# [EM] proportional constraints - help needed

Peter Zbornik pzbornik at gmail.com
Wed Feb 6 10:22:45 PST 2013

```Jameson,

I am not sure if we understand each other here.
I am looking for an election system, where the quoted-in seat gives
(or moves toward) a proportional distribution of the quoted-in gender.
If we fix the seats which will be quoted-in at no. 2 and 5, the
quoted-in gender will in some cases not be proportionally distributed,
for instance when the same group of voters get both quoted-in
candidates at places 2 and 5.
I think the problem is not restricted to STV, so other election
methods might be used and extended to resolve it, like Schulze STV.
The problem is not to quote in the underrepresented gender at place 2,
the problem is to proportionally quote-in the second seat at seat 3, 4
or 5, in order to get a proportional distribution of the quoted-in
gender.

A special case is when two women are elected to seats 1 and 2, and
three men are elected to seats 3, 4 and 5.
Here, the constraints are also breached, but with diferent gender for
seats 1 and 2 and for seats 3, 4 and 5.

Again, it would be unfair, if, with three coalitions, the same
coalition would get both quoted-in candidates.
Now, the solution for this problem would be to look for
proportionality of quoted-in candidates.
I am not sure, that we are looking for proportionality within each
gender, but rather proportionality of quoted-in candidates.

PZ

2013/2/6 Jameson Quinn <jameson.quinn at gmail.com>:
> STV is not my personal favorite PR rule (my favorites are Bucklin
> Transferrable Vote or PAL Representation, and Schulze PR is also better than
> STV). However, if you're starting from STV, the way to do the quota is
> clear. When the quota makes one gender ineligible for a seat, simply ignore
> that gender of candidates on all ballots. That's not just about
> eliminations; it also means the count of the top preferences on each
> (reweighted) ballot means the top eligible preferences.
>
> So say there are 7 piles of votes (as an unrealistic illustrative example):
>
> 18: W0 W1 M1 W2
> 17: W0 W1 M2 W2
> 16: W0 W1 M3 W2
> 15: W0 W1 M4 W2
> 14: W0 W1 M5 W2
> 13: W0 W1 M6 W2 M5
> 7: W3
>
> For the first seat, the unanimous choice W0 wins, and all votes are rescaled
> to 5/6 strength. For the second choice, you ignore the preferences for
> ineligible candidates W1, W2, and W3, and so M6 is eliminated and M5 wins
> with the transferred votes. Etc.
>
> Jameson
>
> 2013/2/5 Peter Zbornik <pzbornik at gmail.com>
>>
>> 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?
>>
>> ---
>>
>> Here is how I have been thinking about the problem myself.
>> I am not sure, however, that my line of thinking is the best or the
>> only one, so please read with a healthy amount of scepticism.
>> The problem can be re-formulated as follows.
>> Which method would make sure,
>> 1) that a large number of voters do not get both of the quoted seats?
>> 2) that the quoted seat is by default seat two and five, unless there
>> are compelling reasons to quote-in seat three or four (or, less
>> probably, seat one)?
>>
>> There is a trade-off between questions 1) and 2) above, i.e.:
>> a) if seat two and five are quoted, then a large number of the voters
>> might get both the quoted seats - which would lead the quotas to be
>> non-proportionally distributed, making some voters dissatisfied.
>> b) assume we always quote in seat two (this could, but need not be
>> necessary). If we, by using some appropriate proportionality measure
>> (has to be defined), quote-in the candidate at seat three, four or
>> five, then a fraction of one vote might decide, that the quoted-in
>> seat should be seat number three instead of seat five, or the rule
>> could "prefer" quoting in at place three, instead of place five, as
>> place three would need to have higher support, than place five. Such a
>> quota rule would ignore the fact, that place three is more important
>> than place five, i.e. that the disturbance in the proportionality of
>> the proportional ranking would be higher, if the candidate would be
>> quoted in at seat three than seat five.
>>
>> 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".
>>
>> I am sure the above was not entirely easy to digest.
>> I am happy to take your questions and will do my best to clarify.
>> Any references to relevant papers would be more than welcome.
>>
>> Best regards
>> Peter Zborník
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

```