[EM] Proportional election method needed for the Czech Green party - Council elections

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Wed, May 5, 2010 at 12:08 AM, Juho <juho4880 at yahoo.co.uk> wrote:
>> (I note that Raph Frank proposed also an approach where the election of the
>> last representative would be free of these sex related requirements. That is
>> one way of relieving the proportionality related problems since at least the
>> last choice that often distorts proportionality the most can be done quite
>> freely. I'm not sure how big the improvement would be. There may be also
>> other more sophisticated approaches as noted above.)
> 
> The approach is to add 1 to the requirements, so the freedom can be
> given in the last step.
> 
> I was thinking of quotas and ensuring that it is actually worth voting
> for candidates.
> 
> If a candidate gets in with 60% of a quota due to gender restrictions,
> then the principle of PR-STV would seem to require an adjustment to
> the quota.  The quota would in effect be to low for all the other
> candidates.
> 
> Maybe there should be a different quota for men and women.
> 
> You could initially set it to the same for each.  If there ends up
> being more men than women, then the quota for women could be
> decreased, and the one for men increased (or vice versa).
> 
> This could be done iteratively (maybe like Meek's method) until the
> balance requirement is just barely met.

This makes me think of my own M-Set Webster (monotone divisor-based) 
method. In it, at least as by my reference implementation, it would be 
easy to set that kind of constraint.
The method ordinarily starts with the set of all councils and goes 
through "at least this many of that coalition" for different solid 
coalitions to get a certain number of candidate councils, which are then 
winnowed down to a single one in the margins phase.
One might add the additional constraints in two ways. The first would be 
to add new coalitions of all-women and all-men, having a fixed (not 
divisor-dependent) criterion of "at least this many" for each. The 
second would be to start with only the permitted councils (i.e. those 
that satisfy the constraints) instead of all possible ones. The outcome 
would be the same.

I am not sure if that method would be monotone, however, as the margins 
phase might consider jumps to inadmissible councils.