How about introducing a badge that rewards downvoting, but only of the sensible kind?
A measure for sensible downvoting would be a
high percentage certain number of downvotes on content that has subsequently been
- Closed (except migrations and duplicates)
Bronze, Silver, and Gold badges would vary in numbers, say
Bronze: cast 50 downvotes on content that was subsequently closed or deleted
This would encourage downvoting (which is great and needed), but of the measurably sensible kind only.
What good actual numbers would be for Bronze, Silver, and Gold would be a separate discussion. Feel free to suggest numbers in your answers, as well as name suggestions (the only I managed to come up with was
Whistleblowerand that isn't really accurate. I'm more imagining the old lady calling the council over some abandoned litter in the streets, or broken windows... but in a good way of course.