Presidentialization

[As long as I made a tweet storm in response to, first, a tweet by Ezra Klein, and then a question by Nicholas Smith, I might as well turn it into a blog post. Process made easy by the Spooler app.]

First the preliminaries and context that got it all going…

Great question! A short thread on “personalization” and “presidentialization” of political parties…

Matthew Shugart

Yes, existing to promote and protect the leader who was separately elected to the country’s top office is the very definition of a presidentialized party (Samuels and Shugart, 2010).

The US, during this presidency, finally has become a more normal presidential democracy. https://twitter.com/ezraklein/status/1177244610931781634 

Ezra Klein

@ezraklein

There is nothing “conservative” about the Republican Party we’re seeing in these hearings. It’s a party that exists to promote and protect Donald Trump.

Nicholas Smith @_SmithNicholas_

What step in the process is it when parties are being created and collapsing solely around a party leader (e.g. IL, UA, FR)?

_____________________ Now for the thread (lightly edited)…

Personalization can happen under any type of democratic political system. In brief, it means that the election turns on the assessment of the leader, rather than on a platform, issues, ideology, or long-run party ID.

Presidentialization is something more. It is the leader becoming the de-facto principal over the party once elected (or even once nominated). It is the selection of an executive candidate who may not share the values of the party because the party needs someone who can win.

This can happen in parliamentary systems, but it is much less likely. It can be avoided in presidential systems, but it is harder to avoid. Why? Parl party leader, including PM (normally) remains accountable to the party (in the legislature). A president, by definition, does not. Presidents and legislative parties, by definition, can have distinct electoral coalitions. But the more they approach being identical, the more likely it is that the party falls in line behind the president, even if the pres. is taking the party places it otherwise would not go. That is, the party legislators’ fates become tied to the fate of the executive. In principle, it remains the reverse in a parliamentary system.

HOWEVER, there are exceptions. Corbyn, maybe Johnson, look pretty “presidentialized” as party leaders (and the latter as PM). There is obviously some degree of separation that has developed in these parties lately, due in part to unusual leadership selection rules and circumstances. However, of course, the voting remains fused–separation can’t extend to how voters vote for party & executive. The original tweet I am responding to mentioned cases of newly formed parties, whereas above I have referred mostly to established parties. Let’s take the mentioned examples

Israel. Blue & White can be seen as a personal vehicle for Gantz to be PM. But it is an alliance. The internal partners are also personal vehicles (Lapid, etc.). A key point is Gantz needed pre-electoral and now post-electoral allies if he is to head the government. Gantz, or any head of a parliamentary party/alliance, can’t present himself to the electorate separately from the party system, as is possible in a presidential or semi-presidential system. He has to get the nomination of an existing party, or form a new one, and the party must win seats.

(Semi-presidential = a popularly elected presidency AND a premier who depends on the confidence of a majority of the assembly. They vary a lot in the constitutional powers of the presidency.)

France. Semi-presidential. Macron formed an entirely new party, totally beholden to him. And benefited from the fact that assembly elections come AFTER presidential. It is sort of presidentialization on steroids!

See (and my earlier posts linked within): (fruitsandvotes.wordpress.com/2017/06/18/fra…)

(Because it’s semi-presidential and not “pure” presidential, he did need his party to do well in assembly elections, in order to be able to choose an ally as PM. In a pure presidential system, one can control the executive without a party, though one would rather have allies in congress, obviously.)

Ukraine. Also semi-presidential. I also wrote about Servant of the President. Oops, I mean to say Servant of the People, here. (fruitsandvotes.wordpress.com/2019/07/21/ukr…)

Israel 2019b, compared to 2019a

Here, following up on the earlier discussion of post-election bargaining scenarios, I want to compare Israel’s two elections of 2019 on several statistical measures. The 2019b (September) results are not quite official yet, but are very unlikely to change other than in the smallest of voting detail.

The table below compares the votes for Netanyahu’s “Bibi bloc” of right-wing and Haredi parties, by various definitions, as well as the indicators of fragmentation: effective number of parties by seats and votes, total number of lists with seats, and the seats won by the largest list. For each measure, there is a comparison of change from April to September. The final three columns refer to output of the Seat Product Model (SPM) for the indicators of fragmentation–what is expected from the model (given an assembly size of 120 and district magnitude also of 120), and ratios of the actual indicators to the expectation.

