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findis comments on Welcome to Less Wrong! (July 2012) - Less Wrong
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I would one-box. I gave the relevant numbers on this in my previous comment; one-boxing has an expected value of $990,000,000 to the expected $10,001,000 if you two-box.
When you're dealing with a problem involving an effective predictor of your own mental processes (it's not necessary for such a predictor to be perfect for this reasoning to become salient, it just makes the problems simpler,) your expectation of what the predictor will do or already have done will be at least partly dependent on what you intend to do yourself. You know that either the opaque box is filled, or it is not, but the probability you assign to the box being filled depends on whether you intend to open it or not.
Let's try a somewhat different scenario. Suppose I have a time machine that allows me to travel back a day in the past. Doing so creates a stable time loop, like the time turners in Harry Potter or HPMoR (on a side note, our current models of relativity suggest that such loops are possible, if very difficult to contrive.) You're angry at me because I've insulted your hypothetical scenario, and are considering hitting me in retaliation. But you happen to know that I retaliate against people who hit me by going back in time and stealing from them, which I always get away with due to having perfect alibis (the police don't believe in my time machine.) You do not know whether I've stolen from you or not, but if I have, it's already happened. You would feel satisfied by hitting me, but it's not worth being stolen from. Do you choose to hit me or not?
If the professor is a perfect predictor, then I would deliberately get most of the problems wrong, thereby all but guaranteeing a score of over 100 points. I would have to be very confident that I would get a score below fifty even if I weren't trying to on purpose before trying to get all the questions right would give me a higher expected score than trying to get most of the questions wrong.
If the professor posts the list on the board, then of course it should affect the answer. If my name isn't on the list, then he's not going to add the 100 points to my test in any case, so my only recourse to maximizing my grade is to try my best on the test. If my name is on the list, then he's already predicted that I'm going to score below 50, so whether he's a perfect predictor or not, I should try to do well so that he's adding 100 points to as high a score as I can manage.
The difference between the scenario where he writes the names on the board and the scenario where he doesn't is that in the former, my expectations of his actions don't vary according to my own, whereas in the latter, they do.
No, I don't, since you have a time-turner. (To be clear, non-hypothetical-me wouldn't hit non-hypothetical-you either.) I would also one-box if I thought that Omega's predictive power was evidence that it might have a time turner or some other way of affecting the past. I still don't think that's relevant when there's no reverse causality.
Back to Newcomb's problem: Say that brown-haired people almost always one-box, and people with other hair colors almost always two-box. Omega predicts on the basis of hair color: both boxes are filled iff you have brown hair. I'd two-box, even though I have brown hair. It would be logically inconsistent for me to find that one of the boxes is empty, since everyone with brown hair has both boxes filled. But this could be true of any attribute Omega uses to predict.
I agree that changing my decision conveys information about what is in the boxes and changes my guess of what is in the boxes... but doesn't change the boxes.
If the agent filling the boxes follows a consistent, predictable pattern you're outside of, you can certainly use that information to do this. In Newcomb's Problem though, Omega follows a consistent, predictable pattern you're inside of. It's logically inconsistent for you to two box and find they both contain money, or pick one box and find it's empty.
Why is whether your decision actually changes the boxes important to you? If you know that picking one box will result in your receiving a million dollars, and picking two boxes will result in getting a thousand dollars, do you have any concern that overrides making the choice that you expect to make you more money?
A decision process of "at all times, do whatever I expect to have the best results" will, at worst, reduce to exactly the same behavior as "at all times, do whatever I think will have a causal relationship with the best results." In some cases, such as Newcomb's problem, it has better results. What do you think the concern with causality actually does for you?
We don't always agree here on what decision theories get the best results (as you can see by observing the offshoot of this conversation between Wedrifid and myself,) but what we do generally agree on here is that the quality of decision theories is determined by their results. If you argue yourself into a decision theory that doesn't serve you well, you've only managed to shoot yourself in the foot.
In the absence of my decision affecting the boxes, taking one box and leaving $1000 on the table still looks like shooting myself in the foot. (Of course if I had the ability to precommit to one-box I would -- so, okay, if Omega ever asks me this I will take one box. But if Omega asked me to make a decision after filling the boxes and before I'd made a precommitment... still two boxes.)
I think I'm going to back out of this discussion until I understand decision theory a bit better.
Feel free. You can revisit this conversation any time you feel like it. Discussion threads never really die here, there's no community norm against replying to comments long after they're posted.