MARS voting: Difference between revisions
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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.
==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
==Examples==
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{{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.
{| class="wikitable
|-
!Voter from/<br />City Choice
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|}
Nashville is the score winner with 293 points
The following table shows preferences time 5 with score added.
{| class="wikitable"
|
|... over '''Memphis'''
|... over '''Nashville'''
|... over '''Chattanooga'''
|... over '''Knoxville'''
|-
|Prefer '''Memphis''' ...
| ---
|42x5 + 210
|42x5 + 210
|42x5 + 210
|-
|Prefer '''Nashville''' ...
|58x5 + 293
| -
|68x5 + 293
|68x5 + 293
|-
|Prefer '''Chattanooga''' ...
|58x5 + 237
|32x5 + 237
| ---
|83x5 + 237
|-
|Prefer '''Knoxville''' ...
|58x5 + 156
|32x5 + 156
|17x5 + 156
|
|}
{| class="wikitable"
|
|... over '''Memphis'''
|... over '''Nashville'''
|... over '''Chattanooga'''
|... over '''Knoxville'''
|-
|Prefer '''Memphis''' ...
| -
|bgcolor="#EE8080"|420
|bgcolor="#EE8080"|420
|bgcolor="#EE8080"|420
|
|Prefer '''Nashville''' ...
|bgcolor="#80EE80"|583
| ---
|bgcolor="#80EE80"|633
|bgcolor="#80EE80"|633
|-
|Prefer '''Chattanooga''' ...
|bgcolor="#80EE80"|527
|bgcolor="#EE8080"|397
| ---
|bgcolor="#80EE80"|652
|-
|Prefer '''Knoxville''' ...
|bgcolor="#80EE80"|446
|bgcolor="#EE8080"|316
|bgcolor="#EE8080"|241
| ---
|}
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
{| class="wikitable" border="1" style="empty-cells: show"
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|}
Resulting in the following pairwise matrix.
{| class="wikitable
|
|... over '''A'''
|... over '''B'''
|... over '''C'''
|-
|Prefer '''A''' ...
| ---
|bgcolor="#EE8080"|34x5+443=613
|bgcolor="#80EE80"|35x5+443=618
|-
|Prefer '''B''' ...
|bgcolor="#EE8080"|33x5+340=505
| ---
|bgcolor="#80EE80"|35x5+340=515
|-
|Prefer '''C''' ...
|bgcolor="#80EE80"|67x5+335=670
|bgcolor="#EE8080"|34x5+335=505
| -
|}
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]]
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.
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===Precinct summability===
== Footnotes ==
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