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.
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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