I would have chosen 1A and 2B, for the following reasons: Any sum of the order of $20,000 would revolutionize my personal circumstances. The likely payoff is enormous. Therefore, I’d pick 1A because I’d get such a sum guaranteed, rather than run the 3% risk (1B) of getting nothing at all. Whereas choice 2 is a gamble either way, so I am led to treat both options as qualitatively the same. But that’s a mistake: if the value of getting either nonzero payoff at all is so great, then I should have favored the 34% chance of winning something over the 33% chance, just as I favored the 100% chance over the ~97% chance in choice 1. Interesting.
I would have chosen 1A and 2B, for the following reasons: Any sum of the order of $20,000 would revolutionize my personal circumstances. The likely payoff is enormous. Therefore, I’d pick 1A because I’d get such a sum guaranteed, rather than run the 3% risk (1B) of getting nothing at all. Whereas choice 2 is a gamble either way, so I am led to treat both options as qualitatively the same. But that’s a mistake: if the value of getting either nonzero payoff at all is so great, then I should have favored the 34% chance of winning something over the 33% chance, just as I favored the 100% chance over the ~97% chance in choice 1. Interesting.