Daniel Sterman
Electoral Math

Who gains and who loses when parties merge

Only one party merger in the last 20 years saw the whole become truly greater than the sum of its parts: the Joint List
How voters shifted between the April and September 2019 elections (Source: Harel Cain)

I used to have a rule of thumb: in the run-up to any Israeli election, there will be at least two party list splits and two party list mergers.

This last year has put that rule of thumb to the test. Surely even Israeli politics is not so anarchic as to afford that much movement, three times, in less than year. No?

But the rule of thumb proved itself. Prior to the April election:

  • The New Right split off of the Jewish Home
  • The Joint List split into four separate parties, which then re-merged into two pairs
  • Gesher split off of Yisrael Beiteinu
  • Israel Resilience, Telem, and Yesh Atid merged to form Blue & White
  • Otzma Yehudit merged with the Jewish Home and Tkuma to form the Union of Right-Wing Parties
  • Hatnua split off of Labor

Between the April and September elections:

  • Stav Shaffir split off of Labor and joined the Green Movement
  • Otzma Yehudit split off of the Union of Right-Wing Parties
  • Meretz merged with the Green Movement and the Israel Democratic Party to form the Democratic Union
  • New Right merged with Jewish Home and Tkuma to form Yamina
  • Kulanu merged with the Likud
  • Labor merged with Gesher
  • Ra’am-Balad merged with Hadash-Ta’al

And between last September and the coming elections on Monday:

  • Stav Shaffir’s Green Movement split off of the Democratic Union
  • Labor and Gesher merged with Meretz
  • Yamina broke up into three separate parties
  • The Jewish Home merged with Otzma Yehudit
  • The New Right merged with Tkuma
  • The Jewish Home split with Otzma Yehudit
  • The Jewish Home merged again with New Right and Tkuma to re-form Yamina

Okay, so that little dance that the Jewish Home did is a bit of a stretch. But the larger point is valid: Israeli politicians simply cannot resist shaking things up in an attempt to find the magic formula that will gain them a couple of extra seats. Even the minor parties get in on this action, with the Pirate Party merging with the Na Nach Party for the election on Monday. (And who can forget 2009’s bizarre combination of the Holocaust Survivors Party with a splinter group from the pro-marijuana Green Leaf?)

But does this actually accomplish anything? How many of these changes actually increase vote share, how many are just a waste of time and effort, and how many are actively detrimental?

He chose…. poorly.

Some party mergers are very obviously terrible decisions. One of the most famous examples was the merger between the Likud and Yisrael Beiteinu in 2013, which picked up a combined 31 seats. This was a disastrous result, far fewer than the 42 seats they had picked up separately in 2009… or even the 36 seats they would pick up when they again ran separately in 2015.

It’s difficult to tell whether Yisrael Beiteinu voters abandoned the alliance because they disliked Likud head Benjamin Netanyahu, or whether Likud voters abandoned it because they disliked Yisrael Beiteinu head Avigdor Lieberman. It could, of course, be both, but the lesson is obvious: be careful who you merge with.

Other choices are less clear. Prior to September’s election, Netanyahu went to a lot of effort to convince Kulanu head Moshe Kahlon to run on a joint list with the Likud; the two parties had separately received 39 seats, while together they only received 32. But how much of that decline is actually the fault of the merger?

A Facebook user by the name of Harel Cain did some impressive statistical analysis of voting patterns that can help us work that out. And the results are an indictment of the Likud’s decision to swallow up Kulanu:

  • Fully half of Kulanu’s voters went to Blue & White;
  • Of the remainder, a third voted for Yisrael Beiteinu and a third voted for Labor;
  • The rest (a mere 1/6 of the Kulanu vote!) went along with the merger and voted Likud.

Now, how do I know those voters weren’t going to abandon Kulanu anyway? I can’t, not for certain. Kulanu and Likud decided to run on a joint list for the 22nd Knesset elections before the 21st was even dissolved, which means it is impossible to do a true before/after comparison of poll numbers.

But one can suspect, based on the fact that Kulanu and the Likud represent the same portion of the electorate, that Kulanu’s base was made up primarily of those voters who wanted to vote for a secular right-wing party but weren’t comfortable voting directly for the Likud. Once that option was taken away from them, fully 5/6 switched their allegiance to parties not in Netanyahu’s coalition. Taking the right-wing non-Likud option away from them was clearly a mistake.

Another recent merger that went awry was Labor’s decision to merge with Gesher for the September elections. According to Cain’s analysis, about half of Gesher’s voters went to the Likud or Blue & White, perhaps feeling that Labor was too far to the left for their tastes (recall that Gesher started as a splinter group off of the right-wing Yisrael Beiteinu).

