[EM] MAM evaluation. Summary of FBC/ABE methods.

[MIKE OSSIPOFF]

Evaluation of MAM:

Forest--

I've been looking at various ways of doing Mutual Acquiescing Majorities (MAM). (I think that was the name that you used).

Initially I thought it worked, and that it had a better set of properties than any comparably simple method.

But then I realized that I couldn't make that method work.

Any success?

My definition of the MAM set:


A set of candidates whom every member of the same majority vote equal to or
over every candidate outside the set.

[end of MAM set definition]

That definition is the 1st paragraph of an MAM definition.

The 3rd paragraph is:

"If there are no MAM sets, then the winner is the most top-rated candidate.

I've tried several 2nd paragraphs for MAM, but none of them works:

1) "If there are 1 or more MAM sets, the winner is the most top-rated candidate who is in a MAM set."

Or

2) "For any MAM set, the winner must come from that set. The winner is the most top-rated candidate
consistent with that requirement."

In the ABE, #1 lets {A,B,C} be an MAM set, and the winner is C, even if the B voters rate A at
middle, or even at top.

#2 requires that the winner come from the intersection of {C,B} and {A,B}

But electing B is the one way to fail in the ABE.

So, as I said, I haven't been able to make MAM work.

Have you?

Summary of FBC/ABE methods:

I don't know there's a way of making MAM work. So, for the purposes of this posting, I'm going to
cautiously assume that such an MAM variation hasn't yet been found.

Then, there are six workable FBC/ABE methods described so far. In rough chronological order of their 
proposing, they are:

MMPO
MDDTR
TTPDTR
MTAOC
MMT
MMMPO

Two of these were introduced by Forest, two were introduced by Chris, and two were introduced by me.

It seems to me that Forest proposed MMPO, some time ago. Chris suggested MDDTR when I asked if
there were a method that passes FBC and the ABE and Kevin's MMPO bad-example.

TTPDTR and MMMPO were recently proposed by Chris and Forest, respectively.

I proposed MTAOC and MMT.

Methods that let one faction unilaterally establish the win of a majority: MMPO, MDDTR, and probably MMMPO

Methods requiring mutuality: MTAOC, MMT.

I don't know which of those two classifications TTPDTR is in.

Here is an incomplete table of properties, for these six methods:

(I hope that format differences don't cause rollover in this table)

MAP means Mono-Add-Plump
KMBE means Kevin's MMPO bad-example
LNHe means Later-No-Help
U means that a majority can be established unilaterally

L means "less imporantly"

I emphasize that I don't consider the MAP & KMBE "failures" of MMPO & MDDTR to be important.
But the "L" means that a criticism is unlikely to be usable for convincing the public.

All of these methods meet FBC, pass in the ABE, and have some majority-rule protection.

.................MAP......KMBE.....LNHe.....U

MMPO........Yes.......No.........No........Yes
MDDTR.......No........Yes........No.......Yes
MMT..........No L.......Yes.......No L.....No
MTAOC......No L.......Yes.......No L......No
TTPDTR
MMMPO.....Yes?..............................Yes?

(I don't have the answers for MMMPO and TTPDTR). Maybe someone else can fill
the table in for those two methods).

Mike Ossipoff












 		 	   		  
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