Majority Acceptable Score voting
- Voters can give each candidate 0, 1, or 2 points.
- a. If there are any candidates given above 0 by a majority, then eliminate all who aren't (that is, those with half or more at 0).
- b. (Repeat step 2a, using "at or below 1" instead of "at 0".)
- The remaining candidate with the highest points wins.
Step 2b probably doesn't matter, because any majority-2 candidate that exists would almost certainly win in step 3 anyway. But step 2b is part of Bucklin voting, which was used in over a dozen US cities during the Progressive era. Also, it lets you say the whole method in one sentence, if the person you're talking to understands medians: "choose the highest score among the candidates with the highest median".
Blank votes are counted as 1 or 0 points in proportion to the fraction of all voters who gave the candidate a 2. For example, if there were any candidates without a majority of 0s, 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: . 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.
As the first round of a two-round system ("MAS with runoff")
If this system is used as the first round of a two-round runoff, then you want to use it to elect at two finalists in the first round. Thus, run the system twice. The first time, instead of eliminating any candidates with a majority below a threshold (as long as there are any with a majority above the threshold), eliminate only those with over 2/3 below the threshold (as long as there are any with 1/3 above).
Then, to find the second winner, if the first-time winner got 1/3 or more of 2's, first downweight those ballots as if you'd eliminated enough of them to make up 1/3 of the electorate. Otherwise, discard all of the ballots which gave the first-time winner a 2. After downweighting or discarding, run MAS normally.
If all the candidates in the first round got a majority of 0's, then you can still find two finalists as explained above. But the voters have sent a message that none of the candidates are good, so one way to deal with the situation would be to have a rule to allow candidates to transfer their 2-votes to new candidates who were not running in the first round, and if those transfers would have made the new candidates finalists, then add them to the second round along with the two finalists who did best in the first round. In that case, since there would be more than 2 candidates in the second round, it would be important to use MAS for the second round too.
Relationship to NOTA
As discussed in the above section, if all the candidates in the first round got a majority of 0's, then the voters have sent a message that none of the candidates are good, akin to a result of "none of the above" (NOTA). MAS still gives a winner, but it might be good to have a rule that such a winner could only serve one term, or perhaps a softer rule that if they run for the same office again, the information of what percent of voters gave them a 0 should be next to their name on the ballot
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 on Wikipedia, the state's largest city, with 42% of the voters, but located far from the other cities
- Nashville on Wikipedia, with 26% of the voters, near the center of Tennessee
- Knoxville on Wikipedia, with 17% of the voters
- Chattanooga on Wikipedia, 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 voters in each city give their own city 2; any city within 100 miles, 1; any city that is over 200 miles away or is the farthest city, 0; and the rest (those between 100 and 200 miles), get 1 or blank with 50/50 chance. (These assumptions can be varied substantially without changing the result, but they seem reasonable to start with.)
|City||2's||explicit 1's||explicit 0's||blanks||total 0's||score|
Memphis and Knoxville are both given 0 by a majority, so they are eliminated. Of the remaining two, Nashville has a higher score and wins.
If Memphis voters tried to strategize by rating Nashville and Chattanooga at 0 in the above scenario, it would take a bit over half of them to successfully execute the strategy. Even if all the Memphis voters strategized, Chattanooga and Knoxville voters could protect Nashville against this strategy as long as under half of those who had given Nashville a blank above switched to giving it a 1 (or a 2). Note that the offensive strategy involves moving a natural 1 down to the extreme value of 0, but the defensive strategy only means changing a lazy blank to a natural 1 (not to the extreme value of 2).