[EM] Forest: MAMT

[fsimmons at pcc.edu]

Chris and Mike,

I think I finally have the right version which I will call MSAC for Majority Support Acquiescing Coalitions:

Definitions:

A coalition is a subset of the candidates.

A ballot acquiesces to a coalition of candidates iff it rates no candidate outside the coalition higher than 
any member of the coalition.

A Majority Support Acquiescing Coalition is a coalition that is acquiesced to by more than half of the 
ballots.

A Majority Support Acquiescing Coalition is minimal if it ceases to be a Majority Support Acquiescing 
Coalition when any one of its members is removed.

Method Definition for MSAC:

(1) First find all of the Minimal Majority Support Acquiescing Coalition.

(2) Among these call the one with the greatest support G.

(3) Elect the member of G with the greatest average rating.


----- Original Message -----
From: "C.Benham" 
Date: Tuesday, December 13, 2011 11:19 am
Subject: Forest: MAMT
To: em 

> 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, 

MSAC also 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.

But under MSAC candidate A still wins, because the {A, B} coalition is the set G, and the range winner 
of this set is A.

Note also that the MSAC winner is C for the following set of ballots:

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

because in this case the coalition {B, C} is the value of G, and C is the range winner of this coalition.


Forest