More choices? Longer decisions. But not linearly.
Decision time increases logarithmically. With the number of choice alternatives. Following the mathematical relationship T = a + b log₂(n).
Where decision time (T) grows predictably. But sub-linearly. As options (n) increase.
Hick's groundbreaking research (1952) demonstrated the pattern. Through controlled reaction time experiments.
The numbers? Clear and consistent.
2 choices? 380ms average reaction time. 4 choices? 520ms. 8 choices? 680ms. 10 choices? 720ms.
The pattern? Logarithmic scaling. Not linear.
Doubling choices added constant time increments. Approximately 150-200ms. Rather than doubling overall decision duration.
This logarithmic scaling reveals something profound. About brain architecture. The brain organizes choices hierarchically. Similar to binary search algorithms. Enabling manageable decision-making. Despite choice proliferation.
Hick formulated this mathematically. T = a + b log₂(n). Where T represents total reaction time. Where a represents base response time. Where b represents decision processing rate. And n represents number of equally probable alternatives.
Each choice between n alternatives requires processing log₂(n) bits of information. Each bit requiring constant processing time.
The principle: More choices take longer. But logarithmically, not linearly. Design accordingly.
Hick's seminal experiments (1952) established precise mathematical relationships between choice quantity and reaction time through rigorous laboratory measurement. Participants faced choice-reaction tasks pressing corresponding buttons when specific lights illuminated—tasks varied from 2-choice scenarios (left/right) to 10-choice scenarios (ten different stimulus-response mappings). Hick measured reaction times across thousands of trials discovering systematic patterns: 2 choices averaged 380ms, 4 choices averaged 520ms, 8 choices averaged 680ms, 10 choices averaged 720ms. These measurements revealed logarithmic scaling—each doubling of choices added approximately 150ms rather than doubling total time.
Hick formulated this pattern mathematically as T = a + b log₂(n) where T represents total reaction time, a represents base response time (non-decision components like stimulus detection and motor execution), b represents decision processing rate (time per "bit" of information processed), and n represents number of equally probable alternatives. This formula quantifies how choice complexity affects performance through information-theoretic framework—each choice between n alternatives requires processing log₂(n) bits of information with each bit requiring constant processing time.
Hyman's complementary research (1953) extended and validated Hick's findings while refining mathematical formulation. His experiments systematically varied both choice quantity and choice probability (some stimuli appeared more frequently than others) demonstrating reaction time correlates with information entropy—the average information content per choice calculated as H = -Σ p(i) log₂ p(i) where p(i) represents probability of each alternative. This revealed that unequal choice probabilities reduce decision time—frequently selected options respond faster than predicted by simple choice counting because brain optimizes for common cases.
Hyman's work established critical boundary condition: Hick's Law applies primarily to unfamiliar choices requiring active decision-making. Well-practiced stimulus-response associations bypass logarithmic scaling approaching constant reaction times regardless of set size because motor programs execute directly without deliberate choice evaluation. Skilled typists selecting among 26 letter keys don't experience 26-choice Hick's Law effects because typing became automatic procedural memory rather than effortful declarative decision-making.
Card, Moran, and Newell's foundational HCI research (1983) through the Model Human Processor framework integrated Hick's Law into systematic interface design methodology. Their work demonstrated that Hick's Law effects compound across sequential decisions creating multiplicative impacts on task completion time. Interfaces requiring users to navigate multiple menu levels, each presenting numerous choices, accumulate decision delays substantially impacting overall efficiency. This established choice architecture optimization as fundamental usability consideration.