We have seen how a rational decision-maker may operate using either the expected value or the expected utility theory. Real-life, however, is not so straightforward about these kinds of outcomes. In a famous Tversky-Kahneman experiment, three groups were presented with three situations.
1: Which of the following do you prefer?
A. a sure win of $30
B. 80% chance to win $45
2: There is a two-stage game with a 25% chance to advance to the second stage. After reaching the second, you get the following choices, but you must give the preference before the first stage. If you fail in the first, you get nothing.
C. a sure win of $30
D. 80% chance to win $45
3: Which of the following do you prefer?
E. 25% chance to win $30
F. 20% chance to win $45
Expected Values
We will look at the expected values of each of the options. You will argue that it’s not how people make decisions in real-life. But, keep it as a reference. Remember: EV = value x chance, summed over.
| Case | EV |
| A | $30 |
| B | $36 ($45 x 0.8) |
| C | $7.5 (0.25 x $30) |
| D | $9 (0.25 x $45 x 0.8) |
| E | $7.5 (0.25 x $30) |
| F | $9 (0.2 x $45) |
What did people say?
In the first group, 78% of the participants chose option A. In the second, it was 74% in favour of option C. It was almost a tie (42% for E and 58% for F) for the final group.
These three problems are, in one way, similar to each other. We will see that next.
Tversky, A.; Kahneman, D., Science, 1981, 211, 453
