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-P: Most preferred candidate (most votes at highest possible rating).

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).

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.