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,
== 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-
* MCA-
* MCA-M: Candidate with the highest score at the rating level where an absolute majority first appears
▲* MCA-P: Most preferred candidate (most votes at highest possible rating)
* 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-M: Candidate with the highest score at the rating level where an absolute majority first appears, or MCA-A if there are no majorities.
* MCA-R: Runoff - One or two of the methods above is used to pick two "finalists", who are then measured against each other using one of the following methods:▼
▲* 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.
== A note on
"Majority Choice Approval" was first used to refer to a specific form, which would be 3-level MCA-AR in the nomenclature above (specifically, 3-MCA-AR-M). Later, [http://betterpolls.com/v/1189 a voting system naming poll] chose
== Criteria
All MCA variants satisfy the [[Plurality criterion]], the [[
All of the methods are [[Summability criterion|
MCA can also satisfy:
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. ▼
* [[Independence of irrelevant alternatives]]
▲The [[Participation criterion|Participation]] and [[Summability criterion]] are not satisfied by any MCA variant, although MCA-P only fails Participation if the additional vote causes an approval majority.
* MCA-IR satisfies [[Condorcet criterion|Condorcet]] if the [[pairwise champion]] 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 [[
▲All of the methods are [[Summability criterion|matrix-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]]".
* MCA-AR satisfies the [[guaranteed majority criterion]], a criterion which can only be satisfied by a multi-round (runoff-based) method.
Thus, the 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).▼
▲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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There is no preferred majority winner. Therefore approved votes are added. This moves Nashville and
Various strategy attempts are possible in this scenario, but all would likely fail. If the eastern and western halves of the state both strategically refused to approve each other, in an attempt by the eastern half to pick
== General strategy and notes ==
If the electorate knows which two candidates are frontrunners, and the pairwise champion is indeed among those two, the stable strategy is for everyone to approve or prefer exactly one of those two, and fill out the rest of the ballot honestly and as expressively as possible. (In the example above, that would mean an east/west split, with Nashville winning 68-32 approval over Chattanooga.) If everyone follows this strategy, the pairwise champion will win with the only absolute majority. And if even half of voters follow this strategy, multiple majorities are highly unlikely.
However, this two-frontrunner strategy does not mean that MCA is subject to [[W:Duverger's law|Duverger's law]]. A pairwise champion who is not one of the perceived frontrunners still has a good chance of winning, especially if they have some strong supporters. This fact, in turn, will affect what "frontrunner" means; an extremist candidate with a strong but sharply-limited base of support - the kind of candidate who, using simple [[runoff voting]], makes it into a runoff with a strong showing of 35% but then gets creamed with only 37% in the runoff - will never be perceived as a frontrunner in the first place.
Thus, overall, many elections should be resolved without need for a resolution method, and so all MCA methods should give broadly similar results. However, if resolution is needed, a lack of majorities is, overall, more likely than multiple majorities. Since the design intent is to minimize these situations, the resolution method chosen should be one which tends to encourage extending approvals; that is, one which comes "close" to fulfilling the [[Later-no-harm criterion]], so that extending approval is unlikely to harm one's favorite candidate. From simple to complex, such methods are: MCA-S, MCA-IR, and MCA-AR.
== 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]]
▲Various strategy attempts are possible in this scenario, but all would likely fail. If the eastern and western halves of the state both strategically refused to approve each other, in an attempt by the eastern half to pick Chatanooga, Nashville would still win. If Memphis, Nashville, and Chatanooga all bullet-voted in the hopes of winning, most Knoxville voters would probably extend approval as far as Nashville to prevent a win by Memphis, and/or at least a few Memphis voters (>8% overall, out of 42%) would approve Nashville to stop Chatanooga from winning. Either one of these secondary groups would be enough to ensure a Nashville win in any of the MCA variants.
[[Category:Graded Bucklin methods]]
[[Category:No-favorite-betrayal electoral systems]]
[[Category:Monotonic electoral systems]]
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