Interested in math, Game Theory, etc.
I wouldn't say there's flaws in reasoning. Just that multiple comparisons are more likely to have issues, it's just a proxy, etc.
It's an interesting idea.
Your second argument seems to imply social neutrality, rather than pro- or anti-. It's not strong enough to match the claim above (although it is following a conditional).
If you keep increasing P, the connection might break.
Other possibilities that spring to mind are:
The question is why does the attic work so well. Why does no one talk about the attic?
Someone dies and you get sued. (All it takes is one allergic reaction, or someone who already had asthma, and you're a murderer.)
Do you wish you didn't have it?
Combine it with getting entrance to a place. It doesn't have last too long, just long enough.
Maybe Scott has a secret identity.
Here's a fictional story:
You decide to study more. Your grades go up. You like that, so you decide to study really really hard. You get burnt out. Your grades go down. (There's also an argument here that the metric - grades - isn't necessarily ideal, but that's a different thing.)*
*There might be a less extreme version involving 'you stay up late studying', and 'because you get less sleep it has less effect (memory stuff)'.
This isn't meant as an unsolvable problem - it's just that:
and
are both true.
Maybe this style of mechanism, or 'causal influence' is rare. But its (biological) nature arguably, may characterize a domain (life). So in that area at least, it's worth taking note of.
I guess I'm saying, if you want to know if you have to be worried about Goodhart's Law, in general, I think it depends. Just spend time optimizing your metric, and spend time optimizing for you metric, and see what happens. If you want more specific feedback, I think you'll probably have to be more specific.