[EM] clone independent kemeny method

Kristofer Munsterhjelm km_elmet at t-online.de
Sun Sep 25 02:50:35 PDT 2016

On 09/25/2016 05:44 AM, Ross Hyman wrote:
> The Kemeny election method finds the rank order that minimizes the
> average Kemeny tau distance between it and each ballot’s ranking.  I
> believe this can be made clone independent by instead of minimizing the
> Kemeny tau distance, minimizing the following distance:
> Define a swap as the swapping of candidates ranked n to n+k with
> candidates ranked n +k +1 to n+k+1+m so that the order would now be  n –
> 2, n-1, n+k+1, n+ k+2, ….n+k+1+m, n, n+1, n+2, … n+k, n+k+1+m+1, …
> Both k and m can be any non negative integers.  They are restricted to 0
> for the Kemeny tau distance. 
> The distance between two rankings is the minimum number of swaps needed
> to turn one into the other.

I suspect this wouldn't be summable (unlike Kemeny itself), since you'd
need more information than what the pairwise matrix can provide.

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