Today, I would like to describe the St. Petersburg paradox. It is important because as it has been studied by economists and psychologists who often use it as an example of showing how people unconsciously calculate utility. Most important however, is the fact that humans' "way" of doing it is very much different from what should be expected from the classical expected value theory.
Consider the following game by Daniel Bernoulli:
If I toss a coin and it lands on heads, you win $1.00. If it doesn't, I toss a coin again. If it lands on heads after the second toss, you win $2.00. If I have to toss a coin three times to finally get heads, you will get $4.00 and so on. The game is run once, that is it ends when the coin lands on heads and you win money.
As you can see, you can't loose any money in this game.
Now the question to you is:
How much would you be willing to pay me in order to take part in this game?
The answer, as calculated by the expected value theory, should be: "anything". That is, you should be willing to pay any amount of money as possible benefit of this game is infinite!
It is not hard to see that no one really thinks like this. In fact, we are very well aware that the prospect of larger benefit diminishes in value as the probability of winning decreases. In other words, we know, for example, that winning $32.00 (heads on the 6th toss) is very unlikely.
This observation is extremely interesting for psychologists as it explains why people differ in their preference for the same gamble. The utility- wealth function derived from St Petersburg paradox shows that utility is strongly affected by one's current wealth in a non-linear manner.
Conclusively, the more wealth one owns, the less attractive the gamble will appear to be and vice versa.
Hardman, D. (2009). Judgment and Decision Making: Psychological Perspective.
Oxford: Blackwell Publishing
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