[EM] Re: Schwartz//SC-WMA

[Chris Benham]

Forest,
I  can't pretend to understand your proposed de-cloning mechanism, and 
I'm surprised that  you are interested in Copeland
because I thought that one of its main problems is that it usually isn't 
very decisive. To me a more attractive  method in need
of decloning is  Woodall's  Quota-Limited Trickle Down (QLTD).

Regarding the clone problem with  Weighted Median Approval  (WMA), you 
wrote:

>2. Does the problem persist in the version of WMA that uses fractional 
>approval at the level where half of the weight is used up?
>
With  symmetric completion, this is a method that I was interested in 
and attracted to for a while, which I called
Quota-Limited Weighted Approval  (QLWA).  Woodall shows that it fails 
Clone-Loser:

>42: A B C	cutoff 8/28 of the way into B
>28: B C A	cutoff 22/30 of the way into C
>30: C A B	cutoff 20/42 of the way into A
>
>Here the weights are A 42, B 28, C 30, total 100.  The cutoffs are as
>shown, giving A: 42+30*20/42 = 56.286, B: 28+42*8/28 = 40,
>C: 30+28*22/30 = 50.533, so A wins. 
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>
Now  C  is cloned.

>42: A B C1 C2	cutoff 8/28 of the way into B
>28: B C1 C2 A	cutoff 7/15 of the way into C2
>15: C1 C2 A B	cutoff 20/42 of the way into A
>15: C2 C1 A B	cutoff 20/42 of the way into A
>
>The weights are A 42, B 28, C1 15, C2 15, total 100.  The cutoffs are as
>shown, giving A: 42+30*20/42 = 56.286, B: 28+42*8/28 = 40,
>C1: 15+15+28 = 58, C2: 15+15+28*7/15 = 43.067, so C1 wins.
>

Chris Benham

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