[EM] DMC the greatest Condorcet? I wish, but doubt it...

[Warren Smith]

It is nice to hear from F. Simmons that DMC is the greatest and resolves
all those nasty Condorcet contentious issues, while unifying
all the Condorcet methods.  And also, I agree DMC is a simpler method than all
or almost all of the methods it unifies.
I am glad I recently joined EM just in time to
reap the fruits of all that.

BUT unfortunately, it seems to me something is wrong with this picture.

**First, I hear Jobst Heitzig himself (DMC's inventor) claims his favorite method
is something else (DFC, whatever that is).  !!??

**Second, I am concerned about "Favorite Betrayal" and "2-party domination."
Earlier on EM I basically constructed a mathematical proof that all
Condorcet methods lead to 2-party domination.  (It may be seen at
http://math.temple.edu/~wds/crv/CondStratPf .)   My proof was then attacked
because (a) it lived in a somewhat unrealistic "random elections" model
(all elections equally likely) - that objection actually did not bother me -
and (b) my proof had assumed that the Condorcet method employed
full-rank-orderings as votes ("equalities" not permitted, truncation of
preferences not permitted, and "margins" assumed to be used).  This
latter criticism b actually does bother me, and it was due to my
ignorance - I not having been exposed to EM was under the false impression
that these assumptions were all part an parcel of what it meant to be
a "Condorcet" method.  Actually my proof can readily be extended even
to permit equality-rankings.

But anyhow - the essential point which was made to rebut me (by Adam Tarr)
was:  Condorcet methods employing BOTH winning-votes AND equalities-permitted
can escape my 2-party-dominance proof and maybe can escape 2-party dominance.

This it seems to me is very important.  It seems to me that from now on, it is just
silly to talk about Condorcet methods unless it is both wv and =permitted,
because 2-party dominance is a failure state as far as I am concerned.

Fine.  But:  DMC, the supposed "unifying new champ", still appears to lead
to 2-party domination.  I want you to modify DMC to get it out of this
trap, or admit you cannot.  Otherwise, it seems to me, DMC has failed to
live up to your hype.  (Also, the "DH3 pathology" - I want you to get DMC out of
that one too, please:   http://math.temple.edu/~wds/crv/DH3.html .)

wds