Either you should speak of a majority _voting_ the candidates in S
over all the other candidates, or else, when saying only that they
prefer the candidates in S to all the others, you should add the stipulation that they vote sincerely.
The latter wording is better, since then we don't have the embarrassment of having to say "Don't apply this criterion to Plurality, because if you do, Plurality will pass."
An alternative way to avoid this is to define plurality as a ranked-ballot method, where the winner is the candidate with the most first-place votes. Of course, since plurality ballots don't actually have spaces to list your uncounted lower choices, this definition is just an artifice to get the voter's sincere preferences onto the ballot.
I remember you saying that you don't like defining it this way, but to me it's just another way of talking about sincere preferences. It gives you roughly the same conclusions as talking about sincere preferences does. Six of one, half-dozen of the other.
-Adam
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