V = A / (1 + kD)

– Delay Discounting: I’m a K, You’re a K

These procedures yield an indifference point, the point at which a person switches from preferring the smaller-sooner to the larger-later outcome (when the value of the two outcomes is about equal).

– Delay Discounting: Trait Variable?

The value of something is what someone is willing to part with for it. When doing homework or work assigned by parents, students sometimes rush to finish. They may reason that the faster they finish the necessary, the faster and for longer, they can engage in what they rather be doing. This reasoning while logical is counterproductive.

Students would be very familiar with the concept of short-term pain and long-term gain. Time spent working is time not spent playing – in whatever form that takes to different students. The thought that time is being spent on something that is not immediately rewarding when there are more immediately rewarding options, can cause pain. The pain seems real and the gain does not. So, there may be resistance. This resistance could mean that they apply less effort than they can on exercises.

The heart of the matter is that they may not see the value of a satisfying performance in the future and so they could seek to merely satisfy expectations placed on them in the present. For them to choose to forgo an immediately rewarding experience, they would need to value the pay-off which comes from hitting their targets in the longer term, highly. Researchers have found that children and adolescents may find it harder to accurately compare the value of an immediately satisfying outcome (ice-cream) with that of an outcome which is delayed but of greater value (health) (Green et al., 1996 as cited in Odum, 2011c).

This phenomenon of choosing the “sooner-smaller” over the “larger-later outcome” (Odum, 2011e) is also experienced by adults. Psychologists have studied this. The concepts and findings in this field of research may help students find the short-term needful, less painful and even gainful.

Two such concepts are delay discounting and indifference point.

Delay discounting refers to the discount applied to the value of a future outcome. When asked to choose between an immediate, small reward and a delayed bigger reward, the bigger reward, because of the distance in time, would appear smaller than what lies before the eyes, within grasp. Since the potential gain from what is immediately available, really appears (in an “objective way”), much greater to the person looking, this then would be the preferred choice.

The indifference point refers to a stage when the person choosing is indifferent to the difference in value between the short-term and long-term rewards. The values of the short-term, long-term rewards as well as the indifference point are represented in numbers. For a person to choose to wait, the number which represents the long-term reward has to be greater than the number which represents the indifference point.

Experiments have been done with animals and humans to understand delay discounting and to ascertain the indifference point. Through experiments, researchers have tried to come up with mathematical equations to understand how people value future outcomes. If it is mathematical, it is immediately comprehensible and also predictable.

Such experiments have sought to understand how, the duration of the delay, the actual value (as opposed to what it looks like to the person choosing) of the reward, whether the prize of patience is real and guaranteed, the personality of the person choosing and the circumstances in which the choice is made, affect the decision.

One such example of an experiment, shared by Odum (2011e) was conducted by Mazur (1987). He worked with pigeons. The pigeons could choose to wait for just 2 seconds to obtain access to “2 seconds of food” or “6 s of grain available after a delay”. From the information collected from his experiment, he proposed an equation. In that equation, there is a factor k which “describes how much value is affected by delay” (Odum, 2011e).

If k is large, the value of the delayed reward will appear very small. The value of k is derived from a graph which plots the indifference value against the delay. A large k value will show a line which drops sharply over time and a low k value will show a line with a more gradual slope. A line with a steep drop represents how little one would rather accept now than wait for a larger, delayed, reward.

Researchers have referred to k as “impulsivity” (Odum, 2011e). Odum (2011c) wondered if k could be a personality trait and did find it to be so. Since k is what causes the value of the delayed reward to appear smaller than it actually is, it would be useful for us to understand exactly what k is.

Researchers are of the view that both circumstances and personality affect patience. It also matters what it is we are waiting for. It has been found for example that people tend to be more willing to wait for monetary pay-outs compared to consumable items such as food (Odum, 2011c).

So how can we reduce or otherwise change k so that it becomes easier to say yes to making choices which would produce long lasting benefits?

There are at least two ways according to Odum (2011c).

The first is known as the “fading” technique. This technique can be used in different ways. Odum (2011c) referred to the pigeon experiment. The pigeons learnt to say no to the smaller reward even when they were given immediate access. Initially the waiting times between the smaller and greater reward were the same and so the pigeons made the natural choice. The waiting time for the smaller reward was gradually reduced over separate trials and the pigeons having repeatedly chosen the larger reward were in time loathe to settle for anything less even if they were given immediate access. The other way is to pair the desired behaviour with a reward and to gradually reduce the reward until the behaviour persists regardless of the reward.

The second is to strengthen the working memory. The working memory helps us to keep the bigger picture in mind and to imagine the future.

There are others who also discussed ways to encourage wiser choices. For example, Bortolotti, Stefania and others (2020) also underscored the importance of the working memory. They suggest that those who are already stressed in the present moment because they have to concentrate would be more likely to give up waiting and choose immediate respite instead.

They offered as a solution the research of Benjamin and others (2013) who found that people “make more patient choices when asked to reflect on their choices and report their reasoning” because this “arguably induces deeper thinking”.

We can therefore conclude that, through fading, strengthening the working memory and by asking students to explain their choices, k can be reduced.

Then when students hear, It’s for your own good, they would go k.

The Brain Dojo