A sure thing for $4 million. Or would you risk it?


“Loss aversion is certainly the most significant contribution of psychology to behavioral economics.”
-Daniel Kahnemann

Psychologist Daniel Kahnemann, with his partner Amos Tversky, earned the 2002 Nobel prize in economics for discoveries in the field of behavioral economics. His 2011 book Thinking Fast and Slow is a treasure for everyone seeking to understand the complicated and highly irrational nature of the economic brain.

Kahnemann’s biggest breakthrough came in the development of what is known as Prospect Theory.

In the 1730’s Daniel Bernoulli correctly showed that different levels of wealth have different levels of utility. Consider an increase in someone’s wealth by $1 million dollars: The person with zero dollars will have much greater utility for $1 million dollars than the man with $9 million who reaches the level of $10 million. The amount is the same, but the utility is much higher for the poor man.

Bernoulli’s Utility Theory found that the utility of wealth could be measured:
$ Millions = 1 2 3 4 5 6 7 8 9 10
Units of Utility: 10 30 48 60 70 78 84 90 96 100

So, if you were given this bet, the choice would be fairly simple:
A 50/50 chance to have either $1 million or $7 million, or a 100% chance to have $4 million.
$1 million x 50% is the utility unit of 10 x 50%
$7 million x 50% is the utility unit of 84 x 50%

(50% x 10) + (50% x 84) = 47 vs. 60 which is the100% certainty of $4 million.
You would choose the sure thing and take the $4 million.

Kahnemann and Tversky, building on the theories of Harry Markowitz, proved that Bernoulli’s theorem doesn’t take into account happiness resulting from a recent change.

Imagine that Jack and Jill each have $5 million today. According to Bernoulli, both Jack and Jill have an equal level of utility. Now assume that yesterday Jack had $1 million and Jill had $9 million. Obviously Jack is ecstatic and Jill is miserable.

Kahnemann’s two key points:

1.Utilities are attached to changes in wealth rather than to states of wealth.

2.Losses loom larger than corresponding gains for the economic mind.

What if you had to have surgery on your knee to repair damaged ligaments. Say the doctor informs you that there is a 5% chance that you could lose your leg. How would you feel if he informed you that there was a 10% chance of losing your leg? The percentage change is the same, but the level of risk is perceived to be much higher in the loss-averse mind.

What if the doctor said the same operation has a 95% success rate? What if he said it was 90% successful? What does that make you feel? Framing the question has a major influence on your perception of risk. The use of a negative outcome is far more influential.

Insurance salesmen have plenty of customers.