Measure April Sept change SPM expected Ratio, April Ratio, Sept.
Bibi bloc (percent votes) 48.7 44.5 -4.2
… plus YB 52.7 51.5 -1.2
… plus Otzma 46.4
… plus YB & Otzma 52.7 53.3 0.6
Effective N, seats 5.24 5.67 0.43 4.93 1.06 1.15
Effective N, votes 6.33 6.11 -0.22 5.23 1.21 1.17
No. of lists with 1 or more seats 11 9 -2 11 1.00 0.82
Seats for largest list 35 33 -2 36 0.97 0.92

The scale of the defeat for the core Bibi bloc is clear. Already in April, these parties had less than 50% of the votes, at 48.7%, which is why they won only 60 seats under Israel’s proportional system. If we include Yisrael Beiteinu in the total Bibi bloc, we get 52.7% (which is why this larger definition of the bloc had 65 seats). As I have explained already–both before and after the most recent election–we should not count YB in the bloc, particularly since it was this party’s actions that precipitated the early elections of 2019–yes, both of them.

In the second election of 2019, this Bibi bloc fell to 44.5% of the vote, a drop of 4.2 percentage points. If we include YB, they do have a narrow majority of votes (51.2%), but we should not include them. However, we probably should include Otzma Yehudit, given that it was part of the Union of Right Wing Parties in April, and probably would have been invited to join a coalition had it cleared the threshold in the September election. But still this is short of a voting majority without YB, at 46.4% (which would mean a loss of 2.3 percentage points off the April showing of 48.7).

For a baseline, consider that the Bibi bloc had 48.4% in 2015, or 53.5% including YB (which was without doubt part of the bloc at that time–their staying out of the coalition initially in 2015 was a surprise). Note that, leaving out YB, they were already below majority voter support in 2015, but had managed 61 seats. The reason they gained ever so slightly in votes in April, yet got only 60 seats, was all the wasted votes for New Right (3.22%), which did not clear the threshold in the April, 2019, election.*

If we include both Otzma and YB in the 2019b election, it looks like a very small gain for the wider bloc. But we should not do this because some of YB’s increased votes probably came from Blue and White or other parties not in the right, due to YB’s promise not to return to a Likud-led government unless it was a “unity” government with Blue and White.

On the fragmentation indicators, the effective number of seat-winning parties went up, from 5.24 to 5.67, despite the drop of the total number of lists winning seats, from 11 to 9. The increase in the effective number is due to the smaller size of the largest party in the more recent election, 33 seats (Blue and White) vs. 35 (tie between Blue & White and Likud).

The effective number of vote-earning parties came down somewhat, from 6.33 to 6.11. None of these measures is much different than what we should expect under the SPM, although the raw number of represented lists this time is actually smaller than expected, while the effective number of seat winning parties was closer to the expectation in April than now.

We should expect the largest party, given this electoral system, to have 30.2% of the seats, which out of 120 works out to 36 (rounded down). The election pretty much nailed that in April, but this election saw a return to a smaller than expected plurality party.

So, strictly from the SPM, this was a slightly less “normal” election than 2019a, although not too far off. From the standpoint of the usual pattern with a “b” election (a second one within a year), it was, as I anticipated, a little unusual. Typically, the effective numbers go down and the size of the largest up. Israel went the opposite way between April and September, and thus government formation still will not be easy.


* We could go back and include Yachad (of which Otzma Yehudit was a part) in the 2015 count, which would bring it to 51.3%, but at the time I do not recall their being taken seriously as part of the bloc. Doing so, of course, increases the scale of the loss of voter support already as of the first election of 2019.

Israel is about to have a very unusual ‘b’ election

Israel is about to hold its second election of 2019, and it will be unusual, relative to other cases of a second election within a year elsewhere. While the number of lists winning seats is likely to go down, other indicators of fragmentation are likely to go up.

Using the National Level Party Systems Dataset (Struthers, Li, and Shugart, 2018), I performed calculations to find out how the standard indicators of party-system fragmentation change from a first election that fails to produce a “stable” government or any government at all, leading to a second election. I looked at all cases in the dataset in which two elections were held in the same Gregorian calendar year, plus all cases where an election is in the second half of a year and followed by another in the first half of the next year. The first table below gives the full list, including the first and second election in each sequence. In one case in the dataset (Greece, 1989-1990) the second election was followed by yet another within a year, indicated by a “3” in the final column. Note that a country’s data sequence begins in the early post-WWII era or when a country democratized and ends in 2016, so any cases outside that timeframe are not included.

