[EM] Final Improved Preference Majority Criterion

[MIKE OSSIPOFF]

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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