It’s roughly on the right track, but here are some inaccuracies in your description that stood out to me:
There is no requirement that the “hidden state space” is finite. It is perfectly fine to consider a credal set which is not a polytope (i.e. not a convex hull of a finite set of distributions).
The point of how market prices are computed, missing from your description, is that they prevent any bettor from making unbounded earnings (essentially, by making them bet against each other). This is the same principle as Garrabrant induction. In particular, this implies that if any of our models is true then the market predictions will converge to lying inside the corresponding credal set.
The market predictions do not somehow assume that “the parts of the universe we don’t observe are out to get us”. Thanks to the pessimistic better, they do satisfy the “not too optimistic condition”, but that’s “not too optimistic” relatively to the true environment.
Your entire description only talks about the “estimation” part, not about the “decision” part.
It’s roughly on the right track, but here are some inaccuracies in your description that stood out to me:
There is no requirement that the “hidden state space” is finite. It is perfectly fine to consider a credal set which is not a polytope (i.e. not a convex hull of a finite set of distributions).
The point of how market prices are computed, missing from your description, is that they prevent any bettor from making unbounded earnings (essentially, by making them bet against each other). This is the same principle as Garrabrant induction. In particular, this implies that if any of our models is true then the market predictions will converge to lying inside the corresponding credal set.
The market predictions do not somehow assume that “the parts of the universe we don’t observe are out to get us”. Thanks to the pessimistic better, they do satisfy the “not too optimistic condition”, but that’s “not too optimistic” relatively to the true environment.
Your entire description only talks about the “estimation” part, not about the “decision” part.