Ah, the low basis theorem does make more sense of Drucker's paper. I thought Turing degrees wouldn't be helpful because there are multiple consistent guessing oracles, but it looks like they are helpful. I hadn't heard of PA degrees, will look into it.

For corporations I assume their revenue is proportional to f(y) - f(x) where y is cost of their model and x is cost of open source model. Do you think governments would have a substantially different utility function from that?

I think you are assuming something like a sublinear utility function in the difference (quality of own closed model - quality of best open model). Which would create an incentive to do just a bit better than the open model.

I think if there is a penalty term for advancing the frontier (say, for the quality of one's released model minus the quality of the open model) that can be modeled as dividing the revenue by a constant factor (since, revenue was also proportional to that). Which shouldn't change the general conclusion.

It seems this is more about open models making it easier to train closed models than about nations vs corporations? Since this reasoning could also apply to a corporation that is behind.

Thanks, fixed.

I don't see how this helps. You can have a 1:1 prior over the question you're interested in (like U1), however, to compute the likelihood ratios, it seems you would need a joint prior over everything of interest (including LL and E). There are specific cases where you can get a likelihood ratio without a joint prior (such as, likelihood of seeing some coin flips conditional on coin biases) but this doesn't seem like a case where this is feasible.