At the same time, however, half of Labor’s voters left the party in favor of the new Democratic Union made up of Meretz, former prime minister Ehud Barak, and formerly-Labor MK Stav Shaffir. As a result, Labor got the same amount of seats – 6 – in both elections, even though Gesher’s vote share in April meant it should have been able to contribute 2 seats to their combined vote share.

Another merger that was almost certainly a mistake is the current one between Labor, Gesher, and Meretz, though we won’t know for sure until the election this Monday. These parties totaled 11 seats when they ran separately, but polls conducted during the negotiation – and every poll since – show them now wavering between 7 and 10. If the polls are correct, it’s very clear the merger hurt the parties and reduced their combined strength.

The lesson here is that you have to be exceedingly careful before you decide to run together with another party. Your voters chose you rather than the other guy for a reason; if there’s something about the other guy that puts them off, you would do well to find out what it is before you make common cause with them.

So… when is merging worth it?

Not very often. In some circumstances, at least, it’s possible to minimize the number of voter defections and keep the merged party at the same size. For instance, when Israel Resilience and Yesh Atid merged to form Blue & White in advance of the April election, polls showed them getting the exact same number of seats together as they did apart. But they didn’t actually gain anything from the change.

A more complicated example is the saga of the various national religious parties in the two elections of 2019 (April and September).

The April election featured two lists representing the national religious community: URWP (a merger of the three rightmost national religious parties) and New Right (the leftmost national religious party). URWP received 5 seats… but New Right didn’t cross the threshold. If the threshold had been a bit lower, it would have received 4 seats, for a total of 8.

Yes, I said 8. Knesset seats don’t just appear out of nowhere, and New Right’s four seats would have been taken from other parties if it had crossed the threshold. One of those would have been taken from the URWP.

Then came September, and these parties organized themselves differently. This time, the three leftmost national religious parties ran on a single list called Yamina, while Otzma Yehudit (the rightmost party) ran alone. Yamina picked up 7 seats, while Otzma fell below the threshold with two seats’ worth of votes.

Whether the reorganization was a good idea is debatable. One combination comfortably got 7 seats, while another got only 5 – but was a razor-thin margin away from getting 8. Which combination you’d prefer probably depends on how risk-averse your personality is.

Does the above imply that the parties would pick up 8 or 9 if they all merged? Almost certainly not. There are sure to be many New Right voters who would be turned away by the presence of Otzma on the list, and vice versa. The loss could well be more than the gain.

So… when is merging actually worth it?

I can think of only one party merger in the last twenty years where the whole actually was greater than the sum of its parts: the Joint List.

Israel’s four Arab parties generally received only 10-11 seats when they ran separately, but when they all ran together they twice managed to reach 13. There seems to be something about unity between the various factions of Israeli Arabs that boosts their get-out-the-vote efforts – something that Israeli Jews would do well to emulate.

Then again, you may be familiar with the old saying, “Two Jews, three opinions”. Figuring out the benefits of unity may be too much to expect of the Jewish Israeli public.

So why do it?

If merging almost always results in a net loss, what benefit do parties see in it? Why would anybody ever merge if it’s virtually guaranteed to make things worse for you?

So far as I can tell, there are four possible reasons:

1) Irrational fear of the threshold

One major impetus behind many mergers is the fear that one or both lists will fall below the threshold, “wasting” all of those votes. This is a concern not only for the merging parties themselves, but also for the other parties in the bloc; after all, if individual lists lose too many seats, the whole bloc could find itself in the minority.

It was on this basis that Netanyahu spend all three election campaigns pushing hard for mergers among the scattered national religious parties, offering them ministries and a place on the Likud list and various other incentives if they merged enough to make sure none of them could fall below the threshold.

Similarly, Labor head Amir Peretz claimed earlier in the current election campaign that “there needs to be one ballot for replacing Netanyahu“, ultimately merging with Meretz to ensure that neither party falls below the threshold, which might potentially hand the election to the other side.

But the math on that doesn’t add up.

How much does a bloc really lose if one of its lists falls below the threshold? Less than you might think. As I’m fond of saying, Knesset seats don’t just disappear. If a list falls below the threshold, the seats it would have won go to other lists instead. About half of these other lists will be in the same bloc as the party that didn’t make it, in which case the bloc wouldn’t shrink in size at all. After all, if New Right falls below the threshold but all of its seats are picked up by the Likud, then New Right’s collapse didn’t matter; the right bloc would have been the same size either way.

