurobiological research in the 2010s uncovered the mechanisms behind Hick’s law at the level of brain systems. A 2017 study published in the journal Frontiers in Human Neuroscience demonstrated that the Hick-Hyman law is mediated by the cognitive control system, primarily the anterior cingulate cortex and the dorsolateral prefrontal cortex. These structures are responsible for monitoring conflicts between response options and choosing between competing responses.

As the number of stimuli increases, activity in these areas increases, which correlates with increased reaction time. Importantly, this pattern is replicated in neuroimaging: the brain literally "works harder" with a greater number of options, and this additional effort translates into milliseconds of reaction time.

Memory-based model

In 2011, David Schneider proposed the Hick’s Law model, based on the mechanisms of long-term memory retrieval. According to this model, response selection involves sequentially "referencing" stimulus-response associations stored in memory; the more such associations, the greater the likelihood of interference between them, which causes slowing.

The model explains why training reduces reaction time: repeating a task strengthens relevant associations and suppresses irrelevant ones, reducing interference. This is consistent with the general picture outlined by Hick’s law: the more predictable the choice environment is for a given person, the less they pay for each additional option.

Comparison with related laws

In cognitive psychology and ergonomics, Hick’s law is associated with several other quantitative laws that describe human interaction with information and interfaces.

Fitts’ Law describes how quickly a user can physically reach an interface element, while Hick’s Law describes how quickly they decide which element to move toward. Both laws are often used together when evaluating the effectiveness of interfaces.

Limits of application

When Hick’s law does not work or works poorly

Hick’s Law predicts a slowdown as the number of options increases, but it doesn’t assert that fewer options are always better. Here are a few situations in which reducing the number of alternatives is not beneficial or even harmful:

• Expert users who are familiar with a domain show little to no slowdown as the number of variants increases above a certain threshold.
• Tasks where the user knows exactly what they’re looking for in advance (for example, by entering a query in the search bar): an excess of options in the search results does not slow down finding the desired one if the ranking is correct.
• Contexts where a large number of variants is valuable in itself: library catalogs, scientific databases, reference works. Here, reducing variants reduces the comprehensiveness of the data.
• Situations in which the probabilities of options are highly uneven: one clearly dominant option makes the choice quick regardless of the total number of alternatives.

Connection with the task and motivation

Reaction times in Hick’s experiments were measured in laboratory settings with simple tasks and neutral stimuli. In real-world situations, motivation, emotional engagement, and social context significantly influence behavior. A person shopping for a wedding dress is willing to spend significantly more time and effort choosing from a hundred options than choosing a pen. The law describes minimal cognitive costs in neutral conditions; real-world choices are always more complex than this model.

Practical principles arising from Hick’s law

The body of research on Hick’s Law yields a set of robust principles applicable to the design of systems, products, and communications.