Forrest--
I'm assuming "approval bad example" is typified by the implicit approval order
in the scenario
49 C
27 A>B
24 B
Yes, A majority prefer A and B to C. They're the voters to whom A is favorite
and the voters to whom B is favorite.
Knowing that the more-numerous A voters will vote for B, the B voters can win
by defection.
You continued:
It seems to me that IF we (1) want to respect the Plurality Criterion, (2)
discourage "chicken" strategy,
(3) stick with determinism, and (4) not take advantage of proxy ideas, then
our method must allow
equal-rank-top and elect C in the above scenario
[endquote]
...when A voters and B voters vote only for their favorites.
If the B voters (in 3-slot balloting) rate B above bottom, and C at bottom,
shouldn't the method
defeat C and elect A or B?
You continued:
, but elect B when B is advanced to top equal with A [by the A voters].
Sure. But what if the A voters vote A top, B middle, and C bottom?
C should lose. Should A lose too, even though they're more numerous, and even
though A pairbeats B,
just because the A voters were the ones who were co-operative and responsible
enough to
rate B above bottom, to defeat C?
You wrote:
in
the middle faction:
[endquote]
But it isn't a matter of one faction in the middle. The A-preferring voters and
the B-preferring voters
all prefer A and B to C. The A and B voters share one end, rather than either
being in the middle.
You continued:
49 C
27 A=B
24 B
Then if sincere preferences are
49 C
27 A>B
24 B>A,
the B faction will be deterred from truncating A.
[endquote]
Is that attainable in a method meeting FBC and Participation?
...or in a method meeting those plus 1CM and 3P?
You continued:
While if the B supporters are sincerely indifferent
between A and C
[endquote]
Ok, but, to me, an essential element of the example is that the A supporters
and the B supporters
all prefer A and B to C.
You continued:
, the A supporters can vote approval style (A=B) to get B elected.
Do we agree on this?
[endquote]
Wait a minute...If the A supporters were indifferent between B and C, then
they'd have
no motive to suppport B against C, unless it would elect A. In some methods
their A>B>C
ballot would achieve that. MDD,TR is such a method.
You continued:
Note that IRV (=whole) satisfies this, but now the question remains ... is
there a method that satisfies
this which also satisfies the FBC?
Chris mentioned something that should have been obvious to me: MDD,TR passes in
the Approval
bad example.
Here's the definition of MDD,TR:
3-slot method: Top, Middle, Bottom (unmarked)
Disqualify any candidate(s) having a majority pairwise defeat.
The winner is the un-disqualified candidate with the most top ratings.
[end of MDD,TR definition]
MDD,TR avoids electing B in the Approval bad example (ABE). In fact, it elects
A, which
seems the fairest outcome, allowing the A voters to defeat C by giving hir a
majority
defeat via B. And by not penalizing the A voters by rewarding the B voters for
defection.
Additionally (unless I'm mistaken), MDD,TR meets FBC and SFC.
Regrettably it fails 1CM and 3P.
MTA better protects a group of factions with similar policy-proposals against
other groups.
MDD,TR doesn't do that as well, but it better protects that group of similar
factions against eachother.
In our electoral system, there is great mutual antagonism among factions and
parties with similar
policy proposals, and so maybe MDD,TR would be better for our elections, as
compared to MTA.
Of course both of those methods fail Participation. It has been pointed out to
me that Participation
failure, while only an "aesthetic embarrassment criterion", might be used by
reform-opponents to
defeat MTA, MDD,TR, MDDA or MDD,ER-Bucklin(whole).
Mike Ossipoff
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