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.
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.