[EM] Feature extraction and criteria for multiwinner elections

Kristofer Munsterhjelm km-elmet at broadpark.no
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.

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