Mike,
I think this fails the FBC. Say sincere is:
45: C
06: D>A
39: A>B
20: B>A
There is no "mutual majority set" (by your latest definition) so C
wins. That is also true if the 6 D>A voters change to D=A or D=A=B or
D=A>B or anything else except A>B or A=B or B>A in which case the winner
changes to A.
It also fails Mono-add-Plump.
49: C
27: A>B
24: B>A
Your latest version of MMT elects A, but if we add between 2 and 21
ballots that plump for A then there is no longer a "majority candidate
set" and so the MMT winner changes from A to C.
49: C
21: A (new voters, whose ballots switch the MMT winner from A to C)
27: A>B
24: B>A
(121 ballots, majority threshold = 61)
I think all reasonable methods will elect A in both cases. Electing C in
the second case will have voters wondering why they bothered switching
from FPP, and is a very bad case of failing Condorcet
and Mutual Dominant Third (DMT). A is voted above all other candidates
on nearly 40% of the votes, and A>C 72-49 and A>B 48-24.
Chris Benham
Mike Ossipoff wrote (6 Dec 2011):
Complete new definition of Mutual-Majority-Top (MMT): A
mutual-majority candidate set is a set of candidates who are each rated
above-bottom by each member of the same majority of voters--where that
set of candidates contains every candidate rated above bottom by any
member of that majority of the voters. If there are one or more
mutual-majority candidate sets, then the winner is the most top-rated
candidate who is in a mutual-majority candidate set. If there are no
mutual-majority candidate sets, then the winner is the most top-rated
candidate. [end of latest definition of MMT]
----
Election-Methods mailing list - see http://electorama.com/em for list info
