[EM] Enhanced DMC

[C.Benham]

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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