MARS voting

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MARS voting is a single-winner electoral system that combines cardinal and ordinal information. The name stand for "Mixed Absolute Relative Score", as it combines score voting with relative preferences. It was created to address shortcomings in STAR voting. In particular cloning and edge cases of favorite betrayal.

Ballots are cast as score ballots (here we assume a 0 to 5 rating). The candidate with the highest score is found. Then, in an automatic runoff step, ballots are examined for preference relative to that candidate. Every candidate scored equal or higher than the score winner gets the maximum rating added to their score, every candidate lower gets the maximum rating subtracted from their score. The candidate with the highest combined (absolute and relative) score wins.

Voting

Voters fill out a score ballot with a 0 to 5 range (blanks count as 0). These are evaluated in three steps.

  1. The candidate with the highest total score is found ("score winner").
  2. Ballots are evaluated again. Each candidate is compared against the score winner ("competitors"). When scored equal or higher they receive 5 points.
  3. For every candidate their scores of step 1. and the ratings of step 2. are added together. Note that for the score winner this will be score+0. The candidate with the highest combined sum wins.
  4. (Optional) Repeat step 2. and 3. with the previous winner in place of the score winner, until the process terminates or a cycle is found. In a cycle the candidate with the highest combined sum in any comparison wins.

To resolve ties between the previous winner and the competitor, pick the previous winner. This is possible since step 3. awards higher or equal ratings to the competitor, thereby slightly favoring the competitor. Asking voters with equal ranking to decide will only ever elect the previous winner.

To resolve a tie between the two competitors with the highest sum perform an automated runoff between them, using only the ranking information.

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, 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

Suppose that 100 voters each decided to grant from 0 to 5 points to each city such that their most liked choice got 5 stars, and least liked choice got 0 stars, with the intermediate choices getting an amount proportional to their relative distance.

Voter from/
City Choice
Memphis Nashville Chattanooga Knoxville Absolute

score

Memphis 210 (42 × 5) 0 (26 × 0) 0 (15 × 0) 0 (17 × 0) 210
Nashville 84 (42 × 2) 130 (26 × 5) 45 (15 × 3) 34 (17 × 2) 293
Chattanooga 42 (42 × 1) 52 (26 × 2) 75 (15 × 5) 68 (17 × 4) 237
Knoxville 0 (42 × 0) 26 (26 × 1) 45 (15 × 3) 85 (17 × 5) 156

Nashville is the score winner with 293 points. All other candidates are compared against it.

Voter from/
City Choice
Memphis Nashville Chattanooga Knoxville Relative

score

Memphis 210 (42 × +5) -130 (26 × -5) -75 (15 × -5) -85 (17 × -5) -80
Nashville 0 (42 × 0) 0 (26 × 0) 0 (15 × 0) 0 (17 × 0) 0
Chattanooga -210 (42 × -5) -130 (26 × -5) 75 (15 × +5) 85 (17 × +5) -180
Knoxville -210 (42 × -5) -130 (26 × -5) 75 (15 × +5) 85 (17 × +5) -180

Adding absolute and relative scores together we get

210 - 80 = 30 for Memphis

293 + 0 = 293 for Nashville

237 - 180 = 57 for Chattanooga

156 - 180 = -24 for Knoxville

Since Nashville is both the score winner and Condorcet winner the result is exaggerated in MARS voting, resulting is a clear victory for Nashville.

Properties

Because MARS voting draws from two types of information and enforces preference rankings even when two candidates are scored equal, the tie rules make it free of true ties at the top. Except for the case of two candidates scored exactly identical by the same number of voters.

Footnotes

Original proposal on the EndFPTP subreddit under the name "score better balance"

Implementation in GO