# [EM] Feature extraction and criteria for multiwinner elections

Mon Jan 5 00:45:01 PST 2009

```Paul Kislanko wrote:
> I'm not sure at all what context this is, but it's fairly simple to define a
> "closest winner" metric that is completely transparent.

Well, it is completely transparent from the point of view of the
designer. The effect I'm talking about is that it hides (obscures,
conceals) disproportionality from a group of voters as long as that
group's preferred candidate is in the council.

The example I gave was this: A* voters and B* voters at 49% each, C*
voters at 2%, all groups prefer lower numbered candidates. Then the council

A1, B1, C1, C2, C3, C4, C5, C6, C7, C8

is very disproportional, but since A1 is there, the A* voters are happy
by the closest-representative metric, and so are the B* voters (and
obviously the C* voters). Since we were trying to find the best outcome
of the proportional method, the metric is lacking, as it ranks a bunch
of other councils (like the disproportional one above) also as "best".

In the case of four candidates, it might even rank a disproportional
allocation above a proportional one:

A1, A2, B1, C1 gives distance zero to all voters, but better is

A1, A2, B1, B2, since that gives 50% (quite close to 49%) of the council
to the A* and B* groups. This gets a worse "closest-distance" score
because the C* voters are no longer represented.

```