Consider the voting method, "Generalized Bucklin", which AFAICT may be the same as "Majority Choice Approval": Voters submit ranked ballots, which may include ties, and need not list all candidates. First-choice votes are tallied; if any candidates get votes from a majority (more than 50%) of the voters, the one with the largest majority wins. If none get a majority, second-choice votes are tallied and added to the first-choice totals; again we look for the largest actual majority. If there is none, third-choice votes are tallied, and so forth.
(1) What are the properties of this method, regarding the usual desiderata of voting methods?
Monotonicity,
It seems pretty obvious it passes. Ditto for clone independence, and Mutual Majority (although some would quibble about the last one).
Independence of Irrelevant Alternatives,
Well, it's a ranked method that's pareto efficient and non-dictatorial, so it fails.
Condorcet-efficiency, Always chooses Condorcet-winner/Never chooses Condorcet-loser,
I would imagine the Condorcet efficiency is very good. It could pick a Condorcet loser, for example:
1% A=B=C 33% A>B=D 33% B>C=D 33% C>A=D
D loses 34%>33% pairwise to each candidate, yet D wins GB/MCA in the second round with 99% approval.
Favorite Betrayal,
There's never an incentive to rank your favorite lower than first place, but there are times where it makes sense to vote someone you like less in tied first place. So it passes "weak favorite betrayal".
incentives for insincere ranking of preferences, and all of those?
Better than some, worse than others. It's pretty solid.
(2) Do Approval advocates regard this method as better or worse than plain-vanilla Approval? Why or why not?
I think that three-slot MCA is almost indisputably better than regular approval. The only argument for regular approval over MCA is simplicity of implementation and explanation, although those are strong pragmatic arguments.
With more slots the strategies in GB/MCA get a little murky. If I were voting in an MCA election I'd probably only use the top few slots, unless I understood the strategy better than I do now.
-Adam
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