grobstein comments on Rationality is Systematized Winning - Less Wrong
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We have such an Omega: we just refer to it differently.
After all, we are used to treating our genes and our environments as definite influences on our ability to Win. Taller people tend to make more money; Omega says "there will be $1mil in box B if you have alleles for height."
If Omega makes decisions based on properties of the agent, and not on the decisions either made or predicted to be made by the agent, then Omega is no different from, well, a lot of the world.
Rationality, then, might be better redefined under these observations as "making the decisions that Win whenever such decisions actually affect one's probability of Winning," though I prefer Eliezer's more general rules plus the tacit understanding that we are only including situations where decisions make a difference.
Quoting myself:
I'll go further and say this distinction doesn't matter unless you assume that Newcomb's problem is a time paradox or some other kind of backwards causation.
This is all tangential, though, I think.