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 <[email protected]>: > 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 <[email protected]>: >> 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. >> ---- Election-Methods mailing list - see http://electorama.com/em for list info
