This could be a privilege to be given after some amount of reputation. Consider accordingly.
When a user receives a down-vote, without having laid a comment for the reason why, that user -right now- gets a recommendation message to leave down a comment for the reason why. Users may ignore that recommendation and they should be able to. It could be that the reason is obvious, or some other thing, so they should be able to.
However, sometimes the guy or the lady who had given the answer, may not understand for what his or her answer could have been voted down. It should be a natural request to ask for what one had done wrong after having disapproved. If one couldn't figure out the reason himself or herself, and not told about it either, then he or she may never know what he or she should do to improve himself/herself.
Back to the part where we ask for the reason: We should be able to do that in this environment as well, just like we can when we are face to face.
Here is what I am suggesting for things to happen:
~ After 200 reputation points, users are to be given this privilege.
~ When someone's answer gets voted down, and that other someone who had cast that vote had not left a comment, then the one who gave the answer is to be given a button to use for asking for why.
~ With the use of that button, the one(s) who voted down the answer are to get informed about the request of the one who answered the question.
~ For each request that does not get fulfilled within 2 days, the corresponding vote is to get discarded.
After this process, an addition to that would be:
~ The comment as the reason is to be marked as a reason by a light blue centre-dot behind the comment.
~ Such comments will be official the reason for the corresponding vote, and be referred as a document for further cases like: Down-vote inspection per request
In general, this would flourish the quality criticism which could really nicely happen in Stack Overflow, but unfortunately does not happen that so often. People would know where they had been wrong, therefore have the opportunity to improve themselves; and people would act more reasonable, literally, since they will be giving reasons for their actions.
Numbers are not strict, feel free to discuss.
This could be extended to questions, if found useful.