I'm not entirely sure what "every decision is made with full access to the problem statement means", but I can't see how it can possibly get around the diagonalisation argument. Basically, Omega just says "I simulated your decision on problem A, on which your algorithm outputs something different from algorithm X, and give you a shiny black ferrari iff you made the same decision as algorithm X"
As cousin_it pointed out last time I brought this up, Caspian made this argument in response to the very first post on the Counterfactual Mugging. I've yet to see anyone point out a flaw in it as an existence proof.
As far as I can see the only premise needed for this diagonalisation to work is that your decision theory doesn't agree with algorithm X on all possible decisions, so just make algorithm X "whatever happens, recite the Bible backwards 17 times".
"I simulated your decision on problem A, on which your algorithm outputs something different from algorithm X, and give you a shiny black ferrari iff you made the same decision as algorithm X"
This is a no-choice scenario. If you say that the Bible-reciter is the one that will "win" here, you are using the verb "to win" with a different meaning from the one used when we say that a particular agent "wins" by making the choice that leads to the best outcome.
A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).