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Roko comments on Counterfactual Mugging - Less Wrong
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I really fail to see why you're all so fascinated by Newcomb-like problems. When you break causality, all logic based on causality doesn't function any more. If you try to model it mathematically, you will get inconsistent model always.
The primary reason for resolving Newcomb-like problems is to explore the fundamental limitations of decision theories.
It sounds like you are still confused about free will. See Righting a Wrong Question, Possibility and Could-ness, and Daniel Dennett's lecture here.
I think I'm not confused about free will, and that the links I gave should help to resolve most of the confusion. Maybe you should write a blog post/LW article where you formulate the nature of your confusion (if you still have it after reading the relevant material), I'll respond to that.
I find the problem interesting, so I'll try to explain why I find it interesting.
So there are these blogs called Overcoming Bias and Less Wrong, and the people posting on it seem like very smart people, and they say very reasonable things. They offer to teach how to become rational, in the sense of "winning more often". I want to win more often too, so I read the blogs.
Now a lot of what these people are saying sounds very reasonable, but it's also clear that the people saying these things are much smarter than me; so much so that although their conclusions sound very reasonable, I can't always follow all the arguments or steps used to reach those conclusions. As part of my rationalist training, I try to notice when I can follow the steps to a conclusion, and when I can't, and remember which conclusions I believe in because I fully understand it, and which conclusions I am "tentatively believing in" because someone smart said it, and I'm just taking their word for it for now.
So now Vladimir Nesov presents this puzzle, and I realize that I must not have understood one of the conclusions (or I did understand them, and the smart people were mistaken), because it sounds like if I were to follow the advice of this blog, I'd be doing something really stupid (depending on how you answered VN's problem, the stupid thing is either "wasting $100" or "wasting $4950").
So how do I reconcile this with everything I've learned on this blog?
Think of most of the blog as a textbook, with VN's post being an "exercise to the reader" or a "homework problem".
Not really - all that is neccessary is that Omega is a sufficiently accurate predictor that the payoff matrix, taking this accuracy into question, still amounts to a win for the given choice. There is no need to be a perfect predictor. And if an imperfect, 99.999% predictor violates free will, then it's clearly a lost cause anyway (I can predict with similar precision many behaviours about people based on no more evidence than their behaviour and speech, never mind godlike brain introspection) Do you have no "choice" in deciding to come to work tomorrow, if I predict based on your record that you're 99.99% reliable? Where is the cut-off that free will gets lost?
Chances are I can predict such a response too, and so won't tell you of my prediction (or tell you in such a way that you will be more likely to attend: eg. "I've a $50 bet you'll attend tomorrow. Be there and I'll split it 50:50"). It doesn't change the fact that in this particular instance I can fortell the future with a high degree of accuracy. Why then would it violate free will if Omega could predict your accuracy in this different situation (one where he's also able to predict the effects of him telling you) to a similar precision?
Then take my bet situation. I announce your attendance, and cut you in with a $25 stake in attendance. I don't think it would be unusual to find someone who would indeed appear 99.99% of the time - does that mean that person has no free will?
People are highly, though not perfectly, predictable under a large number of situations. Revealing knowledge about the prediction complicates things by adding feedback to the system, but there are lots of cases where it still doesn't change matters much (or even increases predictability). There are obviously some situations where this doesn't happen, but for Newcombe's paradox, all that is needed is a predictor for the particular situation described, not any general situation. (In fact Newcombe's paradox is equally broken by a similar revelation of knowledge. If Omega were to reveal its prediction before the boxes are chosen, a person determined to do the opposite of that prediction opens it up to a simple Epimenides paradox.)
On second thoughts, since many clever philosophers spend careers on these problems, I may be missing something.
Nah, they just need something to talk about.