Hi folks,
I was recently asked to clarify the statement on my web site that
approval voting fails independence of clones.
http://fc.antioch.edu/~james_green-armytage/vm/define.htm#clones
This was my reply. Debate is welcome...
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First, I use a consistent means of adapting ranked ballot criteria to
non-ranked methods.
http://fc.antioch.edu/~james_green-armytage/vm/define.htm#nonrankedcrit
So, ICC definition is changed to this, for use in evaluating non-ranked
methods:
1. Clones: A set of candidates such that for every candidate outside the
set, all voters either prefer the outside candidate to all inside
candidates, or prefer all inside candidates to the outside candidate.
2. Independence of clones: If a clone set has two or more members,
removing one of the clones should not have any bearing on whether the
winning candidate comes from the set. Likewise, adding a new clone to the
set should not have any bearing on whether the winning candidate comes
from the set.
Failure example:
Preferences with approval cutoffs:
60: A>R>>S
40: R>S>>A
Approval scores:
A: 60
R: 100
S: 40
R and S are clones. R is the initial winner. However, if you remove
candidate R, the winner is A.
I have proposed a modified version of ICC such that candidates must be
given identical cardinal/approval scores by all voters to qualify as
clones, in addition to the standard qualification rule. I believe that
approval and cardinal pairwise both pass this modified version of ICC, but
not the standard ranked ballot version.
my best,
James
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