Not a mathematical theorem, and not quantitative, but Campbell's Law is relevant: https://en.wikipedia.org/wiki/Campbell%27s_law
Yeah, I'd be interested if there are rigorous bounds on how badly Goodhart/Campell's Law can screw you in theory (or better, in practice).
Maybe this is worth examining: https://arxiv.org/pdf/math/0410076.pdf
Right. In practice, if you want to engineer the rules to be good, (I think) you need both the rigid, pre-defined, unforgiving logical rules, and some inarticulable "I know it when I see it" rules.
I wonder, are there any theorems on the bounds of how far an optimizer can deviate from another's agent's desired outcome if the agent is limited to specifying the rules in n bits and can specify p arbitrary vetoes?
(Made another reply, but kept this separate for its unrelated point.)