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brian_jaress comments on Ingredients of Timeless Decision Theory - Less Wrong
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Here is what I don't understand about the free will problem. I know this is a simple objection, so there must be a standard reply to it; but I don't know what that reply is.
Denote F as a world in which free will exists, f as one in which it doesn't. Denote B as a world in which you believe in free will, and b as one in which you don't. Let a combination of the two, e.g., FB, denote the utility you derive from having that belief in that world. Suppose FB > Fb and fb > fB (being correct > being wrong).
The expected utility of B is FB x p(F) + fB x (1-p(F)). Expected utility of b is Fb x p(F) + fb x (1-p(F)). Choose b if Fb x p(F) + fb x (1-p(F)) > FB x p(F) + fB x (1-p(F)).
But, that's not right in this case! You shouldn't consider worlds of type f in your decision, because if you're in one of those worlds, your decision is pre-ordained. It doesn't make any sense to "choose" not to believe in free will - that belief may be correct, but if it is correct, then you can't choose it.
Over worlds of type F, the expected utility of B is FB x p(F), and the utility of b is Fb x p(F), and FB > Fb. So you always choose B.
If you can't choose whether you believe, then you don't choose whether you believe. You just believe or not. The full equation still captures the correctness of your belief, however you arrived at it. There's nothing inconsistent about thinking that you are forced to not believe and that seeing the equation is (part of) what forced you.
(I avoid the phrase "free will" because there are so many different definitions. You seem to be using one that involves choice, while Eliezer uses one based on control. As I understand it, the two of you would disagree about whether a TV remote in a deterministic universe has free will.)
edit: missing word, extra word
Brian said:
And Alicorn said:
And before either of those, I said:
These all seem to mean the same thing. When you try to argue against what someone said by agreeing with him, someone is failing to communicate.
Brian, my objection is not based on the case fb. It's based on the cases Fb and fB. fB is a mistake that you had to make. Fb, "choosing to believe that you can't choose to believe", is a mistake you didn't have to make.
Yes. I started writing my reply before Alicorn said anything, took a short break, posted it, and was a bit surprised to see a whole discussion had happened under my nose.
But I don't see how what you originally said is the same as what you ended up saying.
At first, you said not to consider f because there's no point. My response was that the equation correctly includes f regardless of your ability to choose based on the solution.
Now you are saying that Fb is different from (inferior to?) fB.