Very interesting! I like this formalization/categorization.
Hm... I'd have filed "Why the tails come apart" under "Extremal Goodhart": this image from that post is almost exactly what I was picturing while reading your abstract example for Extremal Goodhart. Is Extremal "just" a special case of Regressional, where that ellipse is a circle? Or am I missing something?
Very interesting! I like this formalization/categorization.
Hm... I'd have filed "Why the tails come apart" under "Extremal Goodhart": this image from that post is almost exactly what I was picturing while reading your abstract example for Extremal Goodhart. Is Extremal "just" a special case of Regressional, where that ellipse is a circle? Or am I missing something?