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
