Majority Choice Approval: Difference between revisions

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Line 7: 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. Unfortunately, ~~unless~~if voters cluster in certain categories (e.g. if there are ~~many~~only ~~categories,~~a ~~and~~handful ~~voters~~of doratings, ~~not~~or ~~cluster~~if atratings ~~round~~are ~~numbers~~clustered ~~(e.g.~~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. Line 15: * 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-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. * 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: Line 25: == Criteria compliances == All MCA variants satisfy the [[Plurality criterion]], the [[~~Majority~~majority criterion for solid coalitions]], [[Monotonicity criterion\|~~Monotonicity~~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]]). 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]]". ~~The~~MCA fails the [[participation criterion]] and its stronger cousin the [[consistency criterion]], as well as the [[later-no-harm criterion]] ~~are not satisfied by any MCA variant~~, although MCA-P only fails participation if the additional vote causes an approval majority. MCA can also satisfy: ~~Other criteria are satisfied by MCA variants with appropriate tiebreakers, including:~~ * [[Independence of irrelevant alternatives]] * ~~The~~MCA-IR satisfies [[Condorcet criterion\|Condorcet]] ~~is satisfied by MCA-IR~~ if the [[pairwise champion]] ~~(aka CW)~~ is visible on the ballots{{Clarify\|date=April 2024}} and would beat at least one other candidate by an absolute majority. It is satisfied by MCA-AR if at least half the voters at least approve the PC in the first round of voting. These methods also satisfy the [[Strategy-Free criterion]] if an SFC-compliant method such as [[Schulze]] is used to pick at least one of the finalists. All other MCA versions, however, fail the Condorcet and strategy-free criteria. * The [[later-no-help criterion]] and the [[Favorite Betrayal criterion]] are satisfied by MCA-P. They're also satisfied by MCA-AR if MCA-P is used to pick the two finalists. Line 41: * MCA-AR satisfies the [[guaranteed majority criterion]], a criterion which can only be satisfied by a multi-round (runoff-based) method. 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 [[universality criterion]]), are able to seem to "violate [[Arrow's Theorem]]" by ~~simultaneously~~ satisfying ~~monotonicity and~~ [[independence of irrelevant alternatives]] (as well as ~~of course sovereignty and~~ non-dictatorship). == An example ==