[EM] Avoiding Clone Problems in Condorcet Flavored PR methods

[Forest Simmons]

When approval cutoff's are supplied (as they really should be, since
approval information is relatively cheap) there are several ways to
resolve the difficulty, and your way certainly gives the right answers to
the examples below.

I have some other ideas (along these lines) that I will post to the list
later.

Forest

On Tue, 24 Sep 2002, Elisabeth Varin/Stephane Rouillon wrote:

> Forest,
>
> you seem to have the same kind of problem
> than Craig Carey.
>
> Sorry for repeating myself, but I think method
> "K) ranked pairs with residual approval weigths...."
> under the ESD site is what you would like.
> Except that in your multi-members election case
> you need to keep n winners not only one.
>
> The method is not very well explained, I have
> to rewrite the explanations...
>
> > 170 C1>>C2>C3
> > 170 C1>>C3>C2
> > 330 C2>C3>>C1
> > 330 C3>C2>>C1
> >
> First case:
> Ranked pairs with relative margins:
> Lock both C2 > C1 and C3 > C1, C2=C3 after.
> Ranked pair order C2=C3 > C1.
> Eliminate C1 which produces a 340 C1 residual approval weight.
> Ranked pair with relative margins for remaining candidates:
> C2=C3 (500 - 500). Make both scenarii with 1/2 ponderation:
> 1st scenario: C2 eliminated . C2 residual weight 0, C3 residual weight
> 330.
> 2nd scenario: C3 eliminated . C2 residual weight 330, C3 residual weight
> 0.
>
> Final approval weights C1 (340), and both C2 (330) and C3 (330).
> Elect C1, and one of C2 or C3 with a tie-breaker.
>
> > 170 C1>C2>>C3
> > 170 C1>C3>>C2
> > 330 C2>>C3>C1
> > 330 C3>>C2>C1
> >
> Second case:
> Ranked pairs with relative margins:
> Lock both C2 > C1 and C3 > C1, C2=C3 after.
> Ranked pair order C2=C3 > C1.
> Eliminate C1 which produces no C1 residual approval weight (0).
> Ranked pair with relative margins for remaining candidates:
> C2=C3 (500 - 500). Make both scenarii with 1/2 ponderation:
> 1st scenario: C2 eliminated . C2 residual weight 0, C3 residual weight
> 500.
> 2nd scenario: C3 eliminated . C2 residual weight 500, C3 residual weight
> 0.
>
> Final approval weights C1 (0), and both C2 (500) and C3 (500).
> Elect C2 and C3.
>
> Steph.
>

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