Forest,
The "D" in DMC used to stand for *Definite*.
I like (and I think I'm happy to endorse) this Condorcet method idea,
and consider it to be clearly better than regular DMC
Could this method give a different winner from the ("Approval Chain
Building" ?) method you mentioned in the "C//A" thread (on 11 June 2011)?
Initialize a variable X to be the candidate with the most approval.
While X is covered, let the new value of X be the highest approval candidate
that covers the old X.
Elect the final value of X.
For all practical purposes this is just a seamless version of C//A, i.e. it avoids the apparent
abandonment of Condorcet in favor of Approval after testing for a CW.
Assuming cardinal ballots, candidate A covers candidate B, iff whenever B is rated above C on more
ballots than not, the same is true for A, and (additionally) A beats (in this same pairwise sense) some
candidate that B does not.
Your newer suggestion ("enhanced DMC") seems to have an
easier-to-explain and justify motivation.
Chris Benham
Forest Simmons wrote (12 July 2011):
One of the main approaches to Democratic Majority Choice was through the idea that if X beats Y and
also has greater approval than Y, then Y should not win.
If we disqualify all that are beaten pairwise by someone with greater approval, then the remaining set P
is totally ordered by approval in one direction, and by pairwise defeats in the other direction. DMC
solves this quandry by giving pairwise defeat precedence over approval score; the member of P that
beats all of the others pairwise is the DMC winner.
The trouble with this solution is that the DMC winner is always the member off P with the least approval
score. Is there some reasonable way of choosing from P that could potentially elect any of its members?
My idea is based on the following observation:
There is always at least one member of P, namely the DMC winner, i.e. the lowest approval member of
P, that is not covered by any member of P.
So why not elect the highest approval member of P that is not covered by any
member of P?
By this rule, if the approval winner is uncovered it will win. If there are five members of P and the upper
two are covered by members of the lower three, but the third one is covered only by candidates outside
of P (if any), then this middle member of P is elected.
What if this middle member X is covered by some candidate Y outside of P? How would X respond to
the complaint of Y, when Y says, "I beat you pairwise, as well as everybody that you beat pairwise, so
how come you win instead of me?"
Candidate X can answer, "That's all well and good, but I had greater approval than you, and one of my
buddies Z from P beat you both pairwise and in approval. If Z beat me in approval, then I beat Z pairwise,
and somebody in P covers Z. If you were elected, both Z and the member of P that covers Z would have
a much greater case against you than you have against me."
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