# [EM] Feature extraction and criteria for multiwinner elections

Raph Frank raphfrk at gmail.com
Sat Jan 3 16:12:50 PST 2009

```On Sat, Jan 3, 2009 at 1:40 PM, Kristofer Munsterhjelm
> 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.

```