Hick-Hyman Law

The Hick-Hyman law is a psychological principle that predicts that as the number of options individuals face in decision-making processes increases, the time required to make a choice among those options increases linearly. This law emerged from the convergence of two independent studies: one conducted by William Edmund Hick in 1952 and another by Ray Hyman in 1953. Hick empirically supported this relationship, and over time, the law has become a key reference point in numerous fields including human-computer interaction (HCI), user experience (UX) design, neuroscience, and education.

Historical Background and Mathematical Foundation

The fundamental mathematical formula of the Hick-Hyman law is as follows:

<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">RT</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span>

Here, <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">RT</span></span></span></span> represents reaction time; <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> denotes the number of presented options; <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> represent experimentally determined constants. This formula demonstrates that decision time increases logarithmically with the number of options. In Hick’s original study, he observed that the difference in time required to choose between two options and four options remained constant. Hyman examined this relationship in a broader context, and the combined contributions of these two researchers led to the law being named the “Hick-Hyman Law” in the literature.

Psychological Foundations and Experimental Evidence

The Hick-Hyman law sheds light on the cognitive foundations of decision-making. As the number of options increases, individuals must allocate greater cognitive resources to evaluate the probability of each option and select the most appropriate one, resulting in longer decision times. Numerous experimental studies have supported the validity of this relationship. For example, in one experiment, participants were presented with lights that flashed in varying numbers and asked to respond to them. Results showed that reaction time increased as the number of options increased.

Neuroscientific Perspective: The Cognitive Control Network and the Default Mode Network

In recent years, neuroscientific research has investigated the neural basis of the Hick-Hyman law. In one study, functional magnetic resonance imaging (fMRI) was used to examine which brain regions are activated during decision-making processes. Findings revealed that the prefrontal region of the brain, known as the cognitive control network (CCN), becomes active throughout the process from representing uncertainty to generating a response. In contrast, the default mode network (DMN) was active only during the representation of uncertainty and played no role in response generation. These results contribute to a deeper understanding of the neuroscientific underpinnings of the Hick-Hyman law.

Applications

Human-Computer Interaction (HCI) and User Experience (UX) Design

The Hick-Hyman law is a fundamental principle in HCI and UX design. Offering users too many options can prolong decision time and negatively impact user experience. Therefore, designers should limit the number of options to enable users to make quick and accurate decisions. For instance, reducing the number of menu items on a website can help users locate desired information more rapidly.

Education and Instruction

In education, understanding and optimizing students’ decision-making processes is essential. An excessive number of options presented to students can extend decision time and hinder the learning process. Consequently, the number of choices in instructional materials must be carefully structured.

Marketing and Consumer Behavior

In marketing strategies, presenting consumers with too many options can prolong the decision-making process and affect purchasing decisions. This situation may lead to what is known as “choice overload.” Marketers can positively influence purchasing decisions by offering consumers a limited number of options.

Criticisms and Limitations

The Hick-Hyman law is a well-established principle with demonstrated validity across many domains. However, some criticisms exist. For instance, the law focuses solely on the number of options while potentially overlooking other factors that influence decision-making. Individual factors such as prior experience, knowledge level, and motivation can also significantly affect decision processes. Therefore, it is important to evaluate the Hick-Hyman law within a broader contextual framework.

The Hick-Hyman law is a key principle that explains how increasing the number of options affects decision time in human decision-making processes. It finds applications in psychology, neuroscience, HCI, education, and marketing. Understanding its neuroscientific foundations opens important avenues for future research. Moreover, to better comprehend and optimize human decision-making, the Hick-Hyman law should be evaluated in conjunction with other influencing factors.