[EM] proportional constraints - help needed

[Peter Zbornik]

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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