Behavioural economists have found many ways to expose our irrational tendencies. Given a choice between two options, people are sometimes too conservative and at other times too reckless.
One example is whether you’re willing to play a game where you toss a coin and win $20 for heads or lose $10 for tails. From a purely mathematical point of view, almost all people should be willing to play this game. But many are not. Of course the reasons for refusing to play may have nothing to do with math. Some people object to gambling. Others fear that the game is somehow rigged.
Usually, I can overcome any initial irrational feelings about these games to figure out which choice the researchers consider to be the correct choice. However, there is one game that I have a hard time with:
Suppose that you win a prize and your reward is one of the following two choices:
1. $3000 for certain.
2. $4000 with a probability of 80% and nothing with probability 20%.
It turns out that a strong majority of people choose the certain $3000. An insurance company with deep pockets would say the expected value of choice 2 is 80% of $4000 or $3200, which is more than $3000, and therefore choice 2 is better. For those of us without effectively unlimited resources, the calculation is a little more complicated.
To take into account the cost of volatility, it’s best to look at the expected compound return. (For mathy types this is the expected value of the logarithm of your net worth.) It turns out that even if your net worth is only $5000, you should go for choice 2. The majority of us who have much more to our names than $5000 should have a strong preference for choice 2.
However, I can’t shake the feeling that choice 1 feels better. In fact, if I were actually given a chance to play this game only once, I’d probably take the sure $3000. For most of the other test questions I’ve seen researchers use, I’m fairly confident that I could make the more rational choice, but not for this question. So chalk one up for the ancient brain that sees losses in terms of getting eaten by a lion.