Vladimir_Nesov comments on Newcomb's Problem and Regret of Rationality - Less Wrong

64 Post author: Eliezer_Yudkowsky 31 January 2008 07:36PM

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Comment author: Alicorn 22 July 2010 06:08:14AM 10 points [-]

You are disposed to take two boxes. Omega can tell. (Perhaps by reading your comment. Heck, I can tell by reading your comment, and I'm not even a superintelligence.) Omega will therefore not put a million dollars in Box B if it sets you a Newcomb's problem, because its decision to do so depends on whether you are disposed to take both boxes or not, and you are.

I am disposed to take one box. Omega can tell. (Perhaps by reading this comment. I bet you can tell by reading my comment, and I also bet that you're not a superintelligence.) Omega will therefore put a million dollars in Box B if it sets me a Newcomb's problem, because its decision to do so depends on whether I am disposed to take both boxes or not, and I'm not.

If we both get pairs of boxes to choose from, I will get a million dollars. You will get a thousand dollars. I will be monetarily better off than you.

But wait! You can fix this. All you have to do is be disposed to take just Box B. You can do this right now; there's no reason to wait until Omega turns up. Omega does not care why you are so disposed, only that you are so disposed. You can mutter to yourself all you like about how silly the problem is; as long as you wander off with just B under your arm, it will tend to be the case that you end the day a millionaire.

Comment author: cousin_it 22 July 2010 06:58:56AM *  6 points [-]

Sometime ago I figured out a refutation of this kind of reasoning in Counterfactual Mugging, and it seems to apply in Newcomb's Problem too. It goes as follows:

Imagine another god, Upsilon, that offers you a similar two-box setup - except to get the $2M in the box B, you must be a one-boxer with regard to Upsilon and a two-boxer with regard to Omega. (Upsilon predicts your counterfactual behavior if you'd met Omega instead.) Now you must choose your dispositions wisely because you can't win money from both gods. The right disposition depends on your priors for encountering Omega or Upsilon, which is a "bead jar guess" because both gods are very improbable. In other words, to win in such problems, you can't just look at each problem individually as it arises - you need to have the correct prior/predisposition over all possible predictors of your actions, before you actually meet any of them. Obtaining such a prior is difficult, so I don't really know what I'm predisposed to do in Newcomb's Problem if I'm faced with it someday.

Comment author: Vladimir_Nesov 22 July 2010 07:17:55AM *  4 points [-]

This is not a refutation, because what you describe is not about the thought experiment. In the thought experiment, there are no Upsilons, and so nothing to worry about. It is if you face this scenario in real life, where you can't be given guarantees about the absence of Upsilons, that your reasoning becomes valid. But it doesn't refute the reasoning about the thought experiment where it's postulated that there are no Upsilons.

(Original thread, my discussion.)

Comment author: cousin_it 22 July 2010 07:35:46AM *  0 points [-]

Thanks for dropping the links here. FWIW, I agree with your objection. But at the very least, the people claiming they're "one-boxers" should also make the distinction you make.

Also, user Nisan tried to argue that various Upsilons and other fauna must balance themselves out if we use the universal prior. We eventually took this argument to email, but failed to move each other's positions.

Comment author: Vladimir_Nesov 22 July 2010 07:39:07AM *  0 points [-]

Just didn't want you confusing people or misrepresenting my opinion, so made everything clear. :-)