Because of the great desirability of avoiding the ABE problem, it's worth
considering or looking at
all sorts of possible solutions.
MMPO and MDDTR are known to work fine, though they have vulnerability to
non-valid criticisms.
The mutuality-requiring methods work fine too, and, though someone here has
made angry noises about them,
he isn't saying anything other than personal opinion, and would be unlikely to
be able to make a public case
against the mutuality-requiring methods.
Nevertheless, it's always useful to consider other approaches.
I'd spoken of two approaches to avoiding ABE:
1. Counting combined support (even if one-sided) against a candidate.
2. Mutuality-requirement
And now,
3. Faction-size (as a ballot option)
4. Hypothetical cooperation or noncooperation
How they'd work:
3. Faction-size (as a ballot option):
In the kind of ABE situation we've been speaking of, the problem would be solved
if the A voters could indicate on their ballot that their middle-rating for B is
conditional upon B having at least as many top-ratings as A has.
Of course sometimes it's necessary to support a compromise with less
favoriteness,
and so this requirement should be optional.
4. Hypothetical cooperation or noncooperation:
This could be automatic or optional.
There could be a rule that, ballot1's middle rating to a candidate2 who isn't
in
a mutual approval set in common with any of ballot1's top-rated candidates is
counted
only if that candidate2 would outpoll each of ballot1's top-rated candidates
if, for each
candidate1 on ballot 1:
...no ballot top-rating candidate2 and not candidate1 gives a middle-rating to
candidate1
and no ballot top-rating candidate1 and not candidate2 gives a middle-rating to
candidate2.
[end of tentative, work-in-progress, maybe-useful definition of the
hypothetical noncooperation approach]
Alternatively, that last paragraph could replace "no ballot" with "every
ballot". That would be
the hypothetical cooperation approach, which probably amounts to the same thing.
The above could be applied to all the middle-ratings, based on an initial
assumption that
all middle ratings are counted. Of course, the application of the above
requirements
would likely change the conditions that had caused some middle ratings to be
given or
with-held. It would be simplest to disregard that change. To have the system
re-examine the
noncounting of middle-ratings, and re-apply its requirement, could result in an
unstable
outcome that changes with each re-examination.
Just using an initial assumption that all middle ratings are counted might be
adequate for
avoiding the ABE problem. It certainly is, in the simple ABE situation that's
been discussed
here.
----------------------------
I'm not saying that these ABE approaches are as workable or desirable as
approaches #1 and #2. But,
as I said, all possibilities are worth naming, due to the importance of
avoiding the co-operation/
defection problem. Approach #3 seems simple and workable, and useful for
situations like the
usual ABE.
Mike Ossipoff
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