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.

Voting
Ballots are cast as score ballots (here we use a 0 to 5 rating). A pairwise table shows each match. The pairwise scores (M) are calculated as number of votes that prefer (P) the candidate over the competitor times the maximum rating (r), plus the total score (S) for the candidate: M(A,B) = P(A,B) x r + S(A). From within the Schwartz set the hightest scoring candidate is elected.

To resolve a tie, an automated runoff if performed, using only the ranked information.

Clear Winner
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.

Nashville is the score winner with 293 points.

The following table shows preferences time 5 with score added.

By being both the score and Condorcet winner the result is exaggerated 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: A4, B5, C5
 * 34 voters: A4, B0, C5

Resulting in the following pairwise matrix.

There is a cycle A>B>C>A. In case of a cycle the score winner from within that cycle is elected, here A.

Properties
MARS voting reduces the incentive for strategic voting in the form of burying, min-max or bullet voting. Voter can make use of the full range of scores with only a small probability of having a less preferred candidate beat their favorite because of the vote.

It satisfies the following criteria: equal vote criterion ("Frohnmayer balance"), monotonicity, favorite betrayal, precinct summability, reversal symmetry.

MARS voting 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. The amount of true ties that can not be resolved is reduced to a small fraction.

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 are tabulated in a pairwise matrix as seen in the examples above.