And in fact, for various reasons it’s slightly more likely for a lost seat to be picked up by another party in the same bloc. Six parties lost seats to the threshold in the last three elections, and in every single case 50% or more of those seats stayed within the bloc:

  • In 2015 the right-wing Yachad lost 3 seats, of which 2 stayed within the right bloc.
  • In 2015 the left-wing Green Leaf party lost 1 seat, but that seat stayed within the left bloc.
  • In April the right-wing Zehut lost 3 seats, but 2 stayed within the right bloc.
  • In April the left-wing Gesher lost 2 seats, but 1 stayed within the left bloc.
  • In September the right-wing Otzma Yehudit lost 2 seats, but 1 stayed within the right bloc.
  • And the starkest example, the New Right, which missed the threshold by a razor-thin margin of 1500 votes, effectively lost the maximum number of seats you can lose (4), but fully half of those (2) stayed within the bloc, going instead to other parties on the right.

The New Right situation really does represent a worst-case scenario; barring some exceedingly unlikely circumstances involving a dozen major parties falling below the threshold, it is impossible for a party to waste more than four seats’ worth of votes. Yet even in that scenario, the bloc lost a grand total of two seats; to lose more would require a set of terrible coincidences. And notice that New Right was the only party to lose this many; in every other case, the relevant bloc only lost a single seat.

So what? A seat is a seat, right? Isn’t it worth trying to hold on to every possible seat, and not take a single one for granted, if that’s what will put the bloc in power?

But not so fast. I mentioned earlier the idea of voters being turned off by a merger. When the Likud absorbed Kulanu, no less than 5/6 of its voters left Netanyahu’s coalition. That’s three seats worth of voters that the right bloc lost. Three seats lost with certainty, in order to avoid the chance of losing a maximum of two seats if Kulanu had just barely missed the threshold!

In what world is it a good idea to spend three dollars to buy insurance on a two-dollar bill?

The Labor-Gesher-Meretz merger is likely to prove just as big an error, from the bloc’s point of view. In a desperate effort to avoid possibly losing up to 2 seats should one of them fall below the threshold, they have opted for a virtual certainty of losing (according to polling) up to 4 seats.

Now, the polls could be wrong. But if not, this is worse than the Kulanu scenario, spending up to four dollars to buy insurance on a two-dollar bill!

Fear of the threshold leads Israeli politicians to do some pretty stupid and self-defeating things; the decision to absorb and eliminate an allied party whose constituency dislikes you is definitely one of them.

2) Perverse incentives

Pretend for the moment that you are the head of a small party. Polls show you consistently above the threshold, usually at 5 or 6 seats, but that’s close enough to the edge that you’re still a bit worried. There’s always the outside chance of a scandal developing between the list submission deadline and the election itself, which could put you under the threshold and out of the Knesset.

But let’s say you know a little bit of math and you know that merging with another party won’t help the bloc size. Let’s further say that you’ve done a little (honest!) internal polling and you’ve discovered that more than half of your voters really dislike the other party and would jump ship if you merged with them.

You’re still likely to merge. Why? Because it means you get to keep your job.

If parties merge and lose seats as a result, which seats does it lose? The lowest-ranked ones, of course – back-benchers, the least important people on the list. Most of your voters couldn’t name the people sitting at #40 or #17 or even #6. It’s your face, your voice, that appears on every adevertisement. Losing those MKs would be a blow to your party’s strength, but it’s better than taking even a small risk of losing the party in its entirety.

After all, even if you’re being carried on someone else’s shoulders, you are guaranteed to enter the Knesset. If two 5-seat parties merge and only win 8 seats together, it’s the poor guys in places #9 and #10 that lose out; both party leaderships stay in place. And it’s the party leadership, not the MKs at the bottom of the list, who get to make the decision.

You will probably be able to talk yourself into the morality of that choice, of course. After all, would not the country be worse off without you to guide it? If your party were to disappear, would you not be letting down the segment of the population that it represents? Even if another party in the same bloc were to take over your responsibilities, surely you would do a better job if you handled those responsibilities yourself.

These claims might even be true. Either way, however, they’re leading you towards making a mathematically unsound mistake.

But you can safely ignore that, right? After all, the media and your advisors are also constantly telling you that staying above the threshold is the most important thing. They must be right.

3) Believing your own rhetoric

Not every decision to merge is threshold-based. The Likud Beiteinu alliance of 2013 was a merger of two parties that were in no danger whatsoever of falling below the threshold. The same with the Israel Resilience-Yesh Atid alliance that created Blue & White in early 2019.

So what was the idea there?

