This might be a good argument for the general preferences shown by the Allais paradox. If you strictly prefer 2B to 2A, you might nonetheless have a reason to prefer 1A to 1B—you could leverage your certainty to perform actions contingent on actually having $24,000. This might only work if the payoff is not immediate—you can take a loan based on the $24,000 you’ll get in a month, but probably not on the 34% chance of $24,000.
Because there’s a larger jump in expected utility between certainty (up to breach of contract, etc.) of future money and 99% than between (n < 100)% and (n-1)%. However, this means that the outcome of 1A and the winning outcome of 2A are no longer the same (both involve obtaining money at time t_1, but 1A also includes obtaining, at t_0, certainty of future money), and choosing 1A and 2B becomes unproblematic.
Unless I misunderstood, most of your comment was just another justification for preferring 1A to 1B.
It doesn’t seem to support simultaneously preferring 2B to 2A. Further, as near as I can tell, none of what you’re saying stops the vulnerability that’s opened up by having those two preferences simultaneously. I.e. the preference reversal issue is still there and still exploitable.
Haven’t followed too closely, but I think Nick’s saying that the preference reversal issue doesn’t apply and that’s OK, because as we’ve defined it now 2A is no longer the same thing as a 34% chance of 1A and a 66% chance of nothing, because in the context of what thomblake said we’re assuming you get the information at different times. (We’re assuming the 34% chance is not for your being certain now of getting 1A, but for your being certain only later of getting 1A, which breaks the symmetry.)
Yes to what Nick Tarleton said. I didn’t give a justification for preferring 2B to 2A because I was willing to assume that, and then gave reasons for nonetheless preferring 1A to 1B. There are things that certainty can buy you.
Also yes to what steven0461 said. While you can reverse the symmetry, you can’t reverse it twice—once you’ve given me certainty, you can’t take it away again (or at least, in this thought experiment, I won’t be willing to give it up).
Eliezer’s money-pump might still work once (thus making it not so much a money-pump) but inasmuch as you end up buying certainty for a penny, I don’t find it all that problematic.
This might be a good argument for the general preferences shown by the Allais paradox. If you strictly prefer 2B to 2A, you might nonetheless have a reason to prefer 1A to 1B—you could leverage your certainty to perform actions contingent on actually having $24,000. This might only work if the payoff is not immediate—you can take a loan based on the $24,000 you’ll get in a month, but probably not on the 34% chance of $24,000.
Fine, there could be a good reason to strictly prefer 1A to 1B, but then if you do, how do you justify preferring 2B to 2A?
Because there’s a larger jump in expected utility between certainty (up to breach of contract, etc.) of future money and 99% than between (n < 100)% and (n-1)%. However, this means that the outcome of 1A and the winning outcome of 2A are no longer the same (both involve obtaining money at time t_1, but 1A also includes obtaining, at t_0, certainty of future money), and choosing 1A and 2B becomes unproblematic.
Unless I misunderstood, most of your comment was just another justification for preferring 1A to 1B.
It doesn’t seem to support simultaneously preferring 2B to 2A. Further, as near as I can tell, none of what you’re saying stops the vulnerability that’s opened up by having those two preferences simultaneously. I.e. the preference reversal issue is still there and still exploitable.
Haven’t followed too closely, but I think Nick’s saying that the preference reversal issue doesn’t apply and that’s OK, because as we’ve defined it now 2A is no longer the same thing as a 34% chance of 1A and a 66% chance of nothing, because in the context of what thomblake said we’re assuming you get the information at different times. (We’re assuming the 34% chance is not for your being certain now of getting 1A, but for your being certain only later of getting 1A, which breaks the symmetry.)
Yes, that’s what I meant.
Yes to what Nick Tarleton said. I didn’t give a justification for preferring 2B to 2A because I was willing to assume that, and then gave reasons for nonetheless preferring 1A to 1B. There are things that certainty can buy you.
Also yes to what steven0461 said. While you can reverse the symmetry, you can’t reverse it twice—once you’ve given me certainty, you can’t take it away again (or at least, in this thought experiment, I won’t be willing to give it up).
Eliezer’s money-pump might still work once (thus making it not so much a money-pump) but inasmuch as you end up buying certainty for a penny, I don’t find it all that problematic.