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Diego Renato wrote:<br>
<blockquote type="cite">2007/8/18, Gervase Lam:
<span class="gmail_quote"></span>
<blockquote class="gmail_quote"
style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">>
[With a reweight of 0 a] concern [is] that if you approve your
compromise
<br>
> candidate, who ends up being the most approved, you can weaken
your votes<br>
> for your favorite candidate and cause him to fail to qualify for
the<br>
> second round.<br>
<br>
The ideal way to sort out this concern would be have the reweighting be
<br>
1 instead of 0. However, having a reweighting of 1 means that a faction<br>
could get a turkey candidate into the second round, as Chris has pointed<br>
out. The compromise between a reweighting of 0 and 1 is 1/2!<br>
Personally, I agree with dropping rule #2 but would keep the reweighting<br>
at 1/2.</blockquote>
<br>
I devised an example where a reweighting of 0 results CW fail to run
second round (>> is approval cutoff):<br>
<br>
33: Right >> Center > Left<br>
8: R > C >> L<br>
7: C > R >> L<br>
8: C >> R > L<br>
8: C >> L > R<br>
8: C > L >> R<br>
7: L > C >> R<br>
21: L >> C > R
<br>
<br>
First count: R: 48; C: 46; L: 36<br>
Second count: C: 38,5; L: 36 (IAR), C: 31; L: 36 (Chris' proposal)<br>
<br>
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.
<br>
</blockquote>
Diego,<br>
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)<br>
Both methods have C as the first qualifier and R as the second. C
easily pairwise beats both R and L so C wins.<br>
<br>
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.<br>
<br>
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,<br>
so if your example did work I can't see what it would prove.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
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