On Nov 18, 2009, at 11:33 PM, fsimm...@pcc.edu wrote:
How's this for making Kemeny clone free?
Ballots are ordinal with equal rankings and truncation allowed.
The distance between two candidates is the number of ballots on
which they are
distinguished, i.e. one ranked and one not, or both ranked but not
equal.
In normal Kemeny the distance between two ballots is the minimum
number of
transpositions to convert one ballot into the other. My suggestion
is to modify
this count by giving each transposition a weight proportional to the
distance
between the two candidates involved.
The Kemeny order is the permutation of the candidates whose average
Kemeny
distance to the ballots is minimum. I claim that if the suggested
modified
Kemeny distance is used, then the method is clone free.
How about this example.
1: A>B
1: B>A
=> a tie
1: A1>A2>B
1: B>A1>A2
It seems that the method elects now A1. Introduction of a clone would
thus change the balance. Did I get the definition right? (= for each
vote if some pair is not ordered right in the result then add as many
points as the distance between the candidates is in this vote)
Kemeny is NP hard because there are so many permutations to check,
not because
the distances are hard to calculate.
So I suggest that various standard permutations always be checked
along with
each ballot order, as well as as many other orders as anybody wants
to nominate.
Yes, it'd be easy to allow anyone to run some generic optimization
procedures themselves and propose solutions (also and maybe especially
after the votes are already known). The "official calculation
procedure" could also use some monte carlo optimization and thus
include also whatever random permutations. It would be enough to
define the criterion that can be used to identify the best result and
accept any methods to be used to find it (also to make sure that the
best result will not fall outside of the "accepted calculation rules").
Juho
The ballot orders that have truncations or equal rankings should be
completed in
various ways (for this purpose only, not for use in the distance or
average
distance computations) if a complete ordering of the candidates is
desired.
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