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grobstein comments on Rationality is Systematized Winning - Less Wrong
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By construction, Omega's predictions are known to be essentially infallible. Given that, whatever you choose, you can safely assume Omega will have correctly predicted that choice. To what extent, then, is pre-commitment distinguishable from deciding on the spot?
In a sense there is an implicit pre-commitment in the structure of the problem; while you have not pre-committed to a choice on this specific problem, you are essentially pre-committed to a decision-making algorithm.
Eliezer's argument, if I understand it, is that any decision-making algorithm that results in two-boxing is by definition irrational due to giving a predictably bad outcome.
So he's assuming the conclusion that you get a bad outcome? Golly.
True, we don't know the outcome. But we should still predict that it will be bad, due to Omega's 99% accuracy rate.
Don't mess with Omega.
The result of two-boxing is a thousand dollars. The result of one-boxing is a million dollars. By definition, a mind that always one-boxes receives a better payout than one that always two-boxes, and therefore one-boxing is more rational, by definition.
The result of two-boxing is a thousand dollars more than you would have gotten otherwise. The result of one-boxing is a thousand dollars less than you would have gotten otherwise. Therefore two-boxing is more rational, by definition.
What determines whether you'll be in a 1M/1M+1K situation or in a 0/1K situation is the kind of mind you have, but in Newcomb's problem you're not given the opportunity to affect what kind of mind you have (by pre-commiting to one-boxing, for example), you can only decide whether to get X or X+1K, regardless of X's value.
Suppose for a moment that one-boxing is the Foo thing to do. Two-boxing is the expected-utility-maximizing thing to do. Omega decided to try to reward those minds which it predicts will choose to do the Foo thing with a decision between doing the Foo thing and gaining $1000000, and doing the unFoo thing and gaining $1001000, while giving those minds which will choose to do the unFoo thing a decision between doing the Foo thing and gaining $0 and doing the unFoo thing and gaining $1000.
The relevant question is whether there is a generalization of the computation Foo which we can implement that doesn't screw us over on all sorts of non-Newcomb problems. Drescher for instance claims that acting ethically implies, among other things, doing the Foo thing, even when it is obviously not the expected-utility-maximizing thing.
See Arguing "By Definition". It's particularly problematic when the definition of "rational" is precisely what's in dispute.