[EM] proportional constraints - help needed

[Kristofer Munsterhjelm]

On 02/05/2013 06:50 PM, Peter Zbornik 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.
> 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?

How about this:

First run an STV election. When the number of candidates of any gender 
is at two, no more candidates of that gender may be eliminated; instead, 
eliminate the candidate of the other gender with the least first place 
count. When more than one candidate is to be elected, always pick the 
candidate of the minority gender in the council so far; and if a given 
gender has three candidates on the council already, no more candidates 
of that gender may be elected.

(E.g. at the point where there are only two women left, the elimination 
part of STV removes the man with least first place votes instead. And if 
you have two women and a man elected so far, and the next round sees the 
election of both a woman and a man, pick the man first.)

Now you have a council with a 3:2 distribution. Do a sequential 
election. First do a ranked single-winner election for first place. Say 
the first-place candidate is a man. Then you do a ranked single-winner 
election for second. Pick the highest ranked woman in the social 
ordering for second place on the list. Continue in this manner: if the 
rules force you to pick a certain gender, pick the highest ranked 
candidate of that gender.

If you want to save on the sequential elections, just do a single round 
with a single-winner method, then remove elected candidates from the 
ranking as you go. For instance, say that the outcome is

W1 > W2 > M1 > M2 > M3

First place on the list goes to W1. Cross off that candidate and now the 
social ordering is

W2 > M1 > M2 > M3.

Now you can't elect a woman, so the second place on the list goes to M1. 
Cross off and now the ordering is

W2 > M2 > M3.

This ordering can then be transplanted right to the list, so third place 
goes to W2, fourth to M2, and fifth to M3.

This approach isn't ideal: first, the sequential method that STV is 
might not do optimally with restrictions (i.e. might produce more 
disproportional results than you could get with a combinatorial method). 
Second, the single-winner run is majoritarian, so you'd get, at least 
with a good method, centrists at the top of the list and then the wings 
further down. Both of these problems could be solved by using a 
proportional ordering method, but I assume you can't get such a radical 
change, since proportional ordering methods are relatively unknown.