[Updated with final results]

Israel has seemingly defied the Seat Product Model in recent years, with a top seat-winning party smaller than expected, and a number of parties greater than expected, based on its electoral system. To be fair to the Seat Product Model (SPM)–and who would not want to be fair to the SPM?–in earlier years of the state, the largest party had been bigger than expected and the number of parties smaller. On average, over its 70+ years, the State of Israel is pretty close to a normal country, at least as far as the SPM is concerned. But, oh, those fluctuations! And it had been many years since it was not overly fragmented, even given an electoral system that invites fragmentation through use of a single nationwide district.

At last, 2019 produced a result over which we can all sigh with relief. Someone got the memo, and the election produce a totally compliant result!

Here are the seat totals and percentages for each of the parties that cleared the threshold.

Likud | 35 | 29.17 |

B&W | 35 | 29.17 |

Shas | 8 | 6.67 |

UTJ | 8 | 6.67 |

Hadash-Ta’al | 6 | 5.00 |

Labor | 6 | 5.00 |

URWP | 5 | 4.17 |

Yisrael Beitenu | 5 | 4.17 |

Kulanu | 4 | 3.33 |

Meretz | 4 | 3.33 |

Ra’am-Balad | 4 | 3.33 |

120 | 100.00 |

The Seat Product Model gives us a baseline expectation from the “seat product”, which is defined as the mean district magnitude, times the assembly size. Then the seat product is raised to a given exponent, based on deductive logic as to what the outcome of interest should be expected to be, on average. In the case of the largest party, the exponent is –1/8. The largest party in the 2019 Israeli election, Likud, is one seat off the 30% (which would be 36, which actually was the number in the preliminary count), at 29.17%; the expectation is a share of 0.302=(120 x 120)^–1/8. So the ratio of actual to expected is 1.036. So just about right on target.

The SPM exponent for the number of parties winning at least one seat is 1/4, which yields an expectation of 10.95. The actual number was 11. For the effective number of seat-winning parties, the exponent is 1/6, for an expectation of 4.93. The actual value from the above seat shares works out to 5.24, which is 1.062 times the expectation.

All in all, totally normal!

So it will be fun to update the following graph for my forthcoming chapter in the *Oxford Handbook of Israeli Politics and Society*, and show the lines for observed values over time coming back to the expected values, which are marked by the horizontal solid line in each plot. The dashed line marks the mean for the entire period, through 2015. Vertical lines mark changes in electoral-system features other than the district magnitude and assembly size–specifically formula changes or threshold increases. (I have not yet run calculations for deviation from proportionally for 2019.)

So, how did this happen, quite apart from the strong pull of the SPM, given that everyone presumably had plenty of time to read the book, which was published in 2017?

My main answer is strategic voting, following upon strategic alliance formation. The forging of the Blue & White alliance in late February, gave the opposition at least a sense of momentum and opportunity to defeat Netanyahu and Likud. The alliance surely benefited a great deal from voters deserting other parties in the opposition in order to bolster B&W. At the same time, many voters on the right no doubt feared B&W just might win, and so defected to the strongest party in the bloc, Likud. Never mind that this sort of within-bloc strategic voting is not entirely rational–the government will be the set of parties that can reach 61 votes, whether or not that set includes the largest party overall. Voters may not understand that fully, or may expect that if one of the top two parties could be at least a few seats ahead of the other, it might be politically difficult for the second to form the government even if it was mathematically feasible.

Such strategic voting would explain why Labor did so poorly. It had been polling near ten seats, which would have been bad enough for the once grand party. But that it ended up on an embarrassing six is probably attributable to strategic defection to B&W. Similarly, Meretz’s very close scare, winning only 4 seats on 3.63% of the votes. The threshold is 3.25%.

Speaking of the threshold, one of the big stories of the election was the failure of New Right to clear it, ending up at 3.22%, despite having been at 6-8 seats in most polls throughout the campaign. That, too, may be due to strategic defection, to either Likud itself or back to the alliance that New Right leaders Naftali Bennet and Ayelet Shaked split from, Bayit Yehudi (running within the new Union of Right Wing Parties).

The result shows two relatively dominant parties, each at 29.2%, and then a smattering of small parties. The third largest seat total is shared by the two ultra-orthodox parties, Shas and UTJ, which have just 8 apiece (6.7%). Seven other parties have 4-6 seats each. This is a result that actually makes a lot of sense for an electoral system with such a high seat product, which allows sectarian interest (different flavors of religious politics, different tendencies within the Arab minority, different strands of left-Zionism, etc.) to win representation, while still featuring two parties around which potential coalitions could form. (Leave aside for now the trouble B&W would have had forming a government even had it been a couple of seats ahead of Likud; it was still a potential alternative pole of attraction.)

In the recent past, I have felt that the low threshold–formerly 2% and even lower farther back in time–was not the issue driving fragmentation. And, in fact, the increases in the threshold in 2003 and 2015 (with the last increase actually leading to a moderately *high* threshold, not a “low” one) did little to bring fragmentation down, as the graph above shows. The driver of fragmentation was the absence of a real “big” party–with even Likud struggling to break 25%–and a surplus of mid-sized parties, which I am defining as parties with around 10-20 seats apiece. Well, this time the party system really looks different, with a leading party almost exactly the expected size, a second party its equal, and then a bunch of little parties. That implies that a somewhat higher threshold–either 4% or 5%–could make a difference, after all. Now would be a good time to seize the day, and form a unity government to do just that. Of course, that is unlikely to happen for various reasons, some of which I mentioned in the previous post. And high thresholds can have perverse outcomes, leading to greater risk of some relevant segment of the electorate being left out.

