Diego Renato wrote:
2007/8/18, Gervase Lam:
> [With a reweight of 0 a] concern [is] that if you approve your
compromise
> candidate, who ends up being the most approved, you can weaken
your votes
> for your favorite candidate and cause him to fail to qualify for the
> second round.
The ideal way to sort out this concern would be have the
reweighting be
1 instead of 0. However, having a reweighting of 1 means that a
faction
could get a turkey candidate into the second round, as Chris has
pointed
out. The compromise between a reweighting of 0 and 1 is 1/2!
Personally, I agree with dropping rule #2 but would keep the
reweighting
at 1/2.
I devised an example where a reweighting of 0 results CW fail to run
second round (>> is approval cutoff):
33: Right >> Center > Left
8: R > C >> L
7: C > R >> L
8: C >> R > L
8: C >> L > R
8: C > L >> R
7: L > C >> R
21: L >> C > R
First count: R: 48; C: 46; L: 36
Second count: C: 38,5; L: 36 (IAR), C: 31; L: 36 (Chris' proposal)
Under IAR, candidates from right and center compete in the second
round, and centrist wins. Under Crhis' method, the competitors are
from right and left, and rightist wins.
Diego,
I don't think your example works. My approval scores are C53, R48,
L36. (Note there are 107 ballots. FP scores are R41, C38, L28)
Both methods have C as the first qualifier and R as the second. C
easily pairwise beats both R and L so C wins.
For your method the scores in the second count are R40.5, L28.5. In my
suggested method the second count scores are R33, L21.
It obviously isn't possible for any version of top-2 approval runoff to
guarantee the election of a sincere CW when there are more than two
candidates,
so if your example did work I can't see what it would prove.
Chris Benham
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