Contemporaneous accounts from 2013 claim that the intention was to scare Ehud Olmert and Tzipi Livni away from throwing their hat into the ring, by creating a party so large they had no hope of defeating it. Similarly, Gantz and Lapid joined forces in 2019 to create a single large party to take on the Likud.

Both of these decisions are predicated on the same idea: One large party is better than two smaller parties of equal or greater size. And why? Because you can’t form a government if you aren’t the largest party.

This is a claim with a long and storied history, but Netanyahu himself has disproved it – twice. He became Prime Minister in 2009 even though his party was smaller than the incumbent Kadima, and in September he was the first to receive the mandate to form a coalition even though the Likud was smaller than its rival Blue & White.

The claim that “the Likud must be the largest party or the right loses” has formed the backbone of what is known as the gevald campaign style, for which Netanyahu is well known. He has used it on multiple occasions to try to siphon votes from his right-wing allies (a legitimate tactic, because although it doesn’t affect the size of the bloc it reduces their power in coalition negotiations). But it’s entirely false – and it’s no less false when the same claim is made by Yair Lapid in his attempt to siphon votes from his left-wing partners.

Yet sometimes if you say the same lie often enough you start to believe it yourself – especially when the lie is repeated and reinforced by your allies and your rivals in both politics and the media. Everybody knows that it’s the really the size of the bloc that matters, but everybody keeps saying it’s the size of the largest party. So maybe, just maybe, you might convince yourself it’s true, and embark on some foolhardy merge to try to ensure you capture that meaningless title – or refrain from running in an election because you fear the results of somebody else’s foolhardy merge.

4) Goalkeeping

In 2008, a fascinating article appeared in the New York Times. It concerned a study about how goalkeepers behave during penalty kicks: should they jump to the left, jump to the right, or stand in the center?

It turns out that the chances of stopping the ball are maximized by staying in the center. Yet the goalkeeper will jump to one side or another no less than 94% of the time.

Why would they take a step that makes them less likely to succeed? Fear of embarrassment. There is a human drive to be seen to be Doing Something in response to a problem, because otherwise you look weak and ineffectual. A goalie who stands motionless in the center of the net as the ball sails by him will be booed by the crowd and criticized by his coach. What is he going to do, distribute copies of this academic paper to the fans to prove that his inaction was statistically the right thing to do? They won’t listen; all they saw was a goalie Not Trying Hard Enough.

Better to be seen a strong, decisive person who takes strong, decisive action; it matters little if that action turns out to be counterproductive. At Least You Tried.

Well, our political leaders have the same instincts. And in response to political deadlock, or a potential loss, they want to look like they’re taking charge and fixing the problem. They might not even be aware that they’re making the problem worse – harming their own bloc, and thus their own chances of winning the election. But even if it does occur to them, they’ll just rationalize it away. Like the goalkeeper, they prefer to be seen doing something – even the obviously wrong thing – rather than have to face the accusation that they stood idly by and let themselves lose while doing nothing to stop it.

The unexpected cheese

Put all of the above together, and you can see that members of the party leadership are the only people with something to gain from most mergers. By merging, they keep their jobs and look assertive – at the cost of shrinking their bloc by a couple of seats and risking the jobs of their fellow MKs lower down in the list.

But sometimes there’s an unexpected side effect. The two major mergers that happened in the current election campaign (the reconstruction of Yamina and the Labor-Gesher-Meretz alliance) actually ended up harming somebody entirely unrelated: Avigdor Lieberman.

The reason? Vote-sharing agreements. As a result of these mergers, there were very few separate lists running in the election. And other than Lieberman’s Yisrael Beiteinu, most of them were neatly paired off:

  • The Likud and Yamina (right-wing parties)
  • Shas and UTJ (charedi parties)
  • Blue & White and Labor-Gesher-Meretz (left-wing parties)

Each of these pairs signed a vote-sharing agreement. The only major parties remaining are the Joint List and Otzma Yehudit – two parties which Lieberman has spent a great deal of time attacking in recent years, and neither of which is anywhere near him on the political spectrum. There was no chance either of these would sign a vote-sharing agreement with Yisrael Beiteinu.

Without a vote-sharing agreement, Yisrael Beiteinu will be left without a VPS boost when the leftover seats are given out. There is a good chance – though probably still less than 50% – that this will cost the party one of its seats. I am writing a small computer program to try to calculate the odds more exactly, but it is a particularly thorny problem; there are several different ways one can define “losing a seat” in a situation like this one.

But unlike the damage they did to their respective blocs and down-list MKs, this is one victim of their mergers that the orchestrators of the Yamina and Labor-Geshser-Meretz mergers are probably not going to lose any sleep over.

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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