[EM] Avoiding Clone Problems in Condorcet Flavored PR methods

[Elisabeth Varin/Stephane Rouillon]

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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