To all participants:
James says:
I've been discussing the majority and mutual majority criteria with Mike
Ossipoff lately, and the question arose as to how other EM participants
understand these criteria.
My previous understanding was that they only differ in that MC is the
case of MMC where the majority set has one member.For example, here is what I consider to be a standard MC definition, and a standard MMC definition, for application to ranked ballot methods:
MC: If more than one half of the voters vote X over all other candidates (i.e., in first place), X should win.
I reply:
So far so good. That's the standard MC definition, the votes-only definition.
James continues:
MMC: If more than one have [half] of the voters vote all members of set S over
all other candidates, a member of set S should win.
I reply:
Wrong. I defined MMC, and that isn't how I define it. I define MMC as a preference criterion. Maybe Bruce Anderson's original definition was votes only, or maybe it referred to preferences, without any stipulation of the relation between votes and preferences. I don't know how Bruce wrote it, and neither does James. My MMC definition is the earliest one that we have. And it is not as James stated it above.
As James may or may not know, Plurality passes your MMC that he stated above.
James continues:
Below are a few more definitions of the two criteria that I found via a quick google search. I believe that they largely support my interpretation.
I reply:
They contradict eachother. They support my longstanding statement that those criteria are usually defined votes-only, or with reference to preference, but with no stipulation about votes being constrained by preference. When they're written votes-only, there usually is no stipulation that they apply only to rank methods, or that nonrank methods fail. Sometimes there is, as in the case of Blake's criteria. Then you have an inelegant patchwork rules-criterion.
James continues:
"Majority Criterion: If an alternative is ranked first on a majority of ballots, that alternative must win."
I reply:
That's what I've been calling the standard votes-only MC. How does that support James' contention?
James continues:
"Mutual Majority Criterion: If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win." Blake Cretney http://condorcet.org/emr/criteria.shtml
I reply:
Blake modified my MMC. That's his right. I already said that Blake defines MMC & CC as votes-only, and that Blake says that his criteria apply only to rank methods. James missed that part when he quoted Blake's MMC.
James continues:
"Majority criterion: If one candidate is the top choice of more than half the electorate, then that candidate should be the one chosen." Daniel Ullman (George Washington University) http://www2.gwu.edu/~bygeorge/110304/ullman.html
I reply:
It isn't clear what Daniel Ullman of George Washington University means. Does top choice mean vosted top choice, or does Daniel Ullman of George Washington University mean what he says literally, so that top choice means favorite. Who knows.
If Daniel Ullman of George Washington University means "voted top choice", then that's another copy of the standard votes-only MC that I stated. If he means "favorite", then that's another instance of someone defining cariteia according to preference without any stipulation about how preference constrains voting. That's common.
Not entirely clear how that's supposed to support James' contention.
James continues:
"Majority criterion: If a majority of voters strictly prefers a given candidate to every other candidate and votes sincerely, then that candidate should win." Wikipedia http://en.wikipedia.org/wiki/Majority_criterion
I reply:
Who posted that in the wikipedia? James? In any case, that's James' FHC, which, as I said, ridiculously malfunctions in its comparison of Plurality and Approval.
James continues:
"Mutual majority criterion: If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win." Electowiki http://wiki.electorama.com/wiki/Mutual_majority_criterion
I reply:
That's another copy of the votes-only version, which Plurality passes, and which is not MMC. Not only is it not my definition of MMC, but I had many discussions with Bruce Anderson, and I can assure you that Bruce didn't think that Plurality and Approval passed his orilginal MMC.
Of course in this instance we have another ambiguity: What does the verb "rank" mean? Does it mean they vote that set of candidates over all others, or that they do so in a rank-balloting method.
If the former, then it's as I said in the paragraph before last. If the latter, then it's a rules criterion that explicitly applies only to rank methods.
James continues:
"The Majority Criterion: Any candidate receiving a majority of first place votes should be the winner." Larry Bowen (University of Alabama) http://www.ctl.ua.edu/math103/Voting/whatdowe.htm#The%20Majority%20Criterion
I reply:
That's yet another copy of what I've been calling the standard votes-only MC. It isn't clear how James thinks that supports his contention, since that's how I've been defining standard votes-only MC all along.
James continues:
"Review the Majority Criterion. We call Majority Candidate one who has a majority of first place votes." Annalisa Calini (College of Charleston) http://math.cofc.edu/faculty/calini/VotingS05.pdf
I reply:
Another copy of what I've all along been calling the standard votes-only MC definition.
James thinks that he's proven something by posting those mutually contradictory defintiions, which I've already been telling about.
Mike Ossipoff
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