Majority Acceptable Score voting

Majority Acceptable Score voting works as described below. Technically speaking, it's the graded Bucklin method which uses 3 grade levels and breaks median ties using Score voting.

• Voters rate candidates 0, 1, or 2.
• Any candidate rated 0 by a majority is eliminated, if any would remain.
  • (If there are any candidates rated 2 by a majority, you should eliminate any who aren't. But a majority-2 candidate would probably win in the next step anyway, so this step is probably superfluous. It's just included because it's part of Bucklin voting, which was used in over a dozen US cities, and thus it gives this method a stronger pedigree.)
• Then the points are added up for the remaining candidates, and the highest points wins.

Blank votes are counted as ratings of 1 or 0 in proportion to the fraction of all voters who gave the candidate a 2. For example, a candidate could not win with more than 71% blank votes, because even if the other 29% are all 2-ratings, that would leave 71%*71%=50.41% 0-votes, enough to eliminate.

Here's a google spreadsheet to calculate results: [1]. On page 2, it has some hypothetical results for the Egypt 2012 election, showing that this system could have elected a reformer over Morsi, despite vote-splitting among the various reformers. IRV could have elected Morsi.