MARS voting: Difference between revisions
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(Precinct summability) |
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==Properties== |
==Properties== |
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===Ties are rare=== |
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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. |
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. |
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===Precinct summability=== |
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Despite several rounds of comparing candidates, 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. Scores can simply be added up. For the preference we turn a ballot into a preference matrix and add up those for all ballots. For the Tennessee example above the summed up matrix is exemplified below. |
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{| class="wikitable" |
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| |
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|... over '''Memphis''' |
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|... over '''Nashville''' |
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|... over '''Chattanooga''' |
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|... over '''Knoxville''' |
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|- |
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|Prefer '''Memphis''' ... |
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|0 |
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|42 |
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|42 |
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|42 |
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|- |
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|Prefer '''Nashville''' ... |
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|58 |
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|0 |
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|68 |
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|68 |
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|- |
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|Prefer '''Chattanooga''' ... |
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|58 |
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|32 |
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|0 |
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|83 |
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|- |
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|Prefer '''Knoxville''' ... |
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|58 |
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|32 |
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|17 |
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|0 |
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|} |
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In order to compare against Nashville single out Nashville and subtract competing votes. |
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{| class="wikitable" |
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| |
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|... over '''Nashville''' |
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|- |
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|Prefer '''Memphis''' ... |
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|42-58=-16 |
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|- |
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|Prefer '''Nashville''' ... |
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|0 |
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|Prefer '''Chattanooga''' ... |
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|32-68=-36 |
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|Prefer '''Knoxville''' ... |
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|32-68=-36 |
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|} |
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The combined score then is the score plus the number of remaining votes times the maximum range. |
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{| class="wikitable" |
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| |
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|... over '''Nashville''' |
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|Prefer '''Memphis''' ... |
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|210 + (-16 x 5) = 30 |
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|Prefer '''Nashville''' ... |
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|293 + 0 = 293 |
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|Prefer '''Chattanooga''' ... |
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|237 + (-36 x 5) = 57 |
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|Prefer '''Knoxville''' ... |
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|156 + (-36 x 5) = -24 |
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|} |
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== Footnotes == |
== Footnotes == |
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