Majority Choice Approval: Difference between revisions
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'''Majority Choice Approval''' ('''MCA''') is a class of rated voting systems which attempt to find majority support for some candidate. It is closely related to Bucklin Voting, which refers to ranked systems using similar rules. In fact, some people consider MCA a subclass of Bucklin, calling it '''[[ER-Bucklin]]''' (for Equal-Ratings
== How does it work? ==
Voters rate candidates into a fixed number of rating
If one and only one candidate is
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:
* MCA-A: Most approved candidate (most votes above lowest possible rating). This is also called "Majority Top//Approval", or MTA.
* MCA-P: Most preferred candidate (most votes at highest possible rating).
* MCA-M: Candidate with the highest score at the rating level where an absolute majority first appears, or MCA-A if there are no majorities. This is the system closest to traditional [[Bucklin voting]].▼
* MCA-S: [[Range voting|Range]] or Score winner. That is, the candidate with the highest score, counting (in the case of 3 ranking levels) 2 points for each preference and 1 point for each approval.▼
▲* MCA-M: Candidate with the highest score at the rating level where an absolute majority first appears
* MCA-R: Runoff - Two "finalists" are chosen by one or two methods, such as one of the methods above or a equality-allowed Condorcet method over the given ballots. The finalists are then measured against each other using one of the following methods:▼
▲* MCA-S: [[Range voting|Range]] or Score winner.
▲* MCA-R: Runoff
** MCA-IR: Ballots are counted for whichever one of the finalists they rate higher.
** MCA-AR: Actual runoff: Voters return to the polls to choose one of the finalists. This has the advantage that one candidate is guaranteed to receive the absolute majority of the valid votes in the last round of voting of the system as a whole.
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== Criteria compliances ==
All MCA variants satisfy the [[Plurality criterion]], the [[
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]]"
MCA can also satisfy:
* [[Independence of irrelevant alternatives]]
*
* The [[
* MCA-AR satisfies the [[
Thus, the MCA method which satisfies the most criteria is MCA-AR, using [[Schulze]] over the ballots to select one finalist and MCA-P to select the other. Also notable are MCA-M and MCA-P, which, as ''rated'' methods (and thus ones which fail Arrow's ''ranking''-based [[
== An example ==
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== Notes ==
MCA ballots can be modified to do [[Smith//Approval]] with the use of an [[approval threshold]]. Limiting the number of allowed rankings in Smith//Approval makes it closer in design to [[Approval voting]] than to most [[Condorcet method]]<nowiki/>s.
[[Category:Single-winner voting methods]]
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