= 27d567bc2d48d9f40e9ccc20ea370b15)
Tyrrell_McAllister comments on Zeckhauser's roulette - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (45)
Cases B and C are equivalent according to standard decision theory.
Let L be the difference in utility between living-and-not-paying and dying. Let the difference in utility between living-and-paying and living-and-not-paying be X. Assume that you have no control over what happens if you die, so that the utility of dying is the same no matter what you decided to do. Normalize so that the utility of dying is 0.
In Case B, the expected utility of not-paying is 2/3 L + 1/3 0 = 2/3 L. The expected utility of paying is L − X. Thus, you agree to pay if and only if 2/3L ≤ L − X. That is, you pay if and only if X ≤ 1/3 L.
In Case C, the expected utility of not-paying is 1/2 * 0 + 1/2 * 2/3 L = 1/3 L. The expected utility of paying is 1/2 * 0 + 1/2 (L − X) = 1/2 (L − X). Thus, you agree to pay if and only if 1/3 L ≤ 1/2 (L − X). That is, you pay if and only if X ≤ 1/3 L.
Thus, in both cases, you will agree to pay the same amounts.
I understand the argument, but it absolutely depends on your estate being of no value when you're dead. Ok, that's simply one of the rules given in the problem, but in reality, people generally care very much about the posthumous disposal of their assets. The gameshow version makes the problem much clearer, because one can very easily imagine a gameshow run exactly according to those rules.
But then, by making it much clearer, the paradox is reduced: it is easy to understand the equality of the two cases, even if one's first guess was wrong.