Preference Majority Criterion (PMC):
If a set of voters consisting of more than half of the voters prefer X to each one of the other candidates, then they should have a sincere way of electing X.
[end of PMC definition]
PMC and James' FHC are ad-hoc criteria, and so it would be understandable if you don't accept them.
But I claim that, for a majority criterion about preference, and for a majority criterion in general, what most meaningfully conforms to the intent of the Majority Criterion is a majority defensive strategy criterion such as PMC, written as a majority defensive stragegy criterion. Though PMC is a majority defensive strategy criterion, the 5th one, I won't be using PMC much, because Borda is the only proposed method that I know of that fails it.
I've always said that Borda is the only proposed method I know of that fails the Majority Criterion, MC, which is a votes-only criterion. It hadn't occurred to me that CR fails it. But I now say that Borda is the only proposed method that I know of (right at this moment, speaking off-the-cuff) that fails PMC. I"m not saying there isn't another such method, and it would be of interest for someone to post one, maybe a well-known proposed method that fails PMC in a way that I didn't notice. PMC is new, and so that would be understandable.
But even if you reject FHC and PMC because of their ad-hoc nature, that leaves us with the fact that Approval meets MC, the original votes-only Majority Criterion.
And, though non-Approval CR fails MC, I claim that it doesn't fail it in a very meaningful way. Approval passes MC because when you vote X over Y, you _fully_ vote X over Y. Strategic voters will use CR as Approval. If they'd fully vote X over Y in Approval, they'd do so in CR. If they want the best they can get, they'll use CR as Approval. So, as I said, I don't think that CR fails MC in a meaningful sense.
When it's said that a criterion-failure isn't meaningful, that suggests that the criterion might need replacing with something whose answers are more what one would expect. I suggest PMC to replace MC.
A "plurality-inferion" method is a method that, in some way, is known to be worse than Plurality.
Unless we use James' new ad-hoc FHC, Approval isn't plurality-inferior. If we, as I claim makes sense, replace MC with PMC, then Approval and non-Approval CR are both not plurality-inferior. They both meet WDSC and FBC. CR version apparently are the only methods that bring significant improvements without being plurality-inferior. But I fully accept that you might not accept PMC, because the topic of new majority criteria based on preference came up because of a particular method, which could make you question James' motive for proposing FHC, and my motive for proposing PMC.
Mike Ossipoff
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