# [EM] proportional constraints - help needed

Peter Zbornik pzbornik at gmail.com
Tue Feb 5 12:59:28 PST 2013

Hi Kristofer,

I am sending a short P.S. to my email below just to clarify the example
In the example in my email below we get the following result:

Seat/place number (ordered) --- Coalition --- quotas apply
1 --- A, B --- no
2 --- C --- yes
3 --- A --- no
4 --- B --- no
5 --- C --- yes

The problem is, that the quotas apply on the same coalition both
times, which leads to an unproportional distribution of candidates
which were quoted-in between the coalitions.

I am afraid this is not a trivial problem nor a problem.

PZ

2013/2/5 Peter Zbornik <pzbornik at gmail.com>:
> Hi Kristofer,
>
> I am afraid your approach might in some cases not lead to
> proportionally distributed quoted-in candidates.
>
> For instance, say we have three coalitions: A, B, C.
> Coalition A and B get their first place candidate
> Coalition C get their second place candidate quoted-in (i.e. they
> would prefer Agda, but they get Adam due to the quota rules).
> Coalition A and B get the third and fourth place candidates respectively.
> Coalition C, again, get their fifth place candidate quoted in (i.e.
> they would prefer Erica, but they get Eric due to the quota rules).
>
> This approach leads to an unproportional distribution of quoted-in
> seats (candidates) as Coalition C get both of the quoted-in candidates
> and Coalition A and B get none.
>
> Best regards
> Peter Zbornik
>
>
>
> 2013/2/5 Kristofer Munsterhjelm <km_elmet at lavabit.com>:
>> On 02/05/2013 06:50 PM, Peter Zbornik wrote:
>>>
>>> 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.
>>
>>
>> Oh, sorry. I didn't see the part about that you could use a proportional
>> ranking method. In that case, the answer's simple. Pick the highest ranked
>> council extension that doesn't violate the constraints.
>>
>> E.g. for Schulze's proportional ranking method, say the candidates are W1,
>> W2, W3, M1, M2, M3 (for Woman and Man respectively).
>>
>> First round, you have a matrix with W1, W2, W3, M1, M2, and M3. Say the
>> Schulze winner is M1. That's okay, M1 gets first place.
>>
>> Second round, you have a matrix with {M1, W1}, {M1, W2}, {M1, W3}, {M1, M2},
>> and {M1, M3}. Determine the Schulze social ordering according to the Schulze
>> proportional ordering weights (as defined in his paper). Remove {M1, M2} and
>> {M1, M3} from the output social ordering since these aren't permitted. Say
>> {M1, W1} wins.
>>
>> Then you just continue like that. In essence, you're picking the best
>> continuation of the ordering given what the constraints force you to do.
>>
>> You could also just null out the defeat strengths in the proportional
>> ordering matrix, but that would produce strategy incentives since Schulze
>> doesn't satisfy IIA.
>>