Its just occurred to me that, by the definition Ive just posted, in an
Approval election, every subset of the candidates is a clone set, because
its impossible to vote a candidate between any two others in Approval. At
first I incorrectly believed that that meant that the criterion couldn't be
appllied to Approval.
Im not sure if the ICC definition that Ive just posted is the one that we
agreed on in discussion about it. It seems to me that we had a
non-preference ICC definition that applied to Approval, and which Approval
failed.
Well, we had a longer definition of a clone-set:. It might have been this:
Everyone who votes a member of S over some candidate X votes every member of
S over X; and if everyone who votes some candidate X over a member of S
votes X over every member of S; and if everyone who votes a member of S
equal to some candidate X outside of S votes every member of S equal to X.
Having just written this, I dont know if it would treat Approval
differently than the definition in my previous posting.
But I suppose that that ICC definition in my previous posting could be
applied to Approval. The deletion of a candidate shouldnt change the matter
of whether the winner comes from any subset to which that candidate belongs.
Say X wins and we delete X. There are subsets of the candidates that
contain only X and candidates who lose in the subsequent count. So Approval
apparently would fail that ICC. So that ICC definition that I posted in my
posting before this one _does_ treat Approval as one would expect ICC to
treat Approval
Mike Ossipoff
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