On your first point: I agree that the paper just shows that, as you wrote, “if your decision strategy is to just choose the option you (naively) expect to be best, you will systematically overestimate the value of the selected option”.
I also think that “just choose the option you (naively) expect to be best” is an example of a “nonrandom, non-Bayesian decision strategy”. Now, the first sentence you quoted might reasonably be read to make the stronger claim that all nonrandom, non-Bayesian decision strategies have a certain property. However, the paper actually just shows that one of them does.
Is this what you were pointing to? If so, I’ll edit the quoted sentence accordingly, but I first wanted to check if I understood you correctly.
In any case, thank you for your comment!
Yes, exactly. When first reading your summary i interpreted it as the “for all” claim.
Ok, thanks, I now say “Prove that a certain nonrandom, non-Bayesian …”.