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cousin_it comments on Formalizing Newcomb's - Less Wrong
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Already answered above. If agents' rationality is restricted, the problem loses its original point of refining "perfect rationality" and becomes a question of approximations. Okay, my approximation: when confronted with a huge powerful agent that has a track record of 100% truth, believe it. I one-box and win. Who are you to tell me my approximation is bad?
I don't have problems with that. But Omega doesn't tell you "take one box to win". It only tells that if you'll take one box, it placed a million in it, and if you'll take two boxes, it didn't. It doesn't tell which decision you must take, the decision is yours.
The whole thing is a test ground for decision theories. If your decision theory outputs a decision that you think is not the right one, then you need to work some more on that decision theory, finding a way for it to compute the decisions you approve of.
Annoyance has it right but too cryptic: it's the other way around. If your decision theory fails on this test ground but works perfectly well in the real world, maybe you need to work some more on the test ground. For now it seems I've adequately demonstrated how your available options depend on the implementation of Omega, and look not at all like the decision theories that we find effective in reality. Good sign?
Not quite. The failure of a strong decision theory on a test is a reason for you to start doubting the adequacy of both the test problem and the decision theory. The decision to amend one or the other must always come through you, unless you already trust something else more than you trust yourself. The paradox doesn't care what you do, it is merely a building block towards better explication of what kinds of decisions you consider correct.
Woah, let's have some common sense here instead of preaching. I have good reasons to trust accepted decision theories. What reason do I have to trust Newcomb's problem? Given how much in my analysis turned out to depend on the implementation of Omega, I don't trust the thing at all anymore. Do you? Why?
You are not asked to trust anything. You have a paradox; resolve it, understand it. What do you refer to, when using the word "trust" above?
Uh, didn't I convince you that, given any concrete implementation of Omega, the paradox utterly disappears? Let's go at it again. What kind of Omega do you offer me?
The usual setting, you being a sufficiently simple mere human, not building your own Omegas in the process, going through the procedure in a controlled environment if that helps to get the case stronger, and Omega being able to predict your actual final decision, by whatever means it pleases. What the Omega does to predict your decision doesn't affect you, shouldn't concern you, it looks like only that it's usually right is relevant.
"What the Omega does to predict your decision doesn't affect you, shouldn't concern you, it looks like only that it's usually right is relevant."
Is this the least convenient world? What Omega does to predict my decision does concern me, because it determines whether I should one-box or two-box. However, I'm willing to allow that in a LCW, I'm not given enough information. Is this the Newcomb "problem", then -- how to make rational decision when you're not given enough information?
No perfectly rational decision theory can be applied in this case, just like you can't play chess perfectly rationally with a desktop PC. Several comments above I outlined a good approximation that I would use and recommend a computer to use. This case is just... uninteresting. It doesn't raise any question marks in my mind. It should?
Can you please explain why a rational decision theory cannot be applied?
The problem setting itself shouldn't raise many questions. If you agree that the right answer in this setting is to one-box, you probably understand the test. Next, look at the popular decision theories that calculate that the "correct" answer is to two-box. Find what's wrong with those theories, or with the ways of applying them, and find a way to generalize them to handle this case and other cases correctly.
Why shouldn't you adjust your criteria for approval until they fit the decision theory?
Why not adjust both until you get a million dollars?
I'm liking this preference for (Zen|Socratic) responses.