I don’t think the possibility of a money-pump is always a knock-down reductio. It really only makes my preferences seem foolish in the long-run. But there isn’t a long run here: it’s a once-in-a-lifetime deal. If you told me that you would make me the same offer to me thousands of time, I would of course do the clean math that you suggest.
Suppose you are deathly thirsty, have only $1 in your pocket, and find yourself facing two bottled-water machines: The first would dispense a bottle with certainty for the full dollar, and the second would do so with a probability and price such that “clean math” suggests it is the slightly more rational choice. Etc.
The rational choice would be the one that results in the highest expected utility. In this case, it wouldn’t necessarily be the one with the highest expected amount of water. This is because the first bottle of water is worth far more then the second.
The amount of money you make over your lifetime dwarfs the amount you make in these examples. The expected utility of the money isn’t going to change much.
It seems hard to believe that the option of going from B to C and then from C to A would change whether or not it’s a good idea. After all, you can always go from A to B and then refuse to change. Then there’d be no long run. Of course, once you’ve done that, you might as well go from B to C and stop there, etc.
I don’t think the possibility of a money-pump is always a knock-down reductio. It really only makes my preferences seem foolish in the long-run. But there isn’t a long run here: it’s a once-in-a-lifetime deal. If you told me that you would make me the same offer to me thousands of time, I would of course do the clean math that you suggest.
Suppose you are deathly thirsty, have only $1 in your pocket, and find yourself facing two bottled-water machines: The first would dispense a bottle with certainty for the full dollar, and the second would do so with a probability and price such that “clean math” suggests it is the slightly more rational choice. Etc.
The rational choice would be the one that results in the highest expected utility. In this case, it wouldn’t necessarily be the one with the highest expected amount of water. This is because the first bottle of water is worth far more then the second.
The amount of money you make over your lifetime dwarfs the amount you make in these examples. The expected utility of the money isn’t going to change much.
It seems hard to believe that the option of going from B to C and then from C to A would change whether or not it’s a good idea. After all, you can always go from A to B and then refuse to change. Then there’d be no long run. Of course, once you’ve done that, you might as well go from B to C and stop there, etc.