Why do we often refuse a bet even if probability favors us? Why is a casino player convinced he or she can win everything back despite the very low probability of such an occurrence? Why is a trader usually late to sell stock that is losing value? The Prospect Theory uses cognitive bias to help us understand these unwise decisions.
As part of our “We read it for you” section, Daniel Ray, a professor and researcher at Grenoble Ecole de Management, helps us understand the Prospect Theory that earned D. Kahneman a Nobel Prize in Economics in 2002.
Imagine you are offered a 1,000 dollar coin toss. If you win, you win 1,000 dollars, if you lose, you have to pay 1,000 dollars. Do you take the bet?
We know that the chances of winning or losing are 50-50. Classical utilitarian theory would say we have to take the bet because the probabilities and amounts are equal. Yet the majority of us will refuse the bet.
Now imagine a new coin toss bet: If you win, you win 1,300 dollars and if you lose, you still have to pay 1,000 dollars. Do you take the bet?
In this case, potential earnings far outweigh potential losses (1,300 - 1,000 =300 dollars). Yet, the majority of people will still refuse this bet.
The fear of loss creates a bias in our decision-making process
The Prospect Theory by Daniel Kahneman and Amos Tversky explains that even if potential winnings are higher than losses, most of us prefer not to “take the risk”. This risk aversion has negative consequences in our daily lives:
- Certain people prefer to not work more in order to not pay more taxes. The reason is that even if they end up earning more despite higher taxes, the “psychological cost” of more taxes is determined to be higher than potential increased earning.
- Many of us are willing to take on high risks to not accept already incurred losses. For example, when a player refuses to lose at a casino he or she will take the risk of losing much more even if it’s obvious the chances of winning back lost money are very low.
- In the same manner, financial traders often don’t wish to accept loses. This can encourage them to take important risks: instead of selling stock that is depreciating, they will hold on to it in the slim chance it might increase in value later. This explanation of financial irrationality is one of the reasons D. Kahneman earned the Nobel Prize in Economics in 2002.
Are we truly in control of our decision-making processes?
Kahneman and Tversky explain that many of our choices are based on very quick mental operations and intuitive feelings whose aim is to simplify and quicken our decision making process. While these shortcuts can often be very useful, they can also lead to bad decisions. The Prospect Theory explains this irrationality through five levels:
- Our thinking process depends on our current reference point
When we have to make a decision with risk or an unknown outcome, we generally think in terms of a reference point: above that point and we see gains, below that point we see loss. So if I think I will earn 1,000 dollars and I only earn 500, then I’ll feel as if I’ve lost 500 dollars. Thus I will have a hard time being happy about the 500 dollars I did earn!
- Losses weigh more than gains
For most of us, losses and gains are not “worth” the same amount (“Losses loom larger than gains.”): 100 dollars earned is not worth as much as 100 dollars lost. According to Kahneman, the average risk-aversion for losses is around 1.5 to 2.5 times potential earnings depending on the situation. That means that for our previous example with the coin toss, you would have to offer a bet with a prize of 250 dollars and a loss of 100 dollars before most people would accept.
- We systematically prefer to “protect our gains”
When choosing between two potential winnings, we will try to minimize risk and therefore we generally chose the “safest” solution: a certain and immediate earning is worth more than a potentially bigger score that is uncertain or pays out later. This can help understand why stock that is increasing in value will sometimes be sold too early in order to safeguard immediate earnings.
- Risk aversion
At the same time, when faced with a choice that equates to losing (losing according to our point of reference), we are ready to take important risks to avoid this “loss”. This comes into play in many unwise decisions (e.g., casino players who double down, stay in a losing position, etc.)
- Our perceived value of loss or gain is diminished when the loss or gain is far from our reference point
Losses and gains don’t have the same value depending on our reference point. For example, the cost of spending 10,000 dollars versus 10,100 dollars will be perceived as a small difference, while the cost of spending 100 dollars versus 200 dollars will be seen as a much bigger difference. This is a cognitive bias that real estate and car salesmen are well aware of!
The Prospect Theory can help explain certain “stupid” decisions and encourage us to be aware of mental shortcuts. However, it’s important to remember that this approach applies to decisions we consider risky: if the coin toss bet offered gains and losses of 1 dollar instead of 1,000 dollars, we would certainly take the bet easily!
Kahneman D. et Tversky A. (1979), Prospect theory: an analysis of decisions under risk, Econometrica, 47, 2, 263-291.
Pour une lecture plus générale mais aussi plus abordable des apports de D. Kahneman et A. Tversky, on pourra se référer à Kahneman (2011), Système 1, Système 2 ; les deux vitesses de la pensée, Flammarion, Paris, 551p.