I am one of those that thinks that compliance with the Plurality and
Minimal Defense criteria is
desirable, but note that if the ballots are interpreted as purely
relative rankings then examples
of failures can be made to "go away" by cloning the offending winner.
49: A1>A2
24: B
27: C>B>A1
Without the clone A2 Minimal Defense says that A1 can't win but with it
says only that A2 can't
win.
7: A>B>C1
5: B
4: C1>C2
4: C2>C1
With the clone C2 removed Plurality says that A can't win, but with it
it says nothing.
I've been giving some thought as to what is the best method that uses
only the normal gross pairwise
matrix. Smith//Approval (interpreting ranking above at least one other
candidate as approval) can be
done by electing the member of the Smith set with the largest single
gross score in any of the pairwise
comparisons. But it concerns me that in the top example this would mean
electing A1 but without the
covered weak clone A2 the winner is B.
So I suggest as a score that is less vulnerable to clones: a candidate's
biggest gross pairwise score in a
victory over an uncovered candidate.
(A candidate Y is "covered" if there is some candidate X that pairwise
beats Y and also any candidates
that Y pairwise beats.)
So I recommend this simple Condorcet method:
*Elect the CW if there is one, otherwise elect the candidate with the
biggest gross score in a pairwise
victory over an uncovered candidate.*
Any comments?
Chris Benham
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