# [EM] Feature extraction and criteria for multiwinner elections

Paul Kislanko kislanko at airmail.net
Sat Jan 3 18:18:37 PST 2009

```See below for the context.

I thought aloud a few years ago that one way to select a "winning ranked
ballot" would be to find the ballot that is "most like" the consensus
ballot. Order the candidates by their Bucklin rank and ballots by the
Kendall tau "distance" that each ballot is from the Bucklin rank. The ballot
with the least tau distance from the medians is then used to decide the
election.

(Based upon a science fiction short-story from the 1950s, but reasonable
from a mathematical perspective.)

-----Original Message-----
From: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Raph
Frank
Sent: Saturday, January 03, 2009 6:13 PM
To: Kristofer Munsterhjelm
Cc: Election Methods Mailing List
Subject: Re: [EM] Feature extraction and criteria for multiwinner elections

On Sat, Jan 3, 2009 at 1:40 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> A (seemingly) reasonable generalization of the Euclidean distance Voronoi
> would be this: For each point, find the two candidate points so that the
sum
> of the distances to those two points are minimized. Color p according to
the
> composite color of the k closest candidates (for a (k,n) election). But
> doesn't that correspond to the election method where you elect the CW,
then
> remove him and elect the next CW and continue like that until done? That
> method is not PR.

One option would be

for each possible set of N winners
- find the average distance from each voter to the closest winner

The 'best' winning set is the one that minimises this average distance.

This means that the size of the Gaussian would matter.  If all the
voters were concentrated at a single point, then the winner would just
be the double CW like you said.

However, if there is a large spacing between the voters, then it the
effect would be to elect candidates closer to the edges.

> 46: Left > Center > Right
> 46: Right > Center > Left
>  8: Center > Left > Right
>
> which should elect Center in a single-winner election, but Left and Right
in
> a multiwinner one?

Yes, I think this is perfectly reasonable.  Centre is a compromise
between all the voters.  However, if there are 2 seats, then each
faction should be allowed to pick its own winner.

Left + Right means that 92% of the voters get their top choice
elected.  Which is better than Centre + Right or Centre + Left.
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```