I've noticed potentially good questions that are poorly worded or have bad titles and thus have at least a couple of downvotes or even close votes. On occasion, after a quick edit, these questions go on to get at least a couple upvotes. These aren't bad questions, they're just poorly worded--which in my understanding is exactly why we're allowed to change votes after a post has been edited.
It could be a bronze badge, one-time-only to keep it from being too "easy" but I think it would be a good way to encourage people to clean up downvoted posts (that have redeeming potential) rather than killing them. Obviously it shouldn't be obtainable from your own questions to prevent gaming the system, and require some set limit of downvotes/upvotes to activate.