I have worked on MARS voting for some months now, revising it several times and going from complicated to very complicated. The latest version I will present here is simplified to a level where it can be explained to someone with no background in voting theory. But I still think this method is not for use in elections for public offices.
MARS voting is an attempt to find a middle way between Condorcet and utility based philosophies for single winner elections. I hoped that this balances out the strategic incentives in either group, but it might be that the best strategy is a combination of burial and min-max.
It is possible to contrive ridiculous examples to show that either cardinal or Condorcet methods will pick the "wrong" winner.
B scores almost two times the number of points than A, but a majority vote would elect A.
Here 99% prefer A over B, but score elects B.
In MARS voting wins by score or votes are compared to each other and the one that is more significant counts. This rule is very general and can be applied to many Condorcet methods, Minimax and others. For the method presented below I have chosen BTR, because it is relatively easy to explain.
- Voters score candidates on a ballot with 0 to 5 ratings.
- Candidates are ordered top to bottom by score.
- Compare the bottom two candidates by votes that prefer over the other and by score, both measured in %.
- When both metrics lead to different winners, pick the one where the margin of defeat (in %) is higher. Eliminate the loser.
- Repeat last two steps for the whole list and elect the remaining candidate.
In this example A is the score winner and Condorcet loser, while B is the Condorcet winner and score loser.
The candidates are ordered by score: A C B
In the runoff B versus C, B wins by votes 35% to 32% (margin 3%), but C wins by score 65% to 61% (margin 4%). So B is eliminated.
In the runoff C versus A, C wins by votes 65% to 35% (margin 30%), but A wins by score 80% to 65% (margin 15%). So A is eliminated and C is declared winner.
This again is a contrived example. Most of the time the Condorcet and utility winner will be the same, and in most other cases MARS with elect either of them. But even here is an argument to be made for electing C. When we eliminate the "obviously bad" candidates - the Condorcet loser and the utility loser - then only C is left as the least bad choice.
Obviously this method fails many voting criteria. I want to develop a version that is free from favorite betrayal, until then I don't recommend this one. The reason I post it here it to have a place to continue this ongoing discussion.