[EM] STV and single constraints, like gender quotas

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> Dear all,
> 
> do anyone of you know the best way to incorporate single constraints
> into STV and proportional rankings from STV (see for instance:
> http://www.votingmatters.org.uk/issue9/p5.htm)?
> For instance, the constraint can be that at least 1/3 of the elected
> seats go to candidates of each gender.
> I found some information in the links below, but I wonder if there are
> better or more recent suggestions:
> http://www.votingmatters.org.uk/ISSUE9/P1.HTM
> http://www.votingmatters.org.uk/issue9/p5.htm

I don't know of any better rules than the naive rule off the top of my 
head. I will note this, however: if you use a combinatorial method like 
Schulze STV, it is very easy to accommodate both simple and complex 
rules. You just decide to consider only those seat compositions that are 
permitted by the constraints.

For instance, if you need at least one black and at least one woman (but 
they can be the same person), then you enumerate all possible 
permutations and remove those that have no blacks and no women. Then you 
run Schulze STV (or combinatorial method of choice) with respect to 
what's left.

This also works for constraints that can't easily be determined in 
advance or from the ballots themselves. If you say that the CW based on 
the same ballots, or the current chairman's pick, has to be on the 
council, first run the ballots through a Condorcet method (or ask the 
chairman) and only consider the seat compositions where the candidate in 
question is included.

I suppose you could make ordinary STV combinatorial by considering "how 
many voters did we have to overrule to get the composition we wanted" 
(where this is measured as number of last preferences for the candidate 
that was eliminated in each round, less the number of last preferences 
for the candidate that would have been eliminated by ordinary STV rules, 
using a forced elimination sequence that minimizes this number for the 
given composition), but it's not clear to me how you would go about 
actually calculating that minimizing sequence.