Another alternative is a two-axis system. Up-down for agree-disagree, left-right for quality.

Does anything like this exist that you are aware of?

I've never heard of anything like this, though I've thought of it quite a long while back for Reddit. The problem is that it won't solve anything. Most people will still downvote / leftvote things they don't agree with and upvote / rightvote things they do agree with. If the desire to silence a dissenting opinion could be controlled by the majority of people, free speech would not be such a rare thing, let alone need to be written into law.

I agree. That is why I purposely did not equate quality with up and down voting, but left it undefined. Perhaps a solution could be that the quality of a comment was ranked by the number and quality of sub-comments. We would have the beginning of a highly ranked comment thread, for example.