Or maybe some other variation of that, like "20 downvotes anywhere within 1 day". Probably it should be bronze regardless.
It seems like there's a script running against this badge, but that'd be fine. It's just for fun anyway. :D
Well, maybe it will be an incentive for most not getting that. I don't know.
edit: What about this other perspective - out of over 40 badges, all for "good behavior" none is actually "awarded" for "bad behavior". So, having at least 1 could give us a better idea of how people are behaving in the "bad manner". As for how people would actually react to that, I say that guessing here is pure speculation.