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Stuart_Armstrong comments on Omega's subcontracting to Alpha - Less Wrong
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Alpha has sent me the envelope, and would do so whatever Omega decided to do. The causal decision as to why Omega visited me is irrelevant.
This is irrelevant.
"I predicted that you will refuse this £10 if and only if there is £1000 000 in Alpha's envelope." is true. To avoid ambiguity, recast is as: XNOR("I predicted you will refuse this £10", "there is £1000 000 in Alpha's envelope") is true.
As for the large ratio:
Omega snatches the £10 away from you, swallows his words, runs out and returns a bit later with a check for £100 000. "Out of deference to your uncertainties", he says, sighing, "I've decided to renew the experiment with a lesser ratio. But just this once!"
No, it's not. If, conditional on me always rejecting the £10 when Omega makes this specific prediction, Omega would visit when the envelope was empty, offer £10 and make the different prediction that I'd take it (the assumption being that I wouldn't refuse it without reason so Omega can't make the true prediction that I'd do so), or if, conditional on me always taking the £10 when Omega makes this specific prediction, Omega would visit when the envelope was full, offer £10 and make the different prediction that I'd take it that would change the payoff. If only the first was true that would make the scenarios equivalent.
I take it of course.