Majority Choice Approval: Difference between revisions

TheMCA 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.

* 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.

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).