Sure! I would like to clarify, though, that by “logically omniscient” I also meant “while being way larger than everything else in the universe.” I’m also readily willing to admit that Bayesian probability theory doesn’t get anywhere near solving decision theory, that’s an entirely different can of worms where there’s still lots of work to be done. (Bayesian probability theory alone does not prescribe two-boxing, in fact; that requires the addition of some decision theory which tells you how to compute the consequences of actions given a probability distribution, which is way outside the domain of Bayesian inference.)
Bayesian reasoning is an idealized method for building accurate world-models when you’re the biggest thing in the room; two large open problems are (a) modeling the world when you’re smaller than the universe and (b) computing the counterfactual consequences of actions from your world model. Bayesian probability theory sheds little light on either; nor is it intended to.
I personally don’t think it’s that useful to consider cases like “but what if there’s two logically omniscient reasoners in the same room?” and then demand a coherent probability distribution. Nevertheless, you can do that, and in fact, we’ve recently solved that problem (Benya and Jessica Taylor will be presenting it at LORI V next week, in fact); the answer, assuming the usual decision-theoretic assumptions, is “they play Nash equilibria”, as you’d expect :-)
Cool, I will take a look at the paper!