[Election-Methods] Improved Approval Runoff

[Chris Benham]

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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