country year date mo within_yr_seq
Denmark 1953 4/21/53 4 1
Denmark 1953 9/22/53 9 2
Denmark 1987 9/8/87 9 1
Denmark 1988 5/10/88 5 2
Greece 1989 6/18/89 6 1
Greece 1989 11/5/89 11 2
Greece 1990 4/8/90 4 3
Greece 2012 5/6/12 5 1
Greece 2012 6/17/12 6 2
Greece 2015 1/25/15 1 1
Greece 2015 9/20/15 9 2
Iceland 1959 6/28/59 6 1
Iceland 1959 10/25/59 10 2
Ireland 1982 2/18/82 2 1
Ireland 1982 11/24/82 11 2
Japan 1952 10/1/52 10 1
Japan 1953 4/19/53 4 2
Japan 1979 10/7/79 10 1
Japan 1980 6/22/80 6 2
Moldova 2009 4/5/09 4 1
Moldova 2009 7/29/09 7 2
Spain 2015 12/20/15 12 1
Spain 2016 6/26/16 6 2
Sri Lanka 1960 3/19/60 3 1
Sri Lanka 1960 7/20/60 7 2
St. Lucia 1987 4/6/87 4 1
St. Lucia 1987 4/30/87 4 2
Thailand 1992 3/22/92 3 1
Thailand 1992 9/13/92 9 2
Turkey 2015 6/7/15 6 1
Turkey 2015 11/1/15 11 2
UK 1974 2/28/74 2 1
UK 1974 10/10/74 10 2

The list contains 17 cases of an election within twelve months of the preceding one. Not a large sample; fortunately, this sort of thing does not happen very often. (There are 1,025 elections in the sample.)

If elites and/or voters “learn” from the experience of bargaining failure or lack of stability from the first election in such a sequence, we would expect the second to be less fragmented. We can test this by looking at mean differences between the second election and the first. The indicators I have are the number of parties (or lists, more precisely, counting an independent as a “list” of one) that win at least one seat (NS0), the effective number of seat-winning lists (NS), the effective number of vote-earning lists (NV), the seat share of the largest party (s1), and the vote share of the largest party (v1). The first three should go down if there’s an adaptation occurring, while the second two should go up (i.e., the largest party gets bigger).

Here is what we see from the results, reporting the mean differences:

NS0: –0.215

NS: –0.098

NV: –0.469

s1: +0.010

v1: +0.0035

In terms of raw direction, all are as expected. On the other hand, the number of lists winning seats hardly budges (recall that the first number is the actual number, not “effective”), and the effective number on seats changes much less than the one on votes. The implication is that fewer votes are wasted in the second election, as we would expect. On the other hand, the seat share of the largest party–the single most important quantity because it determines whether there is a single-party majority and if not, how far from majority it is–rises by a very small amount, on average. That is partly due to most of these systems being proportional, so large shifts should be unusual. The complete list of elections and their indicators is provided in an appendix below.

As far as statistical significance is concerned, only in NV and v1 is the difference significant (NV at p<0.03; v1 at p<0.10), when comparing these “second” elections to all others. (This is not meant to be a sophisticated test; I am not comparing to a country baseline as I really should.)

We might expect that the first election in such a sequence is anomalously fragmented, hence the need for a second election to calm things down once again. That is also supported, for NV and v1 again, but also, crucially, for s1.

Now, how might the Israeli second election of 2019 compare? We can use the polling average from Knesset Jeremy (using the poll of polls from three weeks before the actual election), and compare to the actual results of 2019a (the first election in the sequence) and the previous election (2015). Also included in the Seat Product Model expectation.

measure 2019b (poll avg) 2019a actual diff 2015 diff SPM expected
NS0 9 11 –2 10 1 11
NS 6.04 5.24 0.801 6.94 –1.70 4.93
NV ? 6.33 ? 7.71 –1.38 5.24
s1 0.258 0.292 -0.034 0.25 0.042 0.3
v1 ? 0.2646 ? 0.234 0.031 0.289

For the number of lists that look likely to clear the threshold, we have the direction expected: currently there are 9 likely to win seats, compared to 11 in April. In turn, the April figure was one seat-winning list higher than in 2015. However, in terms of both NS and s1, the case is anomalous. All indications are that the largest party will be smaller than it was in April, which also will drive up the effective number. Moreover, these measures in April were less fragmented than they had been in 2015; that is, the first election of the 2019 sequence was not unusually fragmented. Quite the contrary; I called it a “normal” election at the time for a reason.

