Daniel Sterman
Electoral Math

Electoral Miscellany

With the polls closing, here are a few little vignettes:

Live results

Since I’ll be staying up half the night with a newborn anyway, I’ll be taking advantage of the opportunity to live-tweet the election results at I’ll be giving up-to-the-minute seat counts as the votes are counted.

I’ll also be looking into various scenarios. What would the current results look like if nobody had a vote-sharing agreement? What if we weren’t using the Bader-Ofer law to distribute seats but rather the Largest Remainder Method? What if the threshold were higher, lower, or even nonexistent? What if Kulanu and Blue & White had a vote-sharing agreement (which they tried and failed to negotiate)? And so on.

And if you want to see me explore a scenario I haven’t mentioned, drop me a line.

How many parties?

A while back I explored an interesting fact: regardless of the size of the threshold or the number of lists in the running, each incoming Knesset has had a remarkably consistent number of factions: between 10-15.

But assuming every list that looks like it will pass the threshold actually does so, how many political parties will be represented?

The answer is a ridiculously high 23:

The Three Seats scenario

It’s commonly reported that the lowest number of seats a list can receive in the elections is four. I’ve already pointed out that this is untrue in at least one way: if a list crosses the threshold but has fewer than four candidates.

There’s only one such list in the current elections, called Brit Olam – and if it crosses the threshold, its single candidate will have a one-person Knesset faction.

But I’ve also hinted at another way.

The electoral threshold is at 3.25% – the equivalent of 3.9 out of the 120 seats in the Knesset. Remember that the first phase of seat allocation gives out only whole numbers of seats, so in this first stage it doesn’t matter how close you are to seat #4. If you don’t actually have four seats (3.33% of the vote), you’re starting off with three.

But in such a scenario, you will be excruciatingly close to that fourth seat: more than 90% of the way there, and that’s if you get the bare minimum of 3.25%. When you’re that close, you’re almost sure to win one of the leftover seats, right? Right?

Right! Even though the Bader-Ofer law favors larger parties, it doesn’t favor them that heavily. And while your chances vary depending on how many parties there are, what vote-sharing agreements they have signed, how many votes went to lists below the threshold, etc., it turns out you’ll get that fourth seat about 5999 out of 6000 times.

So it’s really, really rare, but it really is possible to get into the Knesset with only 3 seats. You have to hit a small window in percentage of the vote (3.25%-3.33%) and the other parties have to be extremely lucky. But it can happen – and the more parties fall in that range, the more likely it is to happen.

So long that none of them fall below the threshold, of course. If 2.5% of the vote goes to parties that fall under the threshold, it raises the bar for the other parties – and the effective minimum becomes 4.

Replacing MKs

When I explained how the Bader-Ofer law works, I also explained how seats get reallocated if a list wins more seats than it has candidates. But there’s an interesting wrinkle that – so far as I can tell – the law doesn’t address. What happens if an MK resigns during the Knesset’s term, and there’s nobody left on the list to replace them?

As far as I can tell, that scenario isn’t accounted for in Israeli law. We know what to do if there’s no candidate available to enter the Knesset in the first place – but the way the law is written, that doesn’t apply to mid-season replacements.

And that’s it… for now

Stay tuned on Twitter for live updates and scenario analysis.


About the Author
Daniel Sterman lives in Jerusalem with his wife and five children. By day he is a not-so-mild-mannered technical writer; by night he dons a cape and mask and sends strongly-worded emails to news organizations to complain about minor mathematical errors.
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