[EM] Fwd: Is Chain Climbing really independent of clones??

[Michael Ossipoff]

It was requested that I forward this message, too, to EM:


---------- Forwarded message ----------
From: Steve Eppley <SEppley at alumni.caltech.edu>
Date: Sun, Apr 20, 2014 at 7:22 PM
Subject: Is Chain Climbing really independent of clones??
To: Michael Ossipoff <email9648742 at gmail.com>


The "least implicit approval" score used in Chain Climbing doesn't look
cloneproof.

Under Plurality Rule, two "top" clones can split their vote, allowing a
third candidate to win by spoiling.  Chain Climbing seems very similar: Two
"bottom" clones can split their "implicit disapproval" so that a third
candidate will instead be added to S.

Begin with the example from my recent email:
     5: A B C
     4: B C A
     3: C A B
First add C to S since C is bottom-ranked by the most (5).
Then add B to S since only B is unbeaten pairwise by a candidate in S.
Then elect B.

Suppose we add a clone of C:
     3: A B C C'
     2: A B C' C
4: B C C' A
     3: C C' A B
First add A to S since A is bottom-ranked by the most (4).
Now B can never be added to S since B is beaten pairwise by a candidate in
S.

Have I made a mistake?

--Steve
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