Let me explain how I intuitively think about clones. Forget the formal
definition and just think of clones as being perfectly identical to each
other.
Suppose a clone of George W. Bush somehow magically appeared in the 2004
election. Call them Bush-A and Bush-B. Voters who wish to support Bush
then need to decide which one to vote for. If they all coordinate and
agree on the same one, they have no problem. But if they don't, they
will split the vote and neither Bush is likely to get elected. So I
would say that plurality fails the independence of clones criterion,
although the voters can theoretically avoid the potential consequences
of the failure with coordination and agreement.
Approval has no such problem because the Bush supporters can simply vote
for both Bush-A and Bush-B. If they tie, a coin is flipped and one is
elected. Since they are exact clones, either one will do.
I think that captures the essence of the concept for plurality and
Approval, but someone will surely correct me if I am wrong.
--Russ
Paul Kislanko kislanko-at-airmail.net |EMlist| wrote:
I am not entirely sure who said what because of the way Mike constructs his
emails, and I don't really care anymore about what you "experts" think one
way or another, but Mike (or somebody) wrote:
Set S is a clone set if, for every particular voter, and for
any candidate X
outside S, if that voter prefers somone in S to X than s/he prefers
everyone in S to X; and if that voter prefers X to someone in
S, then s/he
prefers X to everyone in S; and if that voter is indifferent
between X and
some candidate in S, then s/he is indifferent between X and
every candidate
in S.
A voter is indifferent between X and Y if s/he doesn't prefer
X to Y and
doesn't prefer Y to X.
[end of clone-set definition]
Now, this definition pretty much says there can't be a "clone set", because
any ONE (every particular) voter can break the definition by chosing a
candidate to be included in it or excluded from it. That makes no sense.
If you define "voter clones" for each voter ("every particular voter") then
you just have a different clone set for each voter. I don't know what that
means, but it certainly doesn't make the concept of "clone" in the context
of a method any easier to understand.
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