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Eliezer_Yudkowsky comments on Omega's subcontracting to Alpha - Less Wrong
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Comments (90)
I assume the problem is to be interpreted as Omega saying, "Either (1) (I have predicted you will refuse the $10, and there is $1000,000 in the envelope) xor (2) (I have predicted you will take the $10, and there is $0 in the envelope)", rather than asserting some sort of entanglement above and beyond this.
If so, I take the $10 and formulate the counterfactual, "If I were the sort of person who rejected the $10, Omega would have told me something else to begin with, like 'if you refuse the $10 then the envelope will be empty', but the digit of pi would have been the same".
As previously noted, though, I can't quite say how to compute this formally.
I assume you would consider "You will take this $10 if and only if Barack Obama is president of the United States." true even if you were completely certain you would take the $10 if John McCain was President. If and only if this was the intended meaning I would agree with your conclusion.
Re: "If I were the sort of person who rejected the $10, Omega would have told me something else to begin with"
...but why would he do that? Is there some assumption about Omega's motivation here?
It's correct if we expand it to "Omega would have told me something else or not shown up to begin with", or if we're assuming that Omega will show up and say something. It would have to say something like "if you refuse the $10 then the envelope will be empty" — or some other true thing, not the statement given in the original post — since we're assuming it's a perfect predictor and is being honest.
Omega can say:
"I have predicted you will refuse the $10, and there is $1000,000 in the envelope".
There is absolutely no problem with that - if you are a refuser (as specified in the hypothetical) and if the envelope does indeed contain $1000,000.
True, he would have to say something else, in the case where the envelope is empty.
Ah, yes, you're right.
Now I'm not sure if I was correctly interpreting Eliezer's point or just restating my own.