# [EM] proportional constraints - help needed

Peter Zbornik pzbornik at gmail.com
Thu Feb 7 06:00:48 PST 2013

```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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>>

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