[EM] general understanding of majority and mutual majority criteria?

James Green-Armytage jarmyta at antioch-college.edu
Fri May 6 23:44:42 PDT 2005

```To all EM participants,

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. Or, in other words,
that MMC is a generalization of MC where the majority set can have more
than 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.
MMC: If more than one have of the voters vote all members of set S over
all other candidates, a member of set S should win.

So, I'd like to know how many other EM participants define these two
criteria, and the relationship between the two criteria.

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.

"Majority Criterion: If an alternative is ranked first on a majority of
ballots, that alternative must win."
"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

"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

"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

"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

"The Majority Criterion: Any candidate receiving a majority of first place
Larry Bowen (University of Alabama)
http://www.ctl.ua.edu/math103/Voting/whatdowe.htm#The%20Majority%20Criterion

"Review the Majority Criterion. We call Majority Candidate one who has a