On 7.2.2013, at 22.24, Peter Zbornik wrote: > Hi Juho, > > returning to your original example, again, with slightly modified > number of votes to avoid tie-breaking: > Coalition 1 (C1) - 51: w1 > w2 > m1 > m2 > Coalition 2 (C2) - 49: w3 > w4 > m3 > m4 > > Results: > Seat number, candidate, coalition, quoted in > 1. w1, C1, no > 2. m3, C2, yes > 3. w2, C1, no > 4, w3, C2, no > 5. m1, C1, no > > There is no problem here, as C1 got the majority of candidates, and > kept the constraints, so there was never any issue with > proportionality of quoted-in candidaes. > > Here is an example to illustrate the problem: > Coalition 1: 32: w1>w4>w3>m3 > Coalition 2: 33: w1>w3>w4>m4 > Coalition 3: 35: w2>w5>m1>m2 > > Apply top-down proportional ordering (Otten) for normal STV: > Elect 1st seat - w1 (quota 50) > Elect 2nd seat - m1 (quoted in instead of w2) (quota 33.4) > 3rd seat - w3 (quota 25) > 4th seat - w4 (quota 20) > 5th seat - m4 (quoted in instead of w5) (quota 16.7) > > This leads to the quoted-in candidates being disproportionally > distributed in coalition 3. > > Thus, the right distribution, intuitively is: > 4th seat - m3 > 5th seat - w5
The approach of giving less weight to the quoted-in candidates (= reduce less weight from the votes that supported the election of m1) could lead to the intended outcome here. > > Sorry to have bothered you with this, but on the other hand, I feel > this is an important problem. No problem. Actually I have personal interest in proportional methods with mutiple allocation criteria. So, thanks for taking this topic up and promoting this kind of advanced methods also in real life. Juho > > Best regards > Peter Zborník > > 2013/2/7 Peter Zbornik <[email protected]>: >> Hi Juho, >> >> I have to think this through a bit. >> Thanks for the examples. >> At second sight, I think that giving different quota weights (V) to >> quoted-in candidates would lead to strategic voting leading to the >> weaker-gender candidates being placed at the end in order to be >> quoted-in, as you mention yourself. >> >> Best regards >> Peter Zborník >> >> >> 2013/2/7 Juho Laatu <[email protected]>: >>> 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, >>>> >>>> considering your example >>>> 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 <[email protected]>: >>>>> 2013/2/7 Juho Laatu <[email protected]>: >>>>>> 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 >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> ---- >>>>>> Election-Methods mailing list - see http://electorama.com/em for list >>>>>> info >>>>>> >>> >>> ---- >>> Election-Methods mailing list - see http://electorama.com/em for list info > ---- > Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
