Majority Choice Approval: Difference between revisions

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The [[Condorcet criterion]] is satisfied by MCA-VR if the pairwise champion (PC, aka CW) is visible on the ballots. It is satisfied by MCA-AR if at least half the voters at least approve the PC in the first round. Other MCA versions fail this criterion.
 
[[Strategic nomination|Clone Independence]] is satisfied by most MCA versions. In fact, even the stronger [[Independence of irrelevant alternatives]] is satisfied by MCA-A, MCA-P, MCA-M, and MCA-S. Clone independence is satisfied along with the weaker and related [[ISDA]] by MCA-VRIR and MCA-AR, if ISDA-compliant Condorcet methods (ie, [[Schulze]]) are used to choose the two "finalists". Using simpler methods to decide the finalists, MCA-VRIR and MCA-AR are not clone independent.
 
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.
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None of the methods satisfy [[Later-no-harm criterion|Later-no-harm]].
 
All of the methods are matrix-summable for counting at the precinct level. Only MCA-VRIR actually requires a matrix (or, possibly two counting rounds); the others require only O(N) tallies.
 
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).
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