isn’t this a problem with the frequency you are presented with the opportunity to take the wager? [no, see edit]
the equation: (50% ((18 +$1) + (2 -$3))) + (50% ((18 -$3) + (2 +$1))) = -$20
neglects to take into account that you will be offered this wager nine times more often in conditions where you win than when you lose.
for example, the wager: “i will flip a fair coin and pay you $1 when it is heads and pay you -$2 when it is tails” is -EV in nature. however if a conditional is added where you will be asked if you want to take the bet 90% of the time given the coin is heads (10% of the time you are ‘in a red room’) and 10% of the time given the coin is tails (90% of the time you are ‘in a red room’), your EV changes from (.5)(1) + (.5)(-2) = -.5 to (.5)(.9)($1) + (.5)(.1)(-$2) = $.35
representing the shift from “odds the coin comes up heads” to “odds the coin comes up heads and i am asked if i want to take the bet”
it seems like the same principle would apply to the green room scenario and your pre-copied self would have to conclude that though the two outcomes are +$12 or -$52, they do not occur with 50-50 frequency and given you are offered the bet, you have a 90% chance of winning. (.9)($12) + (.1)(-$52) = $5.6
EDIT: okay, after thinking about it, i am wrong. the reason i was having trouble with this was the fact that when the coin comes up tails and 90% of the time i am in a red room, even though “i” am not being specifically asked to wager, my two copies in the green rooms are—and they are making the wrong choice because of my precommitment to taking the wager given i am in a green room. this makes my final EV calculation wrong as it ignores trials where “i” appear in a red room even though the wager still takes place.
its interesting that this paradox exists because of entities other than yourself (copies of you, paperclip maximizers, etc) making the “incorrect” choice the 90% of the time you are stuck in a red room with no say.
some other thoughts. the paradox exists because you cannot precommit yourself to taking the wager given you are in a green room as this commits you to taking the wager on 100% of coinflips which is terrible for you.
when you find yourself in a green room, the right play IS to take the wager. however, you can’t make the right play without committing yourself to making the wrong play in every universe where the coin comes up tails. you are basically screwing your parallel selves over because half of them exist in a ‘tails’ reality. it seems like factoring in your parallel expectation cancels out the ev shift of adjusting you prior (50%) probability to 90%.
and if you don’t care about your parallel selves, you can just think of them as the components that average to your true expectation in any given situation. if the overall effect across all possible universes was negative, it was a bad play even if it helped you in this universe. metaphysical hindsight.
isn’t this a problem with the frequency you are presented with the opportunity to take the wager? [no, see edit]
the equation: (50% ((18 +$1) + (2 -$3))) + (50% ((18 -$3) + (2 +$1))) = -$20 neglects to take into account that you will be offered this wager nine times more often in conditions where you win than when you lose.
for example, the wager: “i will flip a fair coin and pay you $1 when it is heads and pay you -$2 when it is tails” is -EV in nature. however if a conditional is added where you will be asked if you want to take the bet 90% of the time given the coin is heads (10% of the time you are ‘in a red room’) and 10% of the time given the coin is tails (90% of the time you are ‘in a red room’), your EV changes from (.5)(1) + (.5)(-2) = -.5 to (.5)(.9)($1) + (.5)(.1)(-$2) = $.35 representing the shift from “odds the coin comes up heads” to “odds the coin comes up heads and i am asked if i want to take the bet”
it seems like the same principle would apply to the green room scenario and your pre-copied self would have to conclude that though the two outcomes are +$12 or -$52, they do not occur with 50-50 frequency and given you are offered the bet, you have a 90% chance of winning. (.9)($12) + (.1)(-$52) = $5.6
EDIT: okay, after thinking about it, i am wrong. the reason i was having trouble with this was the fact that when the coin comes up tails and 90% of the time i am in a red room, even though “i” am not being specifically asked to wager, my two copies in the green rooms are—and they are making the wrong choice because of my precommitment to taking the wager given i am in a green room. this makes my final EV calculation wrong as it ignores trials where “i” appear in a red room even though the wager still takes place.
its interesting that this paradox exists because of entities other than yourself (copies of you, paperclip maximizers, etc) making the “incorrect” choice the 90% of the time you are stuck in a red room with no say.
some other thoughts. the paradox exists because you cannot precommit yourself to taking the wager given you are in a green room as this commits you to taking the wager on 100% of coinflips which is terrible for you.
when you find yourself in a green room, the right play IS to take the wager. however, you can’t make the right play without committing yourself to making the wrong play in every universe where the coin comes up tails. you are basically screwing your parallel selves over because half of them exist in a ‘tails’ reality. it seems like factoring in your parallel expectation cancels out the ev shift of adjusting you prior (50%) probability to 90%.
and if you don’t care about your parallel selves, you can just think of them as the components that average to your true expectation in any given situation. if the overall effect across all possible universes was negative, it was a bad play even if it helped you in this universe. metaphysical hindsight.