[EM] Complete MMT definition

[C.Benham]

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]