It’s time to get this nebulous idea of “utility” straight. The term itself was coined by scientist Daniel Bernoulli, who in 1738 proposed a solution to a curious expected value conundrum called the St. Petersburg Paradox.
Here’s the paradox: suppose you and I play the following game. I flip a fair coin until the first heads appears. This first heads turns up on the nth flip and when it does, I will pay you 2n dollars (= 2 * 2 * … * 2, n times). But you first have to pay me a fee to play this game. How much are you willing to pay?
Think it over. I suspect you wouldn’t pay a huge fortune to play this game. Now, using our expected value tools, let’s compute the expected value of the game. The probability that the first flip is ...