[EM] Majority Criterion, actually Mutual Majority Criterion (MMC)

[James Green-Armytage]

>>majority criterion: If a majority of the voters prefers all of the
>members
>>of a given set of candidates over all candidates outside that set, and
>>they vote sincerely, then the winning candidate should come from that
>set.

Bart
>This sounds like
>Woodall's terminology
>
Mike
>
>I'm going to pretend that I didn't hear that  :-)

	I'm sorry, but I did actually refer to Woodall's statement of the
majority property before I wrote this definition. Then I reworded it into
the context of sincere preferences, because Woodall was assuming ranked
ballots, and hence his definition as stated cannot apply to approval
voting. Woodall's statement of the majority property is:

"If more than half the voters put the same set of candidates (not
necessarily in the same order) at the top of their preference listings,
then at least one of those candidates should be elected."

	I didn't realize that Woodall was on some sort of blacklist. I don't
consider him to be some sort of godlike authority, and I think that some
of his ideas are silly, but I think that his statement of this criteria
was reasonable enough to use.

Bart
>This isn't what I generally think of as "majority criterion."  Most
>places I have encountered the term, it refers to a requirement that the
>candidate with a majority of first preferences must win.  Nurmi calls it
>the "majority winner criterion".

	Right, well, the two definitions are very close. Bart's definition above
can be seen as a special case of Woodall's definition, where the set of
candidates only contains one candidate. This is the only difference
between the "majority criterion" and "mutual majority criterion" as Mike
puts it. And actually, I don't think that there is anything wrong with
making that distinction, since there are methods which pass majority in
the one-candidate-set case but do not pass majority in the
multiple-candidate-set case. Indeed I had some discussions some months ago
with Mike where he gave me his definition of the mutual majority criteria,
and I had that in mind when I wrote the definition above. "Majority" is
just a slightly shorter way of saying it than "mutual majority," which is
why I opted to say it that way. No big deal. I think that most people knew
what I was talking about. If not, now it's more clear.

James