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
>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> 
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