Prospect Theory — Understanding Losses And Gains

Aditya Prakash
3 min readDec 11, 2020

Traditional economics has been based on Expected Utility theorem , which simply states under uncertainty, the utility at any given point in time will be presented by the weighted average of the probabilities.

Therefore , if we were to play a game, Which option would you chose and why?

a) Sure win of $ 1000

b) You toss a coin, you gain $ 2000 if it’s a heads and get nothing (zero) if its tails.

Now, as per expected value theorem, a rational person should be indifferent between the 2 options, as the expected value from both the options is $1000

However, that is not what is exhibited by people, a vast majority of people in this game always pick option a) , the reason to this lies in the fact that humans are irrational at times and many of our behaviors cannot be explained by the traditional economics theorems. As Richard Thaler writes in his book Misbehaving , most economists make this mistake of assuming that ordinary people behave like economists , but instead they behave differently. They are at times irrational or even biased. The explanation to the above example was studied many years ago by Daniel Kahneman and Amos Tversky when they introduced Prospect Theory.

Prospect Theory

Based on studies carried out by Tversky and Kahneman it was discovered that ordinary humans did not see losses and gains the same way as described by the expected value theorem. Therefore , the pain of losing of $1000 was not the same as the joy of gaining $1000 , which would have been the case as per expected value theorem.

Prospect theory is able to establish that humans are very risk averse to losses and therefore if given a chance, would be risk averse to prevent losses rather than take risk to increase their wealth. The below graph which many now associate with prospect theory shows if losses and gains ( x- axis) could be plotted against an assigned value on the y-axis, we can see that the value associated with a 0.5$ gain is close to 20 , but the value associated with a loss of 0.5$ is almost twice that at 40.

We can conclude from this graph that losses hurt twice as much as gains. So, the pain of losing $1000, therefore can only be compensated by a gain of $2000.

Now, going back to the game we played at the beginning

If we were to play a game, Which option would you chose and why?

a) Sure win of $ 1000

b) You toss a coin, you gain $ 2000 if it’s a heads and get nothing (zero) if its tails.

Based on our understanding of prospect theory , which states that people are risk averse and hate losing , would mean that a majority of people would pick option 1 , even if both options have the same expected value . Therefore, in gains , we are always risk averse, we do not want to lose a sure win by gambling

However, the scenario is completely changed when we frame the question differently , lets take a look

You have just lost $3000, because I told you so. Now, I ask you to play the following game.

Which option would you pick?

a) Win $3000 if the throw of a die yields 1 or 2 , of gain nothing otherwise

b) A sure win of $1000

Here, the person has already lost $3000, the pain of which will suddenly prompt people to become risk seeking and pick option a) in overwhelming majority.

Thus, even with a sure win of $1000 , people are risk seeking and reject option b) for a) as they want to regain back their losses, which again goes back to prospect theory which states that losses hurt twice as much as gains.

Thus, to conclude, humans will always be risk averse in gains , but risk seeking in losses.

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