Majority Choice Approval: Difference between revisions
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If one and only one candidate is given the highest rating by an [[absolute majority]] of voters, that candidate wins. If not, the second-highest rating is added to each candidate's vote total; again, if there is only one candidate with a majority they win. This process continues until some candidate has a majority. |
If one and only one candidate is given the highest rating by an [[absolute majority]] of voters, that candidate wins. If not, the second-highest rating is added to each candidate's vote total; again, if there is only one candidate with a majority they win. This process continues until some candidate has a majority. |
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Unfortunately, |
Unfortunately, if voters cluster in certain categories (e.g. if there are only a handful of ratings, or if ratings are clustered at multiples of 5 or 10), this procedure is likely to end up with multiple candidates reaching a majority at the same rating. Therefore, a tiebreaking procedure is needed. Some possible resolution methods include: |
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* MCA-A: Most approved candidate (most votes above lowest possible rating). This is also called "Majority Top//Approval", or MTA. |
* MCA-A: Most approved candidate (most votes above lowest possible rating). This is also called "Majority Top//Approval", or MTA. |
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* MCA-M: Candidate with the highest score at the rating level where an absolute majority first appears. This system is equivalent to traditional [[Bucklin voting]]. |
* MCA-M: Candidate with the highest score at the rating level where an absolute majority first appears. This system is equivalent to traditional [[Bucklin voting]]. |
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* MCA-S: [[Range voting|Range]] or Score winner. The candidate with the highest average (mean) score is declared winner, where candidates are given 0 points for the lowest rating, 1 point for the second-lowest, etc. |
* MCA-S: [[Range voting|Range]] or Score winner. The candidate with the highest average (mean) score is declared winner, where candidates are given 0 points for the lowest rating (not rank), 1 point for the second-lowest, etc. |
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* MCA-R: Runoff. Two finalists are chosen by one of the methods above or an equality-allowed Condorcet method over the given ballots. The finalists are then measured against each other using one of the following methods: |
* MCA-R: Runoff. Two finalists are chosen by one of the methods above or an equality-allowed Condorcet method over the given ballots. The finalists are then measured against each other using one of the following methods: |
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== Criteria compliances == |
== Criteria compliances == |
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All MCA variants satisfy the [[Plurality criterion]], the [[ |
All MCA variants satisfy the [[Plurality criterion]], the [[majority criterion for solid coalitions]], [[Monotonicity criterion|monotonicity]] (for MCA-AR, assuming first- and second- round votes are consistent), and [[Minimal Defense criterion|Minimal Defense]] (which implies satisfaction of the [[Strong Defensive Strategy criterion]]). |
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All of the methods are [[Summability criterion|summable]] for counting at the precinct level. Only MCA-IR actually requires a matrix (or, possibly two counting rounds), and is thus "[[Summability criterion|summable for k=2]]"; the others require only O(N) tallies, and are thus "[[Summability criterion|summable for k=1]]". |
All of the methods are [[Summability criterion|summable]] for counting at the precinct level. Only MCA-IR actually requires a matrix (or, possibly two counting rounds), and is thus "[[Summability criterion|summable for k=2]]"; the others require only O(N) tallies, and are thus "[[Summability criterion|summable for k=1]]". |