Majority Choice Approval: Difference between revisions
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* [[Independence of irrelevant alternatives]] |
* [[Independence of irrelevant alternatives]] |
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* MCA-IR satisfies [[Condorcet criterion|Condorcet]] the [[pairwise champion]] 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. |
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* 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. |
* 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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* MCA-AR satisfies the [[guaranteed majority criterion]], a criterion which can only be satisfied by a multi-round (runoff-based) method. |
* MCA-AR satisfies the [[guaranteed majority criterion]], a criterion which can only be satisfied by a multi-round (runoff-based) method. |
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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 |
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). |
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== An example == |
== An example == |