MTAOC, MMT and GMAT work. Their approaches to conditional
middle ratings work.
In particular, mutual approval sets work fine in GMAT. And
conditionality for individual middle ratings works fine in MTAOC.
But conditionality for individual middle ratings by mutual
approval sets doesn’t work. So MMAT doesn’t work.
And mutual approval set conditionality for individual middle
ratings, which doesn’t work, was my favorite approach.
But that still leaves a number of conditional-rating methods
that work, as described in this posting’s first sentences.
A problem with mutual approval set conditionality for
individual ratings can be shown with the usual ABE:
27: A>B
24: B
49: C
Say the A voters’ middle rating of B is conditional by
mutual majority set.
{A,B} is such a set. Such a set needs a set of voters who
rate above bottom each member of the set. That would be the
A voters. And it’s
necessary that, for each voter in that set of voters, the candidate set must
include at least one of hir top-rated candidates. No problem—Candidate A is top
rated by all of the A voters, and the set {A,B} includes A. So {A,B} is a
mutual approval set. The middle rating given by the A voters to B is,
then, one that is given within a mutual
approval set, and so that middle rating qualifies to actually be counted. And B
wins.
But my other conditional-rating FBC/ABE approaches, named
above, are valid and work fine.
I still assert that MMT, GMAT and MTAOC avoid the worst
strategy problems, and have the mildest strategy need.
There, of course, could be an MCAOC, based on MCA, as MTAOC
is based on MTA.
The complete system of mutually-compatible approval election
options consisting of Approval, and conditional versions of Approval, MTA, MCA
and ABucklin is still
available via MTAOC’s kind of
conditionality.
And, by the way, referring to something that I discussed
yesterday, it seems to me that conditional Approval, and Bucklin-like MTA and
MCA are all
compatible with ABucklin, for all to be offered together as options in an
Approval election. …with MTAOC’s kind of
conditionality for individual middle ratings.
There is compatibility between Approval and voting options using any one of the
conditionality approaches that I've described--and maybe
even between voting options using some combinations of different conditionality
approaches.
Earlier, I began to tentatively describe an MABucklin1,
which achieved conditionality in a way similar to MMT and GMAT. No doubt a
system like the one described two paragraphs before this is possible using
that kind of conditionality too.
In summary, Approval is the natural and obvious improvement on Plurality. MTA
is an obvious direct improvement on Approval, by its additional level of
majority rule protection. MTAOC is likewise an obvious and natural improvement
on MTA, to avoid the co-operation/defection problem.
In the same way, using MTAOC's optional conditionality with Approval, which
could be called "AOC", a 3-slot method, naturally brings that same improvement
to Approval.
In AOC, the top-ratings, aside from being counted along with middle ratings as
approvals, are used only for use in the MTAOC-like withdrawal of non-mutual
approvals. It differs from MTAOC in that there's no top-majority count.
And, in a slightly different approach, MMT and GMAT are also obvious
improvements on Approval, to achieve ABE success, even if they aren'tquite as
straightforward and obvious as MTAOC.
In addition to building on Approval and Plurality in an obvious way, some of
those conditional methods, and even some combinations of them, together are
compatible as options in an Approval election.
I’m not modest about the merits of these complete systems of
methods solidly, naturally and obviously based on Approval and Plurality, and
usable as a complete set of mutually compatible options in an Approval
election. Methods that avoid the worst strategy problems and have the mildest
strategy need.
As I said, these methods naturally and obviously extend the
method in use now, Plurality, without adding problems or taking away anything
necessary.
It might be that a way can be found to fix the mutual
approval set conditionality for individual middle ratings, or devise something
similar. But, even if not, the other approaches that I’ve described will
suffice.
I don't claim to have found all of the good conditionality-based ways of
getting rid of the co-operation/defection problem. In fact there may be still
other approaches, other than conditionality, to avoid ABE, without the kinds of
departures from Plurality-behavior shown by MMPO and MDDTR, which seem to upset
some people, and without unproposable wordiness of definition.
Mike Ossipoff
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