The premise is equally likely alternatives considered one by one

What it is

The “number of alternatives” in the Hick-Hyman law assumes alternatives are roughly equally likely and must be discriminated before choosing. If one is selected almost always and another almost never, the visible count is unchanged but actual uncertainty differs. Entropy of the probability distribution is more appropriate than a raw item count.

Why it happens

People exploit priors, spatial position, and situational cues. Frequent responses can be prepared in advance while rare ones need more discrimination, making a skewed set easier than an equally sized uniform set. With practice, serial consideration can also give way to pattern recognition or motor memory.

Studying it

Hold count constant while varying occurrence probability; compare uniform and skewed distributions in reaction time and errors, fitting entropy rather than count. Control repeated location, cues, and practice so location learning is not mistaken for probability. Product logs estimate actual probabilities but should be paired with observation: a rare action may be rare because it is hidden or misunderstood.

Where it stops holding

Frequency advantage fades when users do not know the distribution, tasks switch abruptly, or a rare high-consequence action deserves deliberate confirmation. Promoting frequent actions can lower mean time while making uncommon work hard to find. Observed frequency may itself be a product of design bias rather than need.

Applying it

• Order or highlight common actions using real task frequency, while retaining stable, searchable access to infrequent critical ones.
• Do not review complexity from item count alone; ask whether people can predict the next step or must read every label.
• Compare success and time by task frequency before and after a redesign so average gains do not hide degradation of rare tasks.

Related

• Same group: B1.04.1 Decision time grows logarithmically with the number of alternatives · 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: B1.07 Power law of practice · B1.06 Memory-scanning law
• Search terms: Hick-Hyman law · entropy · choice probability