Any useful treatment of Newcomblike problems will specify explicitly or implicitly how Omega will handle (quantum) randomness.

At the risk of appearing stupid, I have to ask: exactly what is a "useful treatment of Newcomb-like problems" used for?

So far, the only effect that all the Omega-talk has had on me is to make me honestly suspect that you guys must be into some kind of mind-over-matter quantum woo.

Seriously, Omega is not just counterfactual, he is impossible. Why do you guys keep asking us to believe so many impossible things before breakfast? Jaynes says not to include impossible propositions among the conditions in a conditional probability. Bad things happen if you do. Impossible things need to have zero-probability priors. Omega just has no business hanging around with honest Bayesians.

When I read that you all are searching for improved decision theories that "solve" the one-shot prisoner's dilemma and the one-shot Parfit hitchhiker, I just cringe. Surely you shouldn't change the standard, well-established, and correct decision theories. If you don't like the standard solutions, you should instead revise the problems from unrealistic one-shots to more realistic repeated games or perhaps even more realistic games with observers - observers who may play games with you in the future.

In every case I have seen so far where Eliezer has denigrated the standard game solution because it fails to win, he has been analyzing a game involving a physically and philosophically impossible fictional situation.

Let me ask the question this way: What evidence do you have that the standard solution to the one-shot PD can be improved upon without creating losses elsewhere? My impression is that you are being driven by wishful thinking and misguided intuition.