Decision · experts disagree
Pascal's mugging
Named by Eliezer Yudkowsky in 2007; set out as a dialogue by Nick Bostrom in Analysis, 2009.
A stranger stops you in a dark alley and asks for your wallet. He has no weapon. Instead he makes an offer: hand over the ten dollars in it, and tomorrow he will return with a sum of money so vast it would change your life, or, in another version, he will use powers from outside this universe to spare a quadrillion people from suffering. You point out that this is almost certainly a lie. He agrees it is improbable, then asks you to name a probability. One in a trillion? Fine, he says: the payoff he is offering is so much larger than a trillion times ten dollars that the expected value of paying still comes out positive, so by your own decision theory you should pay.
You use expected value to make decisions and want to keep doing so. Do you hand over the wallet?