Hick’s law

The Paradox of Choice – Why More Is Less is a 2004 book by American psychologist Barry Schwartz. In the book, Schwartz argues that eliminating consumer choices can greatly reduce anxiety for shoppers. Autonomy and Freedom of choice are critical to our well being, and choice is critical to freedom and autonomy. Nonetheless, though modern […]

The Paradox of Choice – Why More Is Less is a 2004 book by American psychologist Barry Schwartz. In the book, Schwartz argues that eliminating consumer choices can greatly reduce anxiety for shoppers.

Autonomy and Freedom of choice are critical to our well being, and choice is critical to freedom and autonomy. Nonetheless, though modern Americans have more choice than any group of people ever has before, and thus, presumably, more freedom and autonomy, we don’t seem to be benefiting from it psychologically.

—?quoted from Ch.5, The Paradox of Choice, 2004

Hick’s law, or the Hick–Hyman Law, named after British and American psychologists William Edmund Hick and Ray Hyman, describes the time it takes for a person to make a decision as a result of the possible choices he or she has: increasing the number of choices will increase the decision time logarithmically. The Hick–Hyman law assesses cognitive information capacity in choice reaction experiments. The amount of time taken to process a certain amount of bits in the Hick–Hyman law is known as the rate of gain of information.

Hick’s law is sometimes cited to justify menu design decisions. For example, to find a given word (e.g. the name of a command) in a randomly ordered word list (e.g. a menu), scanning of each word in the list is required, consuming linear time, so Hick’s law does not apply. However, if the list is alphabetical and the user knows the name of the command, he or she may be able to use a subdividing strategy that works in logarithmic time.[1]

Studies suggest that the search for a word within a randomly ordered list – in which the reaction time increases linearly according to the number of items – does not allow for the generalization of the scientific law, considering that, in other conditions, the reaction time may not be linearly associated to the logarithm of the number of elements or even show other variations of the basic plane.

Exceptions to Hick’s law have been identified in studies of verbal response to familiar stimuli, where there is no relationship or only a subtle increase in the reaction time associated with an increased number of elements,[4] and saccade responses, where it was shown that there is either no relationship,[5] or a decrease in the saccadic time with the increase of the number of elements, thus an antagonistic effect to that postulated by Hick’s law.[6]

The generalization of Hick’s law was also tested in studies on the predictability of transitions associated with the reaction time of elements that appeared in a structured sequence.[7] [8] This process was first described as being in accordance to Hick’s law,[9] but more recently it was shown that the relationship between predictability and reaction time is sigmoid, not linear associated with different modes of action. [10]

The power law of practice states that the logarithm of the reaction time for a particular task decreases linearly with the logarithm of the number of practice trials taken. It is an example of the learning curve effect on performance. It was first proposed as a psychological law by Newell & Rosenblom.[1] Delaney et al. showed that the power law fit better than an exponential if the analysis was performed across strategies, for a mental arithmetic task.[2]

However, subsequent research by Heathcote, Brown, and Mewhort suggests that the power function observed in learning curves that are averaged across participants is an artifact of aggregation.[3] Heathcote et al. suggest that individual-level data is better fit by an exponential function and the authors demonstrate that the multiple exponential curves will average to produce a curve that is misleadingly well fit by a power function.

The power function is based on the idea that something is slowing down the learning process; at least, this is what the function suggests. Our learning does not occur at a constant rate according this function; our learning is hindered. The exponential function shows that learning increases at a constant rate in relationship to what is left to be learned. If you know absolutely nothing about a topic, you can learn 50% of the information quickly, but when you have 50% less to learn, it takes more time to learn that final 50%.

Research by Logan suggests that the instance theory of automaticity can be used to explain why the power law is deemed an accurate portrayal of reaction time learning curves.[4] A skill is automatic when there is one step from stimulus to retrieval. For many problem solving tasks, reaction time is related to how long it takes to discover an answer, but as time goes on, certain answers are stored within the individual’s memory and they have to simply recall the information, thus reducing reaction time. This is the first theory that addresses the why of the power law of practice.

Power function:

RT = aP?b + c

Exponential function:

RT = ae?b(P-1) + c


RT = Trial Completion Time
P = Trial Number, starting from 1 (for exponential functions the P-1 argument is used)
a, b, and c, are constants

Practice effects are also influenced by latency. Anderson, Fincham, and Douglass looked at the relationship between practice and latency and people’s ability to retain what they learned. As the time between trials increases, there is greater decay. The latency function relates to the forgetting curve.[5]

Latency Function:

latency = A + B*Td


A = asymptotic latency B = latency that varies T = time between introduction and testing d = decay rate

a third option

Sophie’s choice (plural Sophie’s choices) A choice between two persons or things that will result in the death or destruction of the person or thing not chosen. From the title of the book Sophie’s Choice, by William Styron, in which a … Continue reading

Sophie’s choice (plural Sophie’s choices)

A choice between two persons or things that will result in the death or destruction of the person or thing not chosen.

