Method
Two coin tosses, three seats each way
One Midgam poll took Amcha Israel's chance of 4 seats from 49.7% to 50.8%, and Zionist Home's chance of nothing from 49.3% to 50.5%. Two medians crossed, the printed table went from 52, 57 and 11 to 55, 54 and 11 — and the simulated bloc medians did not move.
Later the same day: the table this piece describes was not two coin tosses. It was one list counted twice, and the model has since changed. “Nine polls, not sixty-nine” says what was wrong and what the page reads now. The piece below is kept as written.
The front of this page now reads 55 for the Netanyahu bloc, 54 for the opposition and 11 for the Arab parties. Two days ago it read 52, 57 and 11. One poll arrived in between, and the simulations that sit behind the page moved by a fifth of a seat. This is about how the printed table moved by three seats each way when the model behind it did not, and it is worth reading before quoting the headline.
What arrived
Midgam for Channel 12, fielded 31 August on a sample of 506, and both sources carry it. It has Yashar on 24 and Likud on 23, Together 15, the Democrats 11, Yisrael Beiteinu 9, Otzma Yehudit 8, United Torah Judaism 8, Shas 7, the Joint List 7, Ra’am 4 and Amcha Israel 4. Below the line it puts Religious Zionism at 2.6%, Zionist Home at 2.6%, Blue & White at 0.9% and Unity at 0.5%.
The model’s window holds 69 polls, as it did on 31 August: one came in and one aged out of the sixty days.
Two medians crossed
The chamber on this page is read off one table, and the rule that builds it is printed beside it. A list takes its median across the simulations. A median below the 4 seats the threshold allows becomes nothing. The seats that leaves over go to the largest lists, one each, until the chamber is full.
Two lists sat almost exactly on the edges of that rule, and one poll pushed each across.
Amcha Israel was given 4 seats or more in 49.7% of simulations on 31 August. Midgam’s 4 makes it 50.8%. That moves the median from 3 to 4, and a median of 4 is one the threshold permits, so the table now seats the list — 4 seats, every one of them in the Netanyahu bloc. The post of 29 August, Amcha Israel: no seats, six points on the bloc, said this was one poll away, and it was.
Zionist Home won nothing in 49.3% of simulations. Midgam’s 2.6% makes it 50.5%. The median goes from 1 to 0, and since a median of 1 was already being printed as nothing, the list looks the same on the page as it did. What changes is the arithmetic underneath it.
Before, the surviving medians added to 117, so three seats were left over and went to the three largest lists: Likud, Yashar and Together. Now they add to 120 exactly, and nothing is left over. The ledger for the two blocs is:
- Netanyahu bloc: +4 from Amcha Israel, −1 as Likud’s extra seat goes back. Net +3, from 52 to 55.
- Opposition: −2 as Yashar’s and Together’s extra seats go back, and Zionist Home’s median of 1 was never printed. Net −3, from 57 to 54.
- Arab parties: 11, unchanged.
Six seats of difference between the two largest blocs, and every one of them is a rounding decision falling the other way.
What the simulations say
The table is built from the simulations, but it is not the simulations, and the page says so: it carries no uncertainty of its own. Here is what the 20,000 draws say, this round against last.
The bloc medians are 54, 55 and 11, both rounds. The means moved from 54.0 to 53.8 for the Netanyahu bloc and from 54.6 to 54.8 for the opposition. The opposition bloc finishes ahead of the Netanyahu bloc in 52.7% of simulations, against 50.2% two days ago; the Netanyahu bloc is ahead in 42.1%, against 44.6%; they are level in 5.3%. The Netanyahu bloc’s chance of 61 went from 7.4% to 6.7% and the opposition’s from 9.3% to 9.9%.
So the simulations moved, slightly, towards the opposition, in the round where the printed table moved three seats towards Netanyahu. Neither is wrong. The table answers “seat each list at its central case and fill the chamber”, and that answer is discontinuous at exactly the two points these lists sit on. The draws answer “how often does each thing happen”, and that answer is smooth. A headline that says the Netanyahu bloc leads with 55 is reading the first; a reader who wants to know which bloc is more likely to be larger should read the second, and the second says the opposition, by a little, and by a little more than before.
The opposition and the Arab parties reach 61 together in 88.7% of simulations, from 87.8%. That is arithmetic and nothing more: six lists that do not act as one, and nothing here says they would.
The two lists on the line
Amcha Israel and Religious Zionism are read together every round, and this round pulled them apart. Midgam puts Religious Zionism below the line, as four polls fielded on 26 and 27 August did, and it moved the list’s chance of 4 seats or more from 60.1% to 55.3%, its mean from 3.97 to 3.76. The median holds at 4. Amcha Israel now has 14 polls in the window, six as a percentage and eight as seats, and is given 4 or more in 50.8% of draws and nothing in 4.4%.
A list seated on a 50.8% is a list one poll from being unseated. If the next poll puts Amcha Israel back at 3, the table will print 52, 57 and 11 again, and the simulations will have moved as little as they did this time. That is not a fault in the poll or in the table. It is the shape of a forecast with two lists sitting on the threshold, and the honest way to read it is that the blocs are level to within the width of that edge.
The top
Likud and Yashar are level at 23 seats apiece, as they have been on every run since 26 August. Likud finishes largest in 50.0% of simulations against Yashar’s 49.7%, which is as near a coin as the corpus has produced. Midgam has Yashar ahead by one.