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RH

Ross Hyman

Sun, Sep 25, 2016 3:44 AM

The Kemeny election method finds the rank order thatminimizes the average Kemeny tau distance between it and each ballot’sranking. I believe this can be made cloneindependent by instead of minimizing the Kemeny tau distance, minimizing thefollowing distance:Define a swap as the swapping of candidates ranked n to n+kwith 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 ofswaps needed to turn one into the other.

The Kemeny election method finds the rank order thatminimizes the average Kemeny tau distance between it and each ballot’sranking. I believe this can be made cloneindependent by instead of minimizing the Kemeny tau distance, minimizing thefollowing distance:Define a swap as the swapping of candidates ranked n to n+kwith 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 ofswaps needed to turn one into the other.

TP

Toby Pereira

Sun, Sep 25, 2016 9:33 AM

Would you be able to illustrate this with an example?
Thanks

Toby

  From: Ross Hyman <rahyman@sbcglobal.net>

To: "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Sent: Sunday, 25 September 2016, 4:44
Subject: [EM] clone independent kemeny method

The Kemeny election method finds the rank order thatminimizes the average Kemeny tau distance between it and each ballot’sranking. I believe this can be made cloneindependent by instead of minimizing the Kemeny tau distance, minimizing thefollowing distance:Define a swap as the swapping of candidates ranked n to n+kwith 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 ofswaps needed to turn one into the other.

Election-Methods mailing list - see http://electorama.com/em for list info

Would you be able to illustrate this with an example? Thanks Toby From: Ross Hyman <rahyman@sbcglobal.net> To: "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> Sent: Sunday, 25 September 2016, 4:44 Subject: [EM] clone independent kemeny method The Kemeny election method finds the rank order thatminimizes the average Kemeny tau distance between it and each ballot’sranking. I believe this can be made cloneindependent by instead of minimizing the Kemeny tau distance, minimizing thefollowing distance:Define a swap as the swapping of candidates ranked n to n+kwith 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 ofswaps needed to turn one into the other. ---- Election-Methods mailing list - see http://electorama.com/em for list info

KM

Kristofer Munsterhjelm

Sun, Sep 25, 2016 9:50 AM

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.

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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clone independent kemeny method

The distance between two rankings is the minimum number ofswaps needed to turn one into the other.