MARS voting
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MARS voting is a single-winner electoral system that combines cardinal and ordinal information. The name stands 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.
Procedure
Ballots are cast as score ballots on a 0 to 5 scale.
Candidates are ordered by total score from best to worst.
The bottom two candidates are matched against each other and the looser removed from the list, until only one candidate (the winner) is left.
To compare candidates, two values are used. 1. The percentage of voters preferring one candidate over the other 2. The score of a candidate as percentage of total possible score. The candidate where sum of these two values is greater wins the match.
Examples
Clear Winner
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) |
|---|---|---|---|
|
|
|
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Suppose that 100 voters each decided to grant from 0 to 5 points to each city such that their most liked choice got 5 points, and least liked choice got 0 points, 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 (42%) |
| Nashville | 84 (42 × 2) | 130 (26 × 5) | 45 (15 × 3) | 34 (17 × 2) | 293 (59%) |
| Chattanooga | 42 (42 × 1) | 52 (26 × 2) | 75 (15 × 5) | 68 (17 × 4) | 237 (47%) |
| Knoxville | 0 (42 × 0) | 26 (26 × 1) | 45 (15 × 3) | 85 (17 × 5) | 156 (31%) |
With 100 votes, the maximum score is 500.
Ordering the candidates by score results in the following list:
- Nashville
- Chattanooga
- Memphis
- Knoxville
Starting from the bottom, Knoxville and Memphis are matched against each other. 42% of voters prefer Memphis over Knoxville and 58% the other way around. To compare these two the percentages of score and votes are combined. Memphis has 42% (score) + 42% (votes) = 84 points (total), while Knoxville has 31% (score) and 58% (votes) = 89 points (total). Knoxville wins the match and Memphis is excluded. The next match is between Knoxville and Chattanooga with 31% + 17% = 48 points, and 47% + 83% = 130 points, respectively. Chattanooga wins and Knoxville is excluded. The last match is Chattanooga against Nashville with 47% + 32% = 79 points, and 59% + 68% = 127 points respectively. Nashville wins the last match and is declared winner.
By being both the score and Condorcet winner the result is unambiguous in MARS voting, resulting is a clear victory for Nashville.
Cycle
Suppose there are three candidates A, B, C and three groups of voters.
- 35 voters: A5, B5, C0
- 33 voters: A3, B5, C5
- 34 voters: A2, B0, C5
| Voters | 35 | 33 | 34 | Absolute
score |
|---|---|---|---|---|
| A | 175 (35 × 5) | 132 (33 × 2) | 136 (34 × 2) | 342 (68.4%) |
| B | 175 (35 × 5) | 165 (33 × 5) | 0 (34 × 0) | 340 (68.0%) |
| C | 0 (35 × 0) | 165 (33 × 5) | 170 (34 × 5) | 335 (67.0%) |
There is a cycle A>B>C>A while score gives the ordering A over B over C.
B and C are matched with 68% + 35% = 103 points for B, and 67% + 34% = 101 points for C. C is eliminated.
B and A are matched with 68% + 33% = 101 points for B, and 68.4% + 34% = 102.4 points for A. B is eliminated and A declared winner.
Properties
MARS voting (trivially) satisfies the following criteria: equal vote criterion and precinct summability.
It intentionally fails the Condorcet winner criterion in cases where the score winner outweighs the Condorcet winner. For the same reason it also fails the Condorcet looser criterion and majority winner, but less so then pure score (consider 51 voters: A0 B1, 49 voters: A5, B0, A wins). Further failed criteria are: Later-no-harm, IIA.
Ties
By using two types of information MARS voting can resolve top ties in most cases.
Precinct summability
Like most Condorcet methods, MARS voting is precinct summable. Ballots need to be counted only once. All we need to know are the scores and for every pair of candidates how many voters prefer one over the other. The results can be tabulated in a pairwise preference matrix.
Footnotes
Original proposal on the EndFPTP subreddit under the name "score better balance"
Implementation in Go by u/sxan