# [EM] proportional constraints - help needed

Jameson Quinn jameson.quinn at gmail.com
Thu Feb 7 09:11:45 PST 2013

```I think V should be 3/4 (if quoted-in) or 1 (if would have won that same
seat anyway). Thus, the quota would be 2/11, and the leftover
(unrepresented) quota at the end would be between 1/11 (Hare-like) and 2/11
(Droop-like).

Jameson

2013/2/7 Juho Laatu <juho4880 at yahoo.co.uk>

> I try to address the targets one more round without taking position on how
> the actual algorithm will work. From this point of view I start from the
> question, what is the value of a quoted-in seat. Maybe we can use a
> constant value (V) that is smaller that the value of a normal seat (1).
>
> One problem that we have is that although the value of a quoted-in seat is
> smaller than 1, the final value of that representative may be equal to 1. I
> mean that if we are electing members of a parliament, all elected candiates
> will have one vote each in the parliament. Therefore, from political
> balance point of view, every representative is equally valuable. The lesser
> value of the quoted-in candidate refers only to the fact that some grouping
> did not get their most favoured candidate throuh.
>
> If one tries to meet e.g. regional proportionality and political
> proportionality requirements at one go simultaneously, the only erros are
> rounding errors in the allocation of the last seats. The quoted-in
> requirements and political proportionality requrements are however in
> conflict with each others. One has to decide how much weight to put to the
> need to elect the most liked candidate of a grouping vs. to give all
> groupings equal weight in the parliament.
>
> In the example below, if we assume that five candidates (w1, m3, w3, w2,
> m4) will be elected, and V = 0.5, the "liked candidate points" of the two
> groups will be < 2, 2 > but the voting weights in the parliament will be <
> 2, 3 >. What is the ideal outcome of the algoritms then? Should the
> algorithm make the "liked candidate points" as equal as possible for all
> groupings, or should the algorithm lead to a compromise result that puts
> some weight also on the voting strengths in the parliament? I guess you can
> do this quite well also by adjusting the value of V, e.g. from 0.5 to 0.75.
>
> So far my conclusion is that one could get a quite reasonable algorithm by
> just picking a good value for V and then using some algorithm that
> optimizes proportionality using these agreed weights (and the gender
> balance requirements).
>
> - - -
>
> Personally I'm still wondering if the "less liked candidate reweighting"
> rules are a good thing to have. One reason is the equal voting weight of
> the elected representatives in the parliament. Sometimes the quoted-in
> candidates could be elected also without the quoted-in rules (e.g. if the
> second set of opinions was 50: w3 > m3 > w4 > m4). The algorithm could thus
> not be accurate anyway (could give false rewards). One could also say that
> if some of the groupings doesn't have any good (= value very close to 1)
> candidates of the underrepresented gender, it is its own fault, and that
> shoudl not be rewarded by giving it more seats.
>
> One more point is that the algorithm might favour the quoted-in grouping
> also for other reasons. I'll modify the example a bit.
>
> 45: w1 > w2 > m1 > m2
> 05: w1 > w2
> 45: w3 > w4 > m3 > m4
> 05: w3 > w4
>
> Here I assume that those candidates that are ranked lower in the votes
> will typically get also less votes in general. Here all male candidates
> have only 45 supporters, while all female candidates have 50 supporters
> each. Here I assume that voters do not generally rank all candiates or all
> candidates of their own grouping (this may not be the case in all
> elections). Anyway, the impact of this possible phenomenon is that at least
> w3 will be automatically ranked third, also without the "less liked
> candidate reweighting" rules. I'll skip the analysis of the fifth seat (it
> gets too complex).
>
> If the green party is determined that there should be some "liked
> candidate" rules, just forget this last part of my message, I'm not a membr
> of the Czech Green Party anyway :-).
>
> In general I think it is possible to generate an algoritm that does pretty
> accurately what it is required to do. The low number of seats of course
> means that there will be considerable "rounding errors". But I guess that's
> just natural, and all are fine with that, as long as the general principles
> that are used to order the list are fair and as agreed to be.
