Majority Choice Approval: Difference between revisions

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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]]".

MCA fails the [[participation criterion]] and its stronger cousin the [[consistency criterion]], as well as the [[later-no-harm criterion]], although MCA-P only fails participation if the additional vote causes an approval majority.

MCA fails the [[participation criterion]] and its stronger cousin the [[consistency criterion]], as well as the [[later-no-harm criterion]], although MCA-P only fails participation if the additional vote causes an approval majority.{{Clarify|date=May 2024}}

MCA can also satisfy:

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* 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 satisfying [[independence of irrelevant alternatives]] ~~(as well as~~ 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 [[universality criterion]]), are able to "violate" [[Arrow's Theorem]] by satisfying [[independence of irrelevant alternatives]] and non-dictatorship.

== An example ==