Nick Naumof: Practical Applications of Prospect Theory

Prospect theory is one of the foundation stones of behavioral economics. Subsequently it has numerous implications for practice and in this post I will present four of them. These four principles were introduced by Richard Thaler. Mr. Thaler is an economist, but what made his work special is that he embraced behavioral insights and incorporated them in his work on economics.

I strongly recommend his book Nudge written with Cass R. Sunstein. It is a wonderful collection of how insights from behavioral sciences can be used.

Before presenting the four principles proposed by Richard Thaler, I would like to invite you to take a look at the graph for the utility (value) function from prospect theory.

As you can see, this function is concave for gains and convex for losses. In simpler words, for gains: in the case of large amounts the benefit per unit decreases. Similarly for loses: in the case of large amounts the pain per unit decreases.

In addition, as you can see from the graph, the slope of the function is steeper for losses compared to the area of gains. This is loss aversion. In brief, a loss hurts more than the pleasure brought by an equal gain.

Keeping this in mind, here are the four principles of integration or segregation of outcomes proposed by Richard Thaler:

First, segregate gains. When faced with a large gain, the utility (benefit) per unit decreases (the function is concave). This implies that two smaller gains are better than a larger one with a value equal to the sum of the two smaller ones.

For example if you are to offer a future discount of 100 Euros in the form of a voucher, it will be better for the client to receive two vouchers of 50 Euros.

In mathematical expression this would go like this:

U(50) + U(50) > U(100)

Second, integrate losses. In the case of losses the function is concave, this implying that the pain of a large loss is smaller than the added pain of two smaller losses that summed up are equal in value with the larger loss.

For example if someone has to suffer a pay cut it is better to say that his overall annual salary will be smaller with 3000 Euros in total than to say that 2000 Euros will be cut from the actual salary and 1000 will be cut from the annual bonus.

In mathematical expression this would go like this:

U(-2000) + U(-1000) > U(-3000)

Don’t get me wrong, I am not saying that the person will not feel pain (disutility). It is just a comparison between two amounts of pain.

Third, cancel losses against larger gains. Since losses loom larger than gains, it is better to have a smaller gain than a larger gain and a loss.

For example, if you have two projects that might or might not pay off and one of them brings a profit of 1000 Euros, while the other failed to become profitable and lead to a loss of 200 Euros. Instead of seeing the outcome as 1000 Euros gain and 200 Euros loss it is much better to see it as 800 Euros gain.

In general losses bring a pain that is twice as large as the pleasure of a gain in equal amount would be. In this case the 200 Euros loss will be perceived as a “pain” that could be compensated by a gain of 400 Euros. This would leave you with the benefit (utility / pleasure) of only 600 Euros.

In mathematical expression this would go like this:

U(-200) + U(1000) < U(800)

Fourth, segregate “silver linings” (large loss, small gain). The utility function is concave in the case of losses, implying that the difference between in the pain generated by a loss of 1000 Euros and the pain generated by a loss of 1010 Euros will be very small. At the same time in the area of gains the function is convex, but only for larger values. This implies that when having to deal with a large loss and a small gain it is better to not integrate them.

For example, if your car broke down and you need to pay 1010 Euros for repairing it and in the same day you play the lottery and win 10 Euros, it is better to see these two outcomes separately. Truly, the pain of losing 1010 Euros is roughly the same as losing 1000. At the same time, the pleasure of wining 10 euros in a lottery is quite large in comparison with no wining anything.

In mathematical expression this would go like this:

U(-1010) + U(10) > U(-1000)

These principles proposed by R. Thaler seem common sense, but at the same time they are very important and sometimes we simply don’t take them into account.