[EM] Dectecting Clone Sets

[Juho]

On Nov 18, 2009, at 11:33 PM, fsimmons at 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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