From the title of the book Sophie’s Choice, by William Styron, in which a mother is forced to decide which of her children will die.

Hobson’s choice (plural Hobson’s choices)

The choice of taking either the primary option or nothing.

After Thomas Hobson (1544-1631) of Cambridge, England, who rented horses and gave his customers the choice of the horse nearest the stable door or no horse at all.

A Morton’s Fork is a specious piece of reasoning in which contradictory arguments lead to the same (unpleasant) conclusion. It is said to originate with the collecting of taxes by John Morton, Archbishop of Canterbury in the late 15th century, who held that a man living modestly must be saving money and could therefore afford taxes, whereas if he was living extravagantly then he was obviously rich and could still afford them.

The name comes from the tax-collecting practices of John Morton, Archbishop of Canterbury and Lord Chancellor under Henry VII. He reasoned that anyone who was living extravagantly was rich, and so could afford high taxes, while anyone who was living frugally had saved a lot, and so could afford high taxes. Bear in mind before you get too crazy that this was typically used to keep people well-known to be well-off anyway from trying to weasel their way into not paying; he wasn’t exactly trying to collect from peasants in hovels. Instead, he was trying to get around a then-common excuse for not paying taxes (that is, not having any money to do so) by discounting the proofs used to support the excuse (actual profligacy and feigned poverty). This is often confused with “Hobson’s choice.” Thomas Hobson leased horses, and in order to make sure all got used and exercised, he had customers automatically assigned the one nearest the door rather than let them pick which one they wanted; the customer’s choice was “Take the horse assigned, or don’t get any horse.” A Hobson’s choice is still a choice, because there are still two different results. A Morton’s Fork is a false choice because both options have the same result.

On September 11, 1942, Meir Berliner, an inmate of the Treblinka Extermination Camp, stabbed Unterscharführer Max Bialas to death with a penknife during evening roll-call. The Nizkor Project summarizes:

Max Bialas

At the evening roll-call of the prisoners, Max Bialas instructed those who had arrived that same day to line up on the side. It was not clear who was to be liquidated — the new arrivals or those who had arrived earlier. At that moment Berliner jumped out from the ranks of the prisoners, lurched toward Bialas and stabbed him with a knife. A great commotion followed. The Ukranian guards opened fire. Berliner was killed on the spot. and in the course of the shooting more than ten other prisoners were killed and others were wounded. When the tumult subsided the prisoners were lined up again for roll-call. Christian Wirth, who was in Treblinka at the time, arrived on the scene accompanied by Kurt Franz, the second in command of the camp. Ten men were removed from the ranks and shot on the spot in full view of all the others. On the following day, during the morning roll-call, another 150 men were taken out, brought to the Lazarett [the so-called “hospital” which was in fact an execution site] and shot there.

Little is known about Berliner.

According to the testimony of fellow-inmate Abraham Krzepicki, he was a middle-aged Jewish citizen of Argentina who had lived in that country for many years.

He and his wife and young daughter traveled to Poland on vacation in the summer of 1939. They could have picked a better time: when Germany invaded on September 1, 1939, the Berliners were unable to return home. Their Argentine passports should have protected them, but they ended up in the Warsaw Ghetto and were transported to Treblinka. Berliner’s wife and child were gassed immediately, but he was spared to work.

This reprieve would be expected to last days, or a few weeks at the most before he too would go to the gas chamber. Berliner became consumed with rage and the thirst for revenge, supposedly saying, “When the oppressors give me two choices, I always take the third.”

And so he took the first opportunity he could to kill one of his tormentors. As Yitzhak Arad said in his book Belzec, Sobibor, Treblinka: The Operation Reinhard Death Camps*: “His was an individual act of heroism and despair.”

As he must have known he would, Berliner died a horrible death — according to Krzepicki, he was beaten to death with a shovel.

Ironically, following Bialas’s murder, conditions for prisoners at Treblinka actually improved.

This was strictly for pragmatic reasons, as Arad noted: “The Jews selected for temporary work were a danger to the Germans, and the Berliner incident had proved it … When people knew they had nothing to lose, an act of despair like that of Meir Berliner could happen again and again.”

Rather than constantly killing and replacing their workers, the Nazis in charge of the camp decided to create a permanent staff of prisoner-workers and treat them with relative humanity. In this way, they hoped to prevent further acts of suicidal violence on the part of the Jews.

The existence of a permanent cadre of workers made it possible to plan and organize a revolt and mass escape from the camp. In August 1943, after months of conspiring and gathering the necessary weapons, the inmates killed most of the guards and made a run for it. About 300 or so actually made it outside of camp; of those, approximately 60 would survive the war.