Israel General Election Thread: March 17 2015

[palandio]

Wikipedia with the same vote totals got Likud 30 and UTJ 6. Maybe they didn't include the Shas+UTJ surplus agreement?

I get the same result as Bacon King: The 120th is the 14th seat for Shas+UTJ with a divisor of <31,163; the (hypothetical) 121th seat would be the 38th seat for Likud+JH with a divisor of <31,037.

[palandio]

Yes, it seems to be the case. In which case JL should be commended on not concluding that stupid agreement with Meretz, and, thus, saving a seat for ZU from going to Shas (?). And, BTW, Meretz should not have signed that agreement with ZU either: it would have had 5 seats otherwise (and ZU 23).

No, it is mathematically impossible that participating in a surplus agreement results in having fewer seats. Even without the ZU+Meretz surplus agreement ZU would have got their 24th seat before Meretz would have got their 5th:
744,643 / 24 = 31,028...
154,648 / 5 = 30,929...
31,028... >  30,929...
What is true though is that if the surplus agreement results in one seat more for an alliance, then a partner that is much bigger has a higher chance of winning the extra seat (from a pre-election perspective). Hence for the smaller parties surplus agreements with other small parties are much more convenient (e.g. Meretz+Hatnuah last time).
E.g. Likud+JH made more sense for JH when JH was polling at 15 seats and Likud at 20-25 seats.
Kulanu+YB made more sense for YB before all the corruption scandals.
Shas+UTJ is kind of the perfect surplus agreement for both.
But remember: The only way a surplus agreement might harm you is in the electoral campaign, but never in the seat calculation afterwards.

[palandio]

Yes, it seems to be the case. In which case JL should be commended on not concluding that stupid agreement with Meretz, and, thus, saving a seat for ZU from going to Shas (?). And, BTW, Meretz should not have signed that agreement with ZU either: it would have had 5 seats otherwise (and ZU 23).

No, it is mathematically impossible that participating in a surplus agreement results in having fewer seats. Even without the ZU+Meretz surplus agreement ZU would have got their 24th seat before Meretz would have got their 5th:
744,643 / 24 = 31,028...
154,648 / 5 = 30,929...
31,028... >  30,929...

That is absolutely true: ZU would get its seat before Meretz. But, if I get this right, even if Meretz were to be ahead of another party (say, Shas) for the purposes of average on its own, by sharing the votes with ZU it would loose its position in the line. I.e., if ZU would have gotten the seat anyway, Meretz sharing with it actually wastes some Meretz vote, which could have been used to get the next seat on its own. So, the issue is not that Meretz would have gotten the seat off ZU - it is that both parties could have gotten the seat on their own, and this way one of them yields to a third party. Why is this not possible under the system here described?

Under the assumption that Meretz and ZU have a surplus agreement, the 28th seat for the alliance would be the 24th for ZU, but the 29th seat would be the 5th for Meretz.
(744,643 + 154,648) / 29 = 31,010...
and this is more than 30,929...
which was Meretz' old quota. Hence the new quota is higher and Meretz has a better position vs. e.g. Shas than when running alone.
It can be proved that this is generally the case.

[palandio]

Under the assumption that Meretz and ZU have a surplus agreement, the 28th seat for the alliance would be the 24th for ZU, but the 29th seat would be the 5th for Meretz.
(744,643 + 154,648) / 29 = 31,010...
and this is more than 30,929...
which was Meretz' old quota. Hence the new quota is higher and Meretz has a better position vs. e.g. Shas than when running alone.
It can be proved that this is generally the case.

Ok, a mathematical proof would be the following:
Let m be the number of votes for Meretz, n the number of votes for ZU.
Assume that Meretz' quota for the xth seat is lower than ZU's quota for the yth seat but higher than ZU's quota for the (y+1)th seat, in formulas we get the
Assumption: n/(y+1) < m/x < n/y.    [In our case x=5 and y=24.]
We want to show that the quota that the alliance needs for it's (x+y)th seat (which would then go to Meretz) is lower than the quota that Meretz needs for ist xth seat, in formulas:
(m+n)/(x+y) > m/x.
Multiplying both sides with x and with x+y (which are both >0) we get that this in equivalent to:
x(m+n) > (x+y)m.
This is equivalent to
xn > ym
which is equivalent to
m/x < n/y
but that is true by our assumption.

[palandio]

Before you put int the algebra, let us clarify what we are modeling. Because your equations do not correspond to how I understood the system. I am, probably, wrong. But, still,  Could you describe again the procedure for dealing with the agreements. Because I do not understand that procedure. The way I understand it is as follows

1. We calculate the full quotas and allocate the seats based on that.

2. We add up the results of the parties with the agreement. If there is an extra full quota based on that we allocate the extra seat to the pair using the largest average to decide who gets it.

3. We then do the largest average, treating each pair with an agreement as a single party. If an agreement pair gets a seat, which member of it gets that seat is determined by largest average as well.

Is that the procedure, or I am misunderstanding something? Because that was the only procedure which gave me the numbers Haaretz had yesterday with the raw votes known at the time.

Yes. We could leave out step 1 and step 2 though and the results would still be the same.
It's all about calculating and ordering the averages.
And you're right that for the overall procedure an agreement is treated as a single party.
What is different in my calculations? How do your calculations look like, e.g. for the Meretz-ZU-Shas example?

[palandio]

I found one mistake in what I was doing: I was not adding 1 to the denominator in computing the highest averages.

Update: yep, it was me goofing up with that +1

And, yes, JL did cost Meretz a seat: they would have gotten an extra quota together and still there would be a large enough average to get them one seat more, so between the two they would have 19 seats (instead of one extra, 2 extras, the second going to Meretz, if I now get this right). So, GalOn is a victim of this.

Yes, it's easy to confound all of these +1 and so.
I'm still not sure whether JL did cost Meretz a seat:
JL+Meretz (436,532+154,648) / 19 = 31,111...
Shas+UTJ (230,735+205,551) / 14 = 31,163... (because that's the 120th seat as of now).

You're right though that JL+Meretz would have yielded a higher expected chance on an extra seat for Meretz because JL and Meretz are more similar in size than ZU and Meretz.

Btw there are still 200k uncounted ballots (military?) so it's quite likely that in the end the arithmetic will be different from now.