[EM] Dectecting Clone Sets

[fsimmons at pcc.edu]

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.

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.

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.