MARS voting: Difference between revisions
Add an example for a cycle and how to resolve it.
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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.
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
==Voting==
Voters fill out a score ballot with a 0 to 5 range (blanks count as 0). These are evaluated in
#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
#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
To resolve a tie
==Examples==
▲To resolve a tie between the two competitors with the highest sum perform an automated runoff between them, using only the ranking information.
===Clear Winner===
{{Tenn voting example}}
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.
Line 110 ⟶ 109:
156 - 180 = '''-24''' for Knoxville
By being both the score and Condorcet winner the result is exaggerated in MARS voting, resulting is a clear victory for Nashville.
===Cycle===
{| class="wikitable" border="1" style="empty-cells: show"
|-
!Voters
!35
!33
!34
!Absolute
score
|-
|A
|175 (35 × 5)
|132 (33 × 4)
|136 (34 × 4)
|443
|-
|B
|175 (35 × 5)
|165 (33 × 5)
|0 (34 × 0)
|340
|-
|C
|0 (35 × 0)
|165 (33 × 5)
|170 (34 × 5)
|335
|}
A is the score winner. When comparing B and C against A the summed scores are: A 443+0=443, B 340-5=335, C 335+160=495. Therefor C wins the first round.
{| class="wikitable" border="1" style="empty-cells: show"
|-
!Voters
!35
!33
!34
!Relative
score
|-
|A
|0 (35 × 0)
|0 (33 × 0)
|0 (34 × 0)
|0
|-
|B
|0 (35 × 0)
|165 (33 × +5)
| -170 (34 × -5)
| -5
|-
|C
| -175 (35 × -5)
|165 (33 × +5)
|170 (34 × +5)
|160
|}
In the second round we compare A and B against the previous winner C. The summed scores are: A 443-160=283, B 340+5=345, C 335+0=335. B wins the second round.
In the third round we compare A and C against the previous winner B. The summed scores are: A 443+5=448, B 340+0=340, C 335-5=330. A wins the third round.
We discovered that 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==
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[https://www.reddit.com/r/EndFPTP/comments/lil4zz/scorebetterbalance_a_proposal_to_fix_some/ Original proposal on the EndFPTP subreddit] under the name "score better balance"
[https://hg.sr.ht/~ser/score-better-balance/browse/main.go Implementation in GO] by sxan
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