Insofar as I understand, you endorse betting on 1:2 odds regardless of whether you believe the probability is 1⁄3 or 1⁄2 (i.e., regardless of whether you have received lots of random information) because of functional decision theory.
But in the case where you receive lots of random information you assign 1⁄3 probability to the coin ending up heads. If you then use FDT it looks like there is 2⁄3 probability that you will do the bet twice with the outcome tails; and 1⁄3 probability that you will do the bet once with the outcome heads. Therefore, you should be willing to bet at 1:4 odds.
That seems strange, and will mean losing money on average. I can’t see how you would get the different probabilities depending on how much random information you receive and still make the same decision about bets.
Actually, I realise that you can get around this. If you use a decision theory that assumes that you are deciding for all identical copies of you, but that you can’t affect the choices of copies that has diverged from you in any way, math says you will always bet correctly.
As I understand it, FDT says that you go with the algorithm that maximizes your expected utility. That algorithm is the one that bets on 1:2 odds, using the fact that you will bet twice, with the same outcome each time, if the coin comes up tails.
I agree with that description of FDT. And looking at the experiment from the outside, betting at 1:2 odds is the algorithm that maximizes utility, since heads and tails have equal probabilities. But once you’re in the experiment, tails have twice the probability of heads (according to your updating procedure) and FDT cares twice as much about the worlds in which tails happens, thus recommending 1:4 odds.
Insofar as I understand, you endorse betting on 1:2 odds regardless of whether you believe the probability is 1⁄3 or 1⁄2 (i.e., regardless of whether you have received lots of random information) because of functional decision theory.
But in the case where you receive lots of random information you assign 1⁄3 probability to the coin ending up heads. If you then use FDT it looks like there is 2⁄3 probability that you will do the bet twice with the outcome tails; and 1⁄3 probability that you will do the bet once with the outcome heads. Therefore, you should be willing to bet at 1:4 odds.
That seems strange, and will mean losing money on average. I can’t see how you would get the different probabilities depending on how much random information you receive and still make the same decision about bets.
Actually, I realise that you can get around this. If you use a decision theory that assumes that you are deciding for all identical copies of you, but that you can’t affect the choices of copies that has diverged from you in any way, math says you will always bet correctly.
Yes, that is shown in Part 2.
As I understand it, FDT says that you go with the algorithm that maximizes your expected utility. That algorithm is the one that bets on 1:2 odds, using the fact that you will bet twice, with the same outcome each time, if the coin comes up tails.
I agree with that description of FDT. And looking at the experiment from the outside, betting at 1:2 odds is the algorithm that maximizes utility, since heads and tails have equal probabilities. But once you’re in the experiment, tails have twice the probability of heads (according to your updating procedure) and FDT cares twice as much about the worlds in which tails happens, thus recommending 1:4 odds.