Speaking, still, of thresholds, I should acknowledge something about the fit to the SPM. The SPM formulas used above do not take thresholds into account. Why not? Simple. Because the formulas work without taking them into account! However, had there been no threshold, the Israeli result would have been different, obviously. Even if we assume no change in party/alliance formation in the absence of a threshold (massive and unrealistic assumption), three more parties would have won seats: Zehut (2.7%) and Gesher (1.7%), in addition to New Right. So then we are up to 14 parties, and some corresponding increase in the effective number and decrease in size of the largest.

In *Votes from Seats*, we propose some “first approximation” predictive models based on thresholds *instead of* the seat product. Given a threshold of 3.25%, these predict a largest party of 42.5% (or a little less with a “second approximation” that I will leave aside here), and an effective number of parties of 3.13. As we can see, these do not do so well on the Israeli election of 2019. So **the SPM has it**, notwithstanding the complication of the threshold making the SPM fit better than it might otherwise for this election.

Finally, a totally normal election in Israel.

Prof. Shugart writes, “In the recent past, I have felt that the low threshold–formerly 2% and even lower–was not the issue driving fragmentation. And, in fact, the increases in the threshold in 2003 and 2015 (with the last increase actually leading to a moderately high threshold, not a “low” one) did little to bring fragmentation down, as the graph above shows. The driver of fragmentation was the absence of a real “big” party–with even Likud struggling to break 25%–and a surplus of mid-sized parties …”

Here is an article arguing that the increase in the threshold did make a difference: https://www.nysun.com/foreign/winner-in-israel-turns-out-to-be-new-voting-law/90646/. I’m not competent to evaluate the historical analysis, or even the claim about the impact of raising the threshold. But it seems like an interesting contrast to the post above.

Less a contrast than a different answer to the question of “makes a difference for what?”. Obviously, the threshold increase mattered in 2015 by leading the Arab parties to form the Joint List and Kadima to fold (referring to parties that would not have cleared the threshold individually if it had been in place in 2013). It also mattered in 2019 by blocking the New Right and Zehut from gaining seats.

However, as we can see from the graphs above, the impact of threshold changes has been either contrary to expectations or fleeting, at the systemic level. The vertical lines in the plots show:

1951: increase from 0.83% to 1%; change from D’Hondt to LR-Hare

1973: change back to D’Hondt

1992: increase to 1.5%

2006: increase to 2%’

2015: increase to 3.25%

The number of lists getting seats (upper left panel) actually increased despite the higher threshold in 1951 (because the formula was more permissive). In the other changes, it has dropped for one election but then risen again at the very next one. This pattern continues in 2019, with 11 lists making it in instead of 10 last time.

The effective number of parties bears almost no relationship to these changes. Sometimes it rises, even though a higher threshold or less proportional formula–i.e., every change except possibly 1951–should lead to a decrease. We could say much the same about the impact on the size of the largest party. Disproportionality (bottom right) seems more responsive, as we might expect it to be.

So threshold or formula changes indeed have impact. Yet the long-term averages are entirely consistent with the expectation from the seat-product model, differing only to a small degree, even as individual election outputs fluctuate considerably. Thus the seat product tells us more about the systemic outcomes than does the threshold.

The bottom line is that, as the post above says, the 2019 election produced almost the exact systemic outcomes on the number of parties and size of largest that we expect from the country’s seat product. That was more due to strategic voting stemming from a perceived close race between the top two than due to the threshold. But, as the first sentence of this comment (and, I think, the post itself) notes, the threshold also seems to have played a role.

Thanks for the comment and the link; this exercise should help me revise the argument for the chapter when I update it to include 2019.

Thank you for the very detailed response!

Bob, you are more than welcome. I am pretty sure it was more detail than you bargained for. On the other hand, you keep coming back to F&V (for which I am most grateful), so I suppose you have come to expect detailed responses!

It is also interesting that Finland had an election, and the eduskunta is far more fragmented than the Knesset. Why would this be the case? Finland has large multiple member districts with the smallest being Lapland with 7 and Uusimaa at 36. What would the Finnish party system be classified as, it is certainly not bipolar?

There is a separate post on that election, by the way, although I have not commented on the result yet.

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The final count has UTJ with one more seat, and Likud with one less. I will update the above calculations later. Obviously, it does not change a lot, but obviously it means that the largest list is very slightly below SPM expectation now, at 29.17%.

And in a very technical sense, Likud is now in second place, as one MK elected on its list is actually from the Union of Right Wing Parties (as part of the deal Netanyahu brokered to save Bayit Yehudi when it looked in danger of not clearing the threshold). On the other hand, if we were to play the game of disaggregating the lists, we’d have to acknowledge that Blue & White is made of up three different parties. The difference is that, at least for now, B&W is likely to sit as one Knesset faction, whereas I believe the URWP MK from the Likud list will not be part of the Likud Knesset faction but will sit with the rest of URWP, giving the latter six seats. (Note that none of this matters for the above calculations, except for the adjusted Likud and UTJ numbers; all of those calculations are based on seats won at the election by the various lists, not what other parties might be in an alliance or what MKs do after the election.)

The current table adds up to 119 seats. I believe it is missing the 8th seat for UTJ. I don’t know if or how that changes the SPM calculation.

You are right. I failed to update the table, but all the calculations should have already reflected that change.

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