One observation on clone independence and electing a centrist
candidate using rankings only and when one of the "extremists" has
majority.
Votes:
51: A>C>B
49: B>C>A
C is the winner.
A will be cloned. The votes could be:
51: A1>A2>C>B
49: B>C>A2>A1
C should still be the winner.
B will be cloned. The votes could be:
51: A>C>B1>B2
49: B2>B1>C>A
C should still be the winner.
The problem is that these two sets of votes are identical:
51: X1>X2>X3>X4
49: X4>X3>X2>X1
In the first set of votes the intended winner C is X3 and in the
latter X2. It is thus impossible for the algorithm in this case and
with this information (rankings only) to satisfy both requirements
and to be fully clone independent.
Similar conclusions could be drawn at least for normalized ratings.
A=100 C=55 B=0 => A1=100 A2=56 C=54 B=0
B=100 C=55 A=0 => B=100 C=56 A1=54 A2=0
or
A=100 C=55 B=0 => A=100 C=56 B1=54 B2=0
B=100 C=55 A=0 => B2=100 B1=56 C=54 A=0
One approach to try to avoid this problem would be to use a more
limited clone concept: candidates that are ranked/rated equal with
each others.
Juho
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