[EM] MMC, CD, and the Condorcet Criterion are compatible.

[Michael Ossipoff]

The Mutual Majority Criterion (MMC), the Chicken Dilemma Criterion (CD),
and the Condorcet Criterion (CC) are mutually compatible.
They're all met by a well-known method: Condorcet-IRV. Condorcet-IRV says
to do a CW search before doing the IRV count.
Because there are different kinds of Condorcet, resulting in different
meanings for CW, Condorcet-IRV is a broad term, covering TUC-IRV, IC-IRV,
and Symmetrical-IC-IRV.
(I use "TUC" to stand for "traditional unimproved Condorcet)
I list two similar definitions. I don't know which is better
TUC-IRV1:
X beats Y iff more ballots rank X over Y, than Y over X.
If there is exactly one unbeaten candidate, then s/he wins.
Otherwise choose by an IRV count among all the candidates.
[end of TUC-IRV1 definition]
TUC-IRV2:
X beats Y iff more ballots rank X over Y, than Y over X.
If there is exactly one unbeaten candidate, then s/he wins.
If all or no candidates are unbeaten, then choose by an IRV count among all
the candidates.
If some, but not all, candidates are unbeaten, then choose among the
unbeaten candidates, by an IRV count with only the unbeaten candidates in
the rankings.
[end of TUC-IRV2 definition]
---------------------------------
Of course the sometime elimination of CWs is the source of IRV's
instability. Condorcet-IRV avoids that problem.
That instability is definitely a disadvantage for IRV. I feel that IRV's
advantages, for the Green scenario, are great enough to justify IRV and
make it desirable, in spite of its instability disadvantage. But
Condorcet-IRV seems to fully retain IRV's impressive advantages, while
avoiding its instability disadvantage.
With IRV, the preferrers of the CW might resent the CW's elimination. Maybe
not. Maybe they'd just be glad that the winner is from the mutual majority
(MM). But maybe, if election of their favorite is paramount to them, then
they might resent hir elimination. The disfavored wing would certainly not
like the election of someone from the opposite wing, instead of the CW. The
disfavored wing, plus the CW preferrers add up to a majority, and so there
could be a majority who are dissatisfied with IRV. That could lead to that
majority throwing out IRV. Condorcet-IRV wouldn't be vulnerable to that
Burlington outcome.
Condorcet-IRV would remove the win-big/lose-big gambling element of IRV,
while retaining IRV's unique advantage of easy, strategy-free,
sincere-ranking, choice for the members of the mutual majority (MM), while
automatically guaranteeing the election of one of the MM's preferred
candidates.
---------------------------------
Similar methods:
Preliminary definitions:
(X>Y) is the number of ballots ranking X over Y.
(Y>X) is the number of ballots ranking Y over X.
(X=Y)T is the number of ballots ranking X and Y at top.
(Not ranking anyone over than, and ranking them over someone)
(X=Y)B is the number of ballots ranking X and Y at bottom.
(Not ranking then over anyone, and ranking someone over them)
IC-IRV differs from TUC-IRV by saying:
X beats Y iff (X>Y) > (Y>X) + (X=Y)T.
Symmetrical-IC-IRV differs from the other two Condorcet-IRV versions, by
saying:
X beats Y iff (X>Y) + (X=Y)B > (Y<X) + (X=Y)T.
--------------------------------
 IC-IRV could have two slight advantages over TUC-IRV:

FBC would be violated less often. Under current conditions, a method that
violates FBC has a serious strategy problem in every election. But, under
Green scenario conditions, that isn't so, and it counts for something if
FBC is failed less often.

IC-IRV makes it easier to help a non-CW, non-reciprocating, compromise, if
one wants to do so.

Symmetrical-IC-IRV brings IC improvement to the bottom-end, as well as the
top-end. I don't know if that would bring any significant improvement over
IC-IRV.

---------------------------------

I suggested, a long time ago, to the IRV organization now known as
FairVote, something that I called "Approval IRV", which could be
abbreviated "AIRV":

Equal ranking allowed. Your ranking gives a full vote to each of your
top-ranked candidates. When all of your rank N candidates are eliminated,
then your ranking gives a full vote to each of its rank N+1 candidates.

In the language of my briefer definition of IRV, all of the not-crossed-off
candidates who share the highest ranking occupied by not-crossed-off
candidates, qualify as "topping the ranking".

Though it doesn't meet CC, AIRV still makes compromise easier, without
favorite-burial, such as for protecting a CW.

----------------------------------

Bottom line:

Though IRV's advantage, in the Green scenario, is enough to outweigh its
instability disadvantage, that disadvantage can be avoided by Condorcet-IRV
(or, to a lesser extent, by AIRV), while retaining IRV's great advantage of
easy, strategy-free, sincere-ranking, choice, for the MM members.

In the Green scenario, Approval, Score, Bucklin, and IRV would be good
methods. But Condorcet-IRV would be better than IRV.

But the way, ERBucklin offers little over Approval if it doesn't have the
delay that confers MMC compliance.But ERBucklin's MMC compliance is greatly
compromised by ERBucklin's failure of CD.

There's little to recommend ERBucklin over Approval or Score.

Michael Ossipoff
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