>
> Juho
>
>
>
> On 7.2.2013, at 16.00, Peter Zbornik wrote:
>
> > Dear Juho,
> >
> > 50: w1 > w2 > m1 > m2
> > 50: w3 > w4 > m3 > m4
> >
> > If we say, that a quoted-in candidate has the value and weight of 1/2
> > of a seat and if we lower the Hagenbach-Bischoff quota accordingly, so
> > that only half of the number of votes are used, then we actually have
> > a 4-seat election instead of a 5-seat election and thus it is
> > appropriate that one coalition gets both women.
> >
> > That approach is interesting.
> >
> > Now how exactly to value a quoted-in candidate compared to a
> > non-quoted in candidate?
> > One way is to determine the largest Hagenbach-Bischoff quota which
> > elects the last elected candidate, which was not quoted-in (call this
> > quota Qmin) and then compare the value with the quoted-in candidate
> > (Q).
> > (Qmax-Q)/Qmax will be the value of the quoted-in candidate.
> > Lacking a better formula to set the value of the quoted-in candidate a
> > value of 1/2 or 2/3 of a seat for the quoted-in candidate could maybe
> > be used.
> >
> > Maybe someone will propose a better formula to value the quoted-in
> candidate,
> > which might (or might not) depend on the number of the seat being
> > elected (i.e. it is worse to get seat no. 2 quoted-in, than seat no.
> > 5).
> >
> > P.
> >
> > 2013/2/7 Peter Zbornik <pzbornik at gmail.com>:
> >> 2013/2/7 Juho Laatu <juho4880 at yahoo.co.uk>:
> >>> On 5.2.2013, at 19.50, Peter Zbornik wrote:
> >>>
> >>> 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
> >>>
> >>>
> >>> 50: w1 > w2 > m1 > m2
> >>> 50: w3 > w4 > m3 > m4
> >>>
> >>> The first seat goes to w1 (lottery). The second seat goes to m3 (male
> >>> representative needed).
> >>>
> >>> I read the rule above so that the third seat should go to w3 (not to
> w2).
> >>> The rule talks about getting both quoted-in seats, but I guess the
> intention
> >>> is that already the first quoted-in seat is considered to be a slight
> >>> disadvantage that shall be balanced by ranking w3 third. Is this the
> correct
> >>> way to read the rule?
> >>
> >> In a sense yes, but I haven't thought about the problem that way.
> >> The question is how to quantify the "disadvantage", for instance if we
> >> had the votes 55 w1 w2 m1 m2 and 45 w3 w4 m3 m4, should we still rank
> >> w3 third, instead of w2?
> >>
> >>>
> >>> The fourth seat goest to w2.
> >>>
> >>> 1) If we read the rule above literally so, that one grouping should
> not get
> >>> both quoted-in seats, the fifth seat goes to m1.
> >>> 2) If we read the rule so that the quoted-in seats are considered
> slightly
> >>> less valuable than the normal seats, then the fifth seat goes to m4.
> >>
> >> That is an interesting point. I guess both interpretations are valid.
> >> Personally, at first sight, I like the second interpretation.
> >> I have to think about that a little.
> >>
> >>>
> >>> Which one of the interpretations is the correct one? My understanding
> is now
> >>> that there is no requirement concerning the balance of genders between
> the
> >>> groupings, so allocating both male seats to the second grouping should
> be no
> >>> problem. But is it a problem to allocate both quoted-in seats to it?
> >>>
> >>> Is the second proportional ordering ( < w1, m3, w3, w2, m4 > ) above
> more
> >>> balanced / proportional in the light of the planned targets than the
> first
> >>> one ( < w1, m3, w3, w2, m1 > )?
> >>>
> >>> (The algorithm could in principle also backtrack and reallocate the
> first
> >>> seats to make it possible to allocate the last seats in a better way,
> but
> >>> that doesn't seem to add anything useful in this example.)
> >>>
> >>> Juho
> >>>
> >>>
> >>>
> >>>
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> info
> >>>
>
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