[EM] Mutual MTA (MMTA). MABucklin2.

[MIKE OSSIPOFF]

I’ve been discussing methods that meet FBC and avoid the
co-operation/defection problem. I’ve posted a number of them already. Here, I’d
like to post a few more.

 

There are at least two ways of achieving those goals (If
there are additional ways, then describe them, starting with their motivation and principle).



 1. Counting combined support (even if unilaterally-voted)
against a candidate:

 

I only know two ways of implementing that approach:

 

MMPO was suggested by Forest.
MDDTR was suggested (but not liked) by Chris.

 

They’re good methods, but each of them is subject to a
criticism which, while not valid, could be problematic to a public proposal.

We’ve discussed those not-valid criticisms, and so I won’t
repeat them here.

 

2. Requiring mutuality.

 

I’ve already posted lots of methods implementing that
approach, and, in this posting, I’d like to describe two more:

 

First, when I named MMABucklin, the “majority” in its name
was redundant, it being a Bucklin version. So I’ll just call it “Mutual
Approval Bucklin  (MABucklin). But,
because I’m going to, here, propose another version of it, then I’ll call that
first version “MABucklin1”.

 

MMTA and MABucklin2:

 

A mutual approval set is defined as before:

 

A mutual approval set is a set of candidates who are all
rated above bottom by the same set of ballots—where, for each those ballots,
the candidate-set includes at least one candidate who is top-rated on that
ballot.

 

Middle ratings given by that set of ballots, of a mutual
approval set, to that mutual approval set’s candidates, are the only middle
ratings that are counted.

 

MMTA is MTA with that provision.

 

MABucklin2 is ABucklin with that provision, where “middle
rating” refers to any vote that has been given to a candidate, other than a 1st
choice vote,  and where “above bottom
rating” refers to any vote that has been given to a candidate.

 

[end of definition of MMTA and MABucklin2]

 

Naming of MMTA:

 

I call it Mutual MTA because it’s MTA with a mutuality
requirement.

 

But a better _procedural_ description might be Majority Top
Mutual Approval (MTMA).  Because MTA  has already been named and discussed, and
because MMTA is just it with the mutuality requirement, I prefer the name MMTA.

 

MMTA and these MABucklins meet Mono-Add-Plump, in addition
to FBC, 3P, 1CM and CD (They don’t have the co-operation/defection problem, the
ABE problem). None of them elects C in Kevin’s MMPO bad-example. MABucklin
additionally meets SDSC and UP, the unlimited counterpart to 3P.

 

3P, UP, 1CM and SDSC are majority-rule criteria. All but
SDSC are defined in recent postings, mostly in November, with their initials in
the subject-line.  The criteria and
methods that I’ve defined will soon be posted to the electowiki. 

 

(Chris said that 1CM is like Minimal Defense. If so, then
maybe I should start calling it “MDCu”. The “u” refers to the fact that, unlike
Minimal Defense, MDCu is universally-applicable.)

 

I mention Mono-Add-Plump and Kevin’s MMPO bad-example
because some FBC/ ABE methods have been criticized here because of those
criteria. I don’t mean to imply that those two criteria are important or
necessary.

 

Approval meets FBC, 2P (like 3P, with one fewer
protection-level), and WDSC, among other criteria. 

 

If the conditional middle ratings that are optional in MTAOC
were made automatic, then we would take out the “O” in MTAOC. The method then
becomes MTAC when all middle ratings are automatically conditional. 

 

I’ve stopped counting how many FBC/ABE methods I’ve
proposed. The point is that there are lots of them to choose from.  FBC/ABE methods don’t give anyone reason to
bury their favorite. And they don’t say, when a voter is considering helping
another faction, to make a winning coalition, “You help, you lose.” 

 

If we adopt or use a method more complicated than Approval,
there’s no excuse to keep the ABE problem, the co-operation/defection problem,
when there are so many ways to avoid it. Avoiding it is the only significant
improvement over Approval. As I’ve said, Approval is better than most people
think it is.

 

Methods worth considering, to replace Plurality:  Approval, Score-Voting, and, the FBC/ABE
methods, if people will accept something a little fancier than Approval.
Of course, the trouble with methods other than Approval and Score-Voting is that there are so many. How to make an argument for why oneparticular one should be chosen instead of another? That's the problem with methods other than Approval.
Well, MTA is an obvious extension of Approval to give two majority rule protection-levels instead of one. And then, MMTA is the obviousway for MTA to avoid the co-operaton/defection problem.
Looking at it another way, if MMTA didn't have its initial top-majority count, it could be called Mutual Approval (MA). MA is the obvious
and natural way for Approval to avoid the co-operation/defection problem. Then, MMTA is the obvious extension of MA to give two
majority-rule protection-levels instead of one.

So I suggest that MA, MTA and MMTA are the obvious extensions of Approval.

As I said above, there's no excuse for using or proposing something more complicated than Approval unless it avoids
the co-operation/defection problem. Avoiding that problem is the only significant  improvement over Approval.

So MA and MMTA are the obvious and natural improvements on Approval.

And MABucklin2 is the obvious extension of MMTA to rankings, to achieve UP compliance, an unlimited number of
majority-rule protection-levels.
 

Mike Ossipoff