Support Accept Reject Abstain voting

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Support Accept Reject Abstain (SARA) works as follows:

  1. Voters can support, accept, reject, or abstain on each candidate. Default is abstain. Candidates get 2 points for each percent of "support" and 1 point for each percent of "accept", for a total of 0-200 points.
    • Obviously, you should support the best candidates (perhaps a quarter of them), and reject the worst (perhaps half of them). For the rest, the candidates who are around average or slightly better, a good rule of thumb is to accept when you're afraid of somebody worse, and abstain when you are hoping for somebody better. There's no need to overthink this decision; often, doing either will work just as well, especially if it's not clear whether hope or fear should win.
  2. Eliminate any candidates rejected by over 50%, unless that leaves no candidates with over 50 points.
    • If possible, the winner shouldn't be somebody opposed by a majority. But this shouldn't end up defaulting to a candidate who couldn't at least get accepted by over 1/2 or supported by over 1/4 (as in, a majority subfaction of a divided majority; for instance, if 26% prefer A over B over C, 25% prefer B over A over C, and 49% prefer C).
  3. Highest points wins. In case of a tie, fewest rejections wins.
    • This finds the candidate with the widest and deepest support.

As the first round of a two-round system ("SARA 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, replace "50%" in step 2 with "2/3".

Then, to find the second winner, if the first-time winner got 1/3 or more support, 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 supported first-time winner. After downweighting or discarding, re-tally the points and SARA again.

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 two candidates in the second round, it would be important to use SARA for the second round too.

Note: this "proportional two-winner SARA" system for the first round is "matrix-summable", that is, summable with O(n²) information per ballot for n candidates. This contrasts with the base SARA method, which is summable with only O(n) information per ballot, and thus can be counted voting equipment designed for counting plurality elections.

Relationship to NOTA

As discussed in the above section, if all the candidates in the first round got a majority "reject", then the voters have sent a message that none of the candidates are good, akin to a result of "none of the above" (NOTA). SARA still gives a winner, but it might be good to have a rule to limit the chance that such a winner would remain in office for multiple terms. This could either be a hard term limit, so that such a winner could only legally serve one term; or perhaps a softer rule that if they run for the same office again, the information of what percent of voters had rejected them should be next to their name on the ballot

An example

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 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)
  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 Support Accept Abstain Reject score
Cutoff
(must be)
<50 >50
Memphis 42 0 0 58 (84)
Nashville 26 0 74 0 52
Chattanooga 15 17 26 42 47
Knoxville 17 15 26 42 49

Chattanooga and Knoxville both get under half a point per voter, and are eliminated. Memphis is explicitly rejected by a majority, and is eliminated. Nashville remains and wins.

If Memphis voters tried to strategize by rejecting Nashville at 0 in the above scenario, it would have no effect.

If Chattanooga and Knoxville tried to strategize by supporting each other, this has a chance of working, but Memphis could safely defend Nashville by accepting it. Since Memphis is essentially guaranteed to be solidly rejected, the Memphis voters have nothing to lose by defensively accepting Nashville like this. A mere 13% of "accept" from Memphis's 42% — that is, under a quarter of the Memphis population — would give Nashville 65 points, more than double the combined size of Chattanooga and Knoxville, safely defending it.