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I've found discussions on up/down vote ratios but another ratio that might be useful is answers to down-votes. If a user has a low number of answers but high number of down-votes then they could be trawling the site poo-pooing but not actually providing useful input. I see that as quite a negative attitude, like they are afraid of contributing and being open to criticism themselves.
I don't think this would be worth displaying anywhere, nor is it badge-worthy but maybe a quiet, system gnerated warning when it reaches a certain level?

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Well, there are useless downvotes - and useful ones. In particular, I find a downvote with an explanatory comment to be a useful contribution. Warning someone away from a bad answer is sometimes just as useful as providing a good one yourself. In particular, if the right answer already exists, then there's no point in adding it again - but by upvoting the right answer and downvoting the wrong one, you'd be making the overall question more useful.

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A good alternative to "downvote + comment" is "downvote + upvote comment" – Super Long Names are Hilarious Jan 22 '10 at 8:25

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