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jsteinhardt comments on Maximize Worst Case Bayes Score - Less Wrong Discussion
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Hi Coscott,
I believe that this article by Peter Grunwald and Phil Dawid is relevant: Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory.
Thanks! This is very relevant.
I am not sure if you are implying that this will help with my conjecture. On my first very quick skim through, it looks like this is only dealing with finite spaces, which allows them to use the standard Bayes score, and not this weighted version that I am using. Unfortunately, my conjecture (and some other stronger stuff I want to prove but didn't post) is easy in the case where there is a finite language.
Sorry, I should have been more clear. The thing that I thought might help you (to prove the thing about independence of Bayes score) was the discussion of equalizer rules in the paper. I do not know if it will actually be helpful, just pattern-matching between your question and the paper. Incidentally, my intuition is that you need some assumptions (maybe some sort of convexity?) for the result to hold in general.