[EM] proportional constraints - help needed

[Juho Laatu]

On 12.2.2013, at 0.33, Kristofer Munsterhjelm wrote:

> I think it could be useful to quantify exactly what is meant by quoted-in proportionality in the sense that the Czech Green Party desires it. Then one may make a "quota proportionality criterion" and design methods from the ground up that pass it.

My best understanding of the quoted-in related requirements is now as follows. The key idea is that if a seat is about to go to a candidate that is of wrong gender, then the fact that this seat must be given to some "less liked" candidate makes the seat in some sense less valuable to the grouping that supports these candidates. The rule is not exactly about one of the sexes since one (quoted-in) seat may be forced to go to a male candidate and another seat (of the same grouping) to a female candiate. The rule is not really about avoinding allocating more than one quoted-in seat to one grouping since sometimes the value of two (less valuable) quoted-in seats is the ideal way to balance the seats between the groupings (best proportionality). To my understanding there is also no requirement to have equal number of male and female representatives in each grouping (only a requirement to do so at top level, i.e. to make the proportinally ordered list balanced with respect to genders).

Since there is also a general proportionality requirement in the traditional sense (each grouping to get a proportional number of representatives), there are two conflicting requirements, and therefore also a need to agree the correct balance between these two requirements (traditional proportionality and need to balance the allocated less valuable (quoted-in) seats). I mean that if the elected quoted-in candidate is 10 points worse than the candidate that would have been elected without the quoted-in rule, then that can be compensated by giving that grouping some fraction of a seat more seats (worth 10 points). All groupings will thus not get all those representatives that they wanted (quoted-in rule), and they will also not get the proportionally correct number of representatives. There is thus a need to agree what the value of one seat is, and what the negative value of getting a quoted-in seat is. These weights must be determined by a political agreement.

Once the weights of these benefits have been determined, it should be a more exact task to determine what algorithm finds the best allocation of the seats. It is however quite difficult to estimate if some candidate that was elected as a quoted-in candidate would or would not have been elected also otherwise. And if not elected without the quoted-in rule, how much the opinions were violated in this particular change of representative. Some agreement is needed also here on how to measure these values. One may also follow some theoretical model that gives "exact" values to the quoted-in representatives (based on the preferences on the ballots). Or maybe there is just one constatnt value for all quoted-in seats.

What would the "quota proportionality criterion" be then? Based on this discussion one should first make some agreements on what the weights of different (conflicting) needs are. Once this has been agreed, and assuming that we have also a rule for determining the "lost value" of each quoted-in candidate, then the algorithm just needs to find the ideal allocation of the weighted seats (different representative sets may have different weights). And the criterion is just a mathematical proportionality criterion, based on the agreed (and/or calculated) weights. Is this close to what you want the criterion to be?

Juho


P.S. Personally I think this algorithm gets already quite complex, and there are also some arguments why there would be no need or why it would be harmful to compensate the quoted-in seats. So also a simpler proportional approach could do. But if the Czech Green Party says that the quoted-in seats shall be compensated, then let's try to find a good algorithm that will do the job (and the correct criterion).