I'm extremely confused with the concept of the Unsung Hero badge, since it counts the answers that are both accepted and upvoted. It suggests that the questioner will accept an answer but not upvote it. Don't you think it's a bit schizophrenic behaviour? Or the badge is for people who accept their own answert, unable to upvote it?
From the Badges page
Zero score accepted answers: more than 10 and 25% of total
It's to reward those people who's answers are accepted but not upvoted. This can be for many reasons - one being that new users can post questions and accept answers, but can't up-vote until they get 15 rep, another being where there are few users who are knowledgeable in a tag.
So it's a way of rewarding those people who help the new users to the site.
I don't think self accepted answers count.