[EM] Enhanced DMC

[fsimmons at pcc.edu]

----- Original Message -----
From:
Date: Friday, August 12, 2011 3:12 pm
Subject: Enhanced DMC
To: election-methods at lists.electorama.com,

>
> > From: "C.Benham"
> > To: election-methods-electorama.com at electorama.com
> > Subject: [EM] Enhanced DMC
>
> > Forest,
> > The "D" in DMC used to stand for *Definite*.
>
> Yeah, that's what we finally settled on.
>
> >
> > 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)?
>
> Yes, I'll give an example when I get more time

Here's a possible scenario:

Suppose that approval order is alphabetical from most approval to least A, B, C, D.

Suppose further that pairwise defeats are as follows:

C>A>D>B>A together with B>C>D .

Then the set P = {A, B} is the set of candidates neither of which is pairwise
beaten by anybody with greater approval.

Since the approval winner  A is not covered by B, it is not covered by any
member of P, so the enhanced version of DMC elects A.

But A is covered by C so it cannot be elected by any of the chain building
methods that elect only from the uncovered set.