# [EM] proportional constraints - help needed

Peter Zbornik pzbornik at gmail.com
Thu Feb 7 12:24:39 PST 2013

```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

Sorry to have bothered you with this, but on the other hand, I feel
this is an important problem.

Best regards
Peter Zborník

2013/2/7 Peter Zbornik <pzbornik at gmail.com>:
> 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
> 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 <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
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> ----
>>>>> Election-Methods mailing list - see http://electorama.com/em for list info
>>>>>
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info

```