[EM] proportional constraints - help needed

[Jonathan Lundell]

On 5 Feb 2013, at 9:50 AM, Peter Zbornik <pzbornik at gmail.com> wrote:
> Dear all,
> 
> We recently managed, after some effort to elect some people in our
> party using STV (five of seven board members of the Czech Green Party
> and more recently some people to lead the Prague organisation etc.).
> We used standard fractional STV, with strict quotas, valid empty
> ballots, Hagenbach-Bischoff quota, no Meek.
> It was the first bigger usage of STV in the Czech republic.
> As a footnote, I would like to add, that one big advantage of
> proportional election methods, is that it elects "the best people",
> i.e. meaning the people, who have the biggest support in the
> organisation.
> 
> Now we would like to go on using STV for primary elections to party
> lists in our party.
> I have a good idea on how to do it using proportional ranking, but am
> not entirely confident in how to implement the gender quotas.
> So here I would like to ask you, the experts, for help.
> I have only found some old papers in election-methods, but they are
> not of any great help to resolve the following problem, unfortunately.
> 
> The problem (after a slight simplification) is as follows:
> We want to elect five seats with any proportional ranking method (like
> Schulze proportional ranking, or Otten's top-down or similar), using
> the Hagenbach-Bischoff quota
> (http://en.wikipedia.org/wiki/Hagenbach-Bischoff_quota) under the
> following constraints:
> Constraint 1: One of the first two seats has to go to a man and the
> other seat has to go to a woman.
> Constraint 2: One of seat three, four and five has to go to a man and
> one of those seats has to go to a woman.

Why the two constraints, as opposed to a single constraint the overall gender distribution must be 3:2 or 2:3? Constraints are hard enough (OK, impossible in the general case) to square with proportionality without making them stricter than required.

> Say the "default" proportional ranking method elects women to all five
> seats, and thus that we need to modify it in a good way in order to
> satisfy the constraints.
> 
> Now the question is: How should the quoted seats be distributed in
> order to insure
> i] that the seats are quoted-in fairly proportionally between the
> voters (i.e. the same voters do not get both quoted-in seats) and at
> the same time
> ii] that the proportional ranking method remains fairly proportional?

Define "fairly proportional", please.