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Anything that gets 5 or more downvotes after counting any accidental up votes before getting closed and all within a short time period should be a badge. Unless its not that rare of course... Im hoping it is rare :)
I don't think we want to reward "bad" behavior with a badge! Now the opposite might be worthwhile - a "0 to 60" badge for a question or answer that garners a number of upvotes very quickly.