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 1, it has some examples of how different combinations of ratings would come out, suggesting that it could work well in both chicken dilemma and center squeeze scenarios. 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.
An example
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.
The candidates for the capital are:
- Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
- Nashville, with 26% of the voters, near the center of Tennessee
- Knoxville, with 17% of the voters
- Chattanooga, with 15% of the voters
The preferences of the voters would be divided like this:
| 42% of voters (close to Memphis) |
26% of voters (close to Nashville) |
15% of voters (close to Chattanooga) |
17% of voters (close to Knoxville) |
|---|---|---|---|
|
|
|
|
Assume half of voters in each city rate one city 2, one city 1, and two cities 0; and half rate one 2, leave two blank, and one 0.
| City | 2's | explicit 1's | explicit 0's | blanks | total 0's | score |
|---|---|---|---|---|---|---|
| Memphis | 42 | 0 | 58 | 0 | 58 | (84) |
| Nashville | 26 | 21 | 16 | 37 | 43 | 83 |
| Chattanooga | 15 | 22 | 21 | 42 | 57 | (59) |
| Knoxville | 17 | 8 | 55 | 20 | 72 | (45) |
Only Nashville is rated above 0 by a majority, so Nashville (the Condorcet winner) wins, even though Memphis has a slightly higher score.
If Memphis voters rated Nashville at 0 in the above scenario, they could cause Memphis to win. But Chattanooga and Knoxville voters could protect against this as long as at least 3/4 of them (24% from their combined total of 32%) gave Nashville a 1 (or a 2).