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Vladimir_Nesov comments on Omega's subcontracting to Alpha - Less Wrong
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Comments (90)
Not good. All you've achieved is redirected Omega to situations in which you don't take its money. It's better to have Omega where you do take its money, it's free money.
For some reason, this reply specifically cemented the argument for me. Thank you - I now agree with you.
Edit: If it helps, my confusion was the appearance of causation from I-refuse-the-£10 to I-receive-the-£1e6. When you made this comment, I mentally went back and saw that the fraction of possible worlds in which Alpha gives me the million is unchanged by Omega's prediction, and therefore that I can take the tenner without affecting it.
Right - and finally I am there as well :-)
If there was a 50% chance Omega in the future visits someone who would refuse to take the £10 and gives them £1'000'000, and a 50% chance Omega visits someone who would accept the £10 and gives them £10 and an empty envelope, what would you prefer? Depending how you would behave if Omega visited you the probability of either the first or the second person being you is zero.
Refuse obviously. You've described how my choice controls the payoff, which is not the case with Alpha.
Would you still get the envelope if Omega wasn't going to visit you? I had automatically assumed that Omega initiated the whole situation because the title said that Omega was subcontracting, but I see that the body doesn't actually state that.
Edited to make this clear
Yes, this seems to be assumed, though it didn't actually happen this way, Omega did visit you.
If that's the scenario and if the only method Omega uses to ensure its prediction is accurate is selective visits your conclusion is obviously correct. I doubt there is anyone here who (correctly?) understood it that way and disagrees.
The main problem with such thought experiments is understanding them correctly (or better, having your formal decision theory represent them correctly), from where the conclusion usually follows trivially. Just try convincing a game theorist to cooperate in Prisoner's dilemma, even experimental observations contradicting the theory of rational defection won't help.