[EM] proportional constraints - help needed

[Kristofer Munsterhjelm]

On 02/09/2013 09:41 PM, Richard Fobes wrote:
>  > 2013/2/6 Richard Fobes<ElectionMethods at votefair.org>:
>  >> How many candidates would/could compete for the five (open)
>  >> party-list positions?
> On 2/6/2013 3:12 PM, Peter Zbornik wrote:
>  > Say twenty, for instance.
>
> To: Peter Zbornik
>
> After considerable thinking about your request, I've come up with a
> recommended election method for your situation.
>
> The method has these advantages:
>
> * Uses open-source software that is already available.
>
> * Does not require any modification of the software.
>
> * Provides proportional results for the five seats.
>
> * Provides quota-based representation for women -- which, as I
> understand it, you specified as requiring a woman in one of the top two
> positions, and another woman in the next three positions.
>
> * Is very resistant to strategic voting.
>
> * Produces better representation compared to using STV (single
> transferable vote).
>
> The method consists of running VoteFair _representation_ ranking
> calculations. Five levels of representation would be requested. As a
> part of that calculation, VoteFair _popularity_ ranking results are also
> calculated for all twenty or thirty candidates.

Although what I'm going to say may be a bit offtopic, I think I should 
say it. I think it could be useful to quantify exactly what is meant by 
quoted-in proportionality in the sense that the Czech Green Party 
desires it. Then one may make a "quota proportionality criterion" and 
design methods from the ground up that pass it.

It's very easy to otherwise come up with something that sounds nice 
(hey, I did it myself) but that doesn't pass the idea of quota 
proportionality as envisioned.

(Also, speaking of criteria: if I had enough time, I would try to find a 
monotone variant of Schulze STV. I think one can make monotone 
Droop-proportional multiwinner methods, since I made a Bucklin hack that 
seemed to be both monotone and Droop-proportional. However, I have no 
mathematical proof that the method obeys both criteria.)