= 27d567bc2d48d9f40e9ccc20ea370b15)
Vaniver comments on Newcomb's Problem and Regret of Rationality - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (588)
Suppose my decision algorithm for the "both boxes are transparent" case is to take only box B if and only if it is empty, and to take both boxes if and only if box B has a million dollars in it. How does Omega respond? No matter how it handles box B, it's implied prediction will be wrong.
Perhaps just as slippery, what if my algorithm is to take only box B if and only if it contains a million dollars, and to take both boxes if and only if box B is empty? In this case, anything Omega predicts will be accurate, so what prediction does it make?
Come to think of it, I could implement the second algorithm (and maybe the first) if a million dollars weighs enough compared to the boxes. Suppose my decision algorithm outputs: "Grab box B and test it's weight, and maybe shake it a bit. If it clearly has a million dollars in it, take only box B. Otherwise, take both boxes." If that's my algorithm, then I don't think the problem actually tells us what Omega predicts, and thus what outcome I'm getting.
In the first case, Omega does not offer you the deal, and you receive $0, proving that it is possible to do worse than a two-boxer.
In the second case, you are placed into a superposition of taking one box and both boxes, receiving the appropriate reward in each.
In the third case, you are counted as 'selecting' both boxes, since it's hard to convince Omega that grabbing a box doesn't count as selecting it.
The premise is that Omega offers you the deal. If Omega's predictions are always successful because it won't offer the deal when it can't predict the result, you can use me as Omega and I'd do as well as him--I just never offer the deal.
The (non-nitpicked version of the) transparent box case shows what's wrong with the concept: Since your strategy might involve figuring out what Omega would have done, it may be in principle impossible for Omega to predict what you're going to do, as Omega is indirectly trying to predict itself, leading to an undecideability paradox. The transparent boxes just make this simpler because you can "figure out" what Omega would have done by looking into the transparent boxes.
Of course, if you are not a perfect reasoner, it might be possible that Omega can always predict you, but then the question is no longer "which choice should I make", it's "which choice should I make within the limits of my imperfect reasoning". And answering that requires formalizing exactly how your reasoning is limited, which is rather hard.