[EM] proportional constraints - help needed

[Peter Zbornik]

2013/2/5 Jonathan Lundell <jlundell at pobox.com>:
> 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.

We dont want to quote-in the women at the last places on the party
list, where they are practically unelectable.
This is how we have defined the constraints it in our statutes, so the
constraints 1 and 2 cannot be "simplified".

>
>> 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.

If "fairly proportional" will be defined, then I my question will be
easy to answer.
The definition of  "fairly proportional" is at the core of my question.
I think there is a trade-off between "ranking proportionality" and
"quota proportionality",
i.e. you cannnot in all cases maximalize the proprtionality of both
the ranking and the distribution of the quoted seats at the same time.

To quote my previous email:
I.e. we search for
a) a quota proportionality measure and
b) a proportional ranking measure and
c) a rule, which "optimises" both the "quota proportionality" and the
"proportional ranking proportionality".

The optimization in c) above, is what I mean by "fairly proportional".

PZ