[EM] Forest: MAMT

[C.Benham]

Mike,

I can see how MAMT tries to meet Mono-add-Plump, but it fails.

49: C
27: A>B
24: B>A

MAMT (like all reasonable methods) elects A, but say we add 20 ballots 
that plump for A.

49: C
27: A>B
24: B>A
20: A  (new ballots)

(120 ballots, majority threshold 61).

Now there are two "minimal subset" acquiescing majorities: {AB} 71 and 
{CA}69. All three candidates are qualified so the most top-rated 
candidate (C) wins.

A better method would  (instead of  "acquiescing majorities") use the 
set I just defined in my last post.

*If there is a solid coalition of candidates S (as measured by the 
number of ballots on which those candidates are strictly voted above all 
others) that is bigger than the sum of all its rival solid coalitions
(i.e. those that contain some candidate not in S), then those candidates 
not in the smallest such S are disqualified. Elect the most top-rated 
qualified candidate.*

That does meet  Mono-add-Plump.  In the second election {AB}51's only 
"rival" is {C}49.

But I'm not a fan of this either because it doesn't handle the small 
wing spoiler smoothly like IRV  (and some other methods):

49: A
48: B
03: C>B

It, like MAMT and MMT  elects A   This is a failure of  Mutual Dominant 
Third (met by IRV) and Condorcet and Minimal Defense.
Of course if the B voters change to B>C the winner changes to B, a 
failure of Later-no-Help.

Chris Benham



Mike Ossipoff wrote (12 Dec 2011):

Forest:

Thanks for the suggestion of MAMT.

MAMT is an addition to the list of FBC/ABE methods to choose from.

People should be looking into its properties.

Tell me what you know, so far, about its properties, and,
in particular, how its properties differ from those of ordinary MMT (MMT2).

I think it's encouraging that there are an increasingly large list
of FBC/ABc methods. One of them will be the most winnable as a public
proposal. The more FBC/ABC methods proposed, the more likely that one
of them will be sufficiently winnable.

I thank everyone who is helping me by adding to that list of FBC/ABE

Mike Ossipoff.