I think that the "U/P" name is awkward. I was looking for a descriptive, pronounceable acronym, and I came up with MUMA, for Most Upvoted Majority Acceptable. This gives the heart of the method in four words: of those with majority above-bottom votes, find the one with the most top votes. Here's the full definition: For each candidate, you can downvote (rate "unacceptable"); upvote (rate "preferred"); or neither. All candidates downvoted by a majority of those voting in the election, or with fewer than half the upvotes of the most-upvoted candidate, are eliminated, unless that would eliminate everyone. Of those remaining, the most-upvoted wins. Optionally, if you want to give this system a bit of a NOTA twist, you can have an additional rule that it is noted on the ballot when there's a candidate who got majority "unacceptable" in the previous election for the same post. This would mostly affect incumbents who had previously won in elections where all candidates had majority "unacceptable".