MARS voting
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.
Ballots are cast as score ballots (in this Article we use 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.
- The candidate with the highest total score is found ("score winner").
- Ballots are evaluated again. Each candidate is compared against ("competitor") the score winner . When scored equal or higher they receive 5 points. When scored lower they loose 5 points.
- 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.
- 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
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) |
|---|---|---|---|
|
|
|
|
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
By using two types of information MARS voting can resolve top ties in most cases. The amount of true ties that can not be resolved is reduced to a small fraction.
Footnotes
Original proposal on the EndFPTP subreddit under the name "score better balance"