[EM] proportional constraints - help needed

[Peter Zbornik]

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.
>