Majority Acceptable Score voting

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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.

  1. Voters can support, accept, or reject each candidate. Blanks count as 2/3 of a rejection and 1/3 of an acceptance (so 75% blanks counts as 50% rejections).
  2. a. If there are any candidates not rejected by a majority, then eliminate all who are.
    • b. (If there are any candidates supported by a majority, then eliminate all who aren't.)
  3. Give remaining candidates 2 points for each voter who supports them, and 1 point for each who accepts them (or every three who leave them blank).
  4. Highest points wins.

Step 2b probably doesn't matter, because any majority-supported candidate that exists would almost certainly win in step 4 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, using the idea of medians: "choose the highest score among the candidates with the highest median".

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. (Note: the spreadsheet does not actually check step 2b.)

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 essage 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

An example

Tennessee's four cities are spread throughout the state
Tennessee's four cities are spread throughout the state

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)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis

Assume voters in each city give their own city 2; any city within 100 miles, 1; any city between 100 and 200 miles, a blank; and any city that is over 200 miles away or is the farthest city, 0. (These assumptions can be varied substantially without changing the result, but they seem reasonable to start with.)

City 2's 1's 0's blanks 0's+2/3 b's score
Memphis 42 0 58 0 58 (84)
Nashville 26 0 0 74 49.7 76.3
Chattanooga 15 17 42 26 59.7 (75.7)
Knoxville 17 15 42 26 59.7 (77.7)

Memphis is explicitly given 0 by a majority, and is eliminated. Chattanooga and Knoxville are both given 0 by a majority implicitly, so they are eliminated. Nashville remains and wins.

If Memphis voters tried to strategize by rating Nashville at 0 in the above scenario, Chattanooga and Knoxville voters could protect against this strategy if 2/3 of them gave Nashville a 1.