Paul Kislanko wrote:
This still makes no sense to me, since C has no more a majority in case 2
than it had in case 1.
If mutual majority selects (A B) in case 1 and (A B C) in case 2, it makes
no sense at all and should never be mentioned again.
Mutual majority can still be useful. Let's make an analogy to Condorcet.
The Condorcet criterion elects the CW if there is one. In other words,
if there is a CW and that CW is candidate X, then the set from which
Condorcet methods elect is { X }. If there is no CW, and the candidates
for election are {A B C ... X }, then the set from which Condorcet
methods elect is {A B C ... X }.
Thus, Condorcet is useful when there is indeed a CW, but does nothing
when there isn't.
So it is with mutual majority as well. When there's a set that a
majority ranks above all the others, then a method that passes mutual
majority must elect from that set. When there is no such set, the method
is free to pick any candidate yet still pass mutual majority.
In that light, mutual majority seems very reasonable indeed: if there is
a set so that a majority prefers that set to all others outside the set,
then a candidate within that set should be elected. It's simply
"majority" transported to sets.
(And on another note, sorry for not mailing you this directly as well,
Paul, but airmail.net seems to think my ISP is a dirty spammer.)
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