It was suggested that requiring a category for a down-vote would create an asymmetry between up- and down-votes, so I am amending my suggestion to include up-votes along with down-votes.
This may be a partial duplicate, but the two ideas seem to belong together, so I am repeating the "comment" suggestion, (but adding to it the suggestion that an anonymous comment feature be added for down-votes.)
When I invest considerable time and effort in formulating and composing a question which I post to math.se, and have it down-voted, that is discouraging. It reduces my motivation to contribute, and rarely communicates anything helpful. I often suspect some kind of bigotry, bias or other petty motive is behind the down-vote, rather than an effort to improve quality of content.
As I understand it, the reason down-voting is anonymous is that it encourages people to down-vote because, for some reason down-votes are considered valuable. IMO this encourages quantity over quality of down-votes.
I will suggest that down-votes be categorized. In other words, down-voting would require the selection of a reason (poorly formulated|off-topic|insufficient effort|is open-ended|don't like user|that's homework you should do on your own). I also recommend including the suggestion that the down-voter leave a comment (possibly anonymously) explaining the reason.
I understand that anonymity of down-voting is a way of avoiding "down-vote wars", but it has its drawbacks as well.
I believe the suggested features would also encourage participants to be more thoughtful in their voting practices. That is, it would remind them of what a vote is intended to communicate.