Kevin--
James had said:
Definition of strong majority rule criterion: If voters cast ballots sincerely, and the voting method in question always chooses a member of the sincere Smith set, the method passes the strong majority rule criterion. Otherwise, the method fails the strong majority rule criterion.
You replied:
You don't need to suppose that ballots are cast sincerely, since there is no way to fill out ballots such that they couldn't possibly be sincere.
I reply:
Sure there is. If a ballot is not sincere, then it couldn't possibly sincere. That's because it can't be both sincere and not sincere. For that reason, if you fill out a ballot in such a way that it is not sincere, then you've filled it out in such a way that (given your preferences) it couldn't possibly be sincere.
Of course if you meant "couldn't" to mean "couldn't, if you had different preferences", then it would indeed be difficult or impossible to ever fill out a ballot that couldn't possibly be sincere.
But none of this is relevant to James posting of my Smith Criterion, because it doesn't say "a ballot that couldn't possibly be sincere". It stipulates sincere voting, and I've posted a definition of sincere voting.
You continue:
If a method fails Smith for any set of ballots, it must fail your criterion.
I reply:
You mean "Mike's criterion".
And yes, that criterion is the Smith Criterion. My preference version of the Smith Criterion.
But though that's an exact word-for-word rendition of my Smith Criterion, there have been more than one Smith Criterion defined. For instance, Blake's Smith Criterion (if it's as it was when I last checked it) explicitly stipulates that it applies only to rank methods. That makes it very different from my Smith Criterion, which has no such limitation of applicability.
Sometimes the Smith Criterion is stated in such a way that Plurality passes it.
So it wouldn't be true to say that all Smith Criterion versions are the same.
You continue:
So this criterion isn't different from the "Smith criterion."
I reply:
That depends on which Smith Criterion you're referring to. Yes, what James posted is a word-for-word rendition of my Smith Criterion. No, it is definitely different from Blake's Smith Criterion, if Blake's Smith Criterion is as it was when I last checked it.
Mike Ossipoff
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