Majority Choice Approval: Difference between revisions

'''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-[allowed] Bucklin).

Voters rate candidates into a fixed number of rating classes. There are commonly 3categories, 4, 5, or even 100 possible rating levelse.g. The following discussion assumes 3 ratings"Good, called" "preferred"Neutral, "approved", and "unapproved"Bad."

If one and only one candidate is preferredgiven the highest rating by an [[absolute majority]] of voters, that candidate wins. If not, approvalsthe aresecond-highest rating is added to preferences,each candidate's vote andtotal; again, if there is only one candidate with a majority they win. This process continues until some candidate has a majority.

* MCA-AP: Most approvedpreferred candidate (most votes aboveat lowesthighest possible rating).

"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 this term as a more-accessible replacement for "ER-Bucklin" in general. This is also sometimes known as "median ratings", because it can be defined as "the highest median rating wins".

All MCA variants satisfy the [[Plurality criterion]], the [[Majoritymajority criterion for solid coalitions]], [[Monotonicity criterion|Monotonicitymonotonicity]] (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]]".

TheMCA fails the [[Participationparticipation criterion]] and its stronger cousin the [[Consistencyconsistency criterion]], as well as the [[Laterlater-no-harm criterion]] are not satisfied by any MCA variant, although MCA-P only fails Participationparticipation if the additional vote causes an approval majority.

* TheMCA-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 [[Laterlater-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.

* MCA-AR satisfies the [[Guaranteedguaranteed 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 [[Universalityuniversality 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).

There is no preferred majority winner. Therefore approved votes are added. This moves Nashville and ChatanoogaChattanooga above 50%, so a winner can be determined. All the given resolution methods would pick Nashville, which is also the [[pairwise champion]] in this example.

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 ChatanoogaChattanooga, Nashville would still win. If Memphis, Nashville, and ChatanoogaChattanooga 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 ChatanoogaChattanooga from winning. Either one of these secondary groups would be enough to ensure a Nashville win in any of the MCA variants. It would take a conjunction of four separate conditions for ChatanoogaChattanooga to plausibly win: it could happen only if Knoxville voters also preferred ChatanoogaChattanooga, and Nashville voters (un-strategically) approved ChatanoogaChattanooga, and no Memphis voters preferred Nashville, and the MCA-P variant were used.

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 ChatanoogaChattanooga.) 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.