# [EM] proportional constraints - help needed

Juho Laatu juho4880 at yahoo.co.uk
Thu Feb 7 01:00:55 PST 2013

```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?

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.

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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