Remember Pascal’s Wager? It was an argument for the existence of God based on the idea of a payoff matrix, which is heavily dominated by the case in which God exists. So, the conclusion was to believe in God without seeking evidence. Something similar to Pascal’s wager but doesn’t require infinite rewards is Pascal’s mugging, a concept made by Eliezer Yudkowsky and later elaborated by Nick Bostrom.
Pascal was walking down the street. He was stopped by a shady-looking man asking for his wallet. It was an attempt to mug but without having any arms to threaten the victim. Knowing he has no gun to threaten Pascal, the mugger offers a deal. “Give me your wallet and I will give back double the money tomorrow.”
A utilitarian who trusts the expected value theory can make the following calculations and make a decision:
Imagine I have $10 in my wallet, and the minimum probability expected from the mugger keeping his promise is 50% for a break-even value.
This is because the expected value = – 10 + 0.5 x 20 = 0. Since the shady-looking man is not convincing enough to have such a high chance of repaying, I decide not to hand over my wallet.
Hearing the answer, the mugger increases the deal to 10x. That means if Pascal thinks the mugger has a 1/10 chance of paying 10x, he can hand over the wallet. The answer again was negative. The mugger increases the payment to 1000, 10000, and a million. What would Pascal do?
Now, Pascal is in a dilemma. On the one hand, he knows that the probability that the mugger will pay a million dollars is close to zero, and therefore, he must not hand over the wallet. However, as a rational utilitarian, he can’t ignore the fact that the calculations give a profit if the payback is 1 million dollars.
