TobyBartels comments on Newcomb's Problem: A problem for Causal Decision Theories - Less Wrong
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Then the prediction has been based on a simulation that took place under different circumstances, since Omega (being perfectly honest) did not say this to the simulation.
But as others have said, this is beside the point. After reading all of these irrelevant objections and the irrelevant responses to them, I'm convinced that (at least when addressing people who understand decision theory up to the point of doing calculations with statistics) it's better to phrase the question so that Omega is simply a clever human being who has achieved very high accuracy with very high correlation on a very large number of previous trials, instead of bringing perfection into it.
I'm thinking something like this:
Also, make the amounts $1 and $1000 so that utility will be very close to linear in amount of money (at least to middle-class First-Worlders like me).