So the Israeli sequence of two elections in 2019 is unusual indeed.


Appendix

Below are two tables. One has all the “second” elections, and changes in the various measures. The second has all “first” elections. In each case, the comparison is just to the immediately preceding election (not to all other elections), so we can see how much short-term fluctuations were affecting the process in each sequence.

Elections ocurring within one year of previous, compared to previous results
country year mo diff_Ns0 diff_Ns diff_Nv diff_s1 diff_v1
Denmark 1953 9 1 -0.2199998 -0.1000001 0.014 0.009
Denmark 1988 5 -1 0.0100002 0 0.005 0.005
Greece 1989 11 1 -0.0800002 -0.1700001 0 0
Greece 1990 4 5 0.05 0.0700002 0.005 0.017
Greece 2012 6 0 -1.07 -3.75 0.07 0.108
Greece 2015 9 1 0.1490002 -1.19 -0.014 -0.008
Iceland 1959 10 0 0.24 . 0 .
Ireland 1982 11 -1 -0.01 0.03 0 0
Japan 1953 4 . 0.8099999 0.8999999 -0.088 -0.091
Japan 1980 6 -8 -0.3999999 -0.24 0.074 0.033
Moldova 2009 7 1 0.8699999 0.27 0 -0.048
Spain 2016 6 -1 -0.3700004 -0.7999997 0.04 0.043
Sri Lanka 1960 7 . -1.22 -2.52 0.166 0.032
St. Lucia 1987 4 0 0 -0.1099999 0 0.007
Thailand 1992 9 0 -0.0999999 0.0999999 0 0.017
Turkey 2015 11 . -0.322 0.03 -0.126 -0.089
UK 1974 10 -1 -0.01 -0.02 0.028 0.021
Election that is the first in a series of two within a year, compared to preceding election
country year mo diff_Ns0 diff_Ns diff_Nv diff_s1 diff_v1
Denmark 1953 4 0 -0.1300001 -0.0900002 0.013 0.008
Denmark 1987 9 0 0.27 0.5799999 -0.009 -0.023
Greece 1989 6 1 0.26 0.1400001 -0.044 -0.006
Greece 2012 5 2 2.24 5.79 -0.173 -0.25
Greece 2015 1 0 -0.6700001 -0.77 0.067 0.066
Iceland 1959 6 0 -0.28 . 0.035 .
Ireland 1982 2 -2 -0.05 -0.1699998 -0.039 0.009
Japan 1952 10 . . . . .
Japan 1979 10 -1 0.1199999 -0.2199998 -0.002 0.027
Moldova 2009 4 1 0.1400001 0.1600001 -0.079 0.035
Spain 2015 12 -3 1.93 3.23 -0.18 -0.159
Sri Lanka 1960 3 . 1.456 2.26 -0.206 -0.043
St. Lucia 1987 4 -1 0.55 -0.0800002 -0.295 -0.049
Thailand 1992 3 . . . . .
Turkey 2015 6 . 0.4320002 0 0.002 0.005
UK 1974 2 2 0.1900001 0.6900001 -0.05 -0.077

 

Ukraine honeymoon election today

Ukrainians are voting today in an assembly election. It is a relatively extreme “honeymoon” election, as the new president, Volodomyr Zelensky, was just elected in March-April of this year (two rounds). There was already an assembly election scheduled for October of this year, which certainly would have qualified as a honeymoon election. But in his inauguration, Zelensky announced he would dissolve the Verkhovna Rada and call an election even earlier.

And why not? Based on much experience in presidential and semi-presidential systems, we know that there is a strong tendency for the party of a newly elected president to gain a large boost in votes the earlier it is held following the presidential election. This topic of the impact of election timing has been a theme of my research ever since my dissertation (1988), an early APSR article of mine (1995), and most recently in a whole chapter of Votes from Seats (2017).

At the time Zelensky was elected, various news commentary had the all-too-typical concern that the new president would be weak, because he is an “outsider” with no established political party. We got similar useless punditry when Emannuel Macron was elected in France in 2017. And we know how that turned out–his formed-on-the-fly party did slightly better than the 29% of votes I projected, based on an equation in Votes from Seats, prior to Macron’s own runoff win. (The electoral system helped turn that into a strong majority in the assembly.)

In May of this year, I projected that Zelensky’s Servant of the People party could get around 34.5% of the votes in an election held on 28 July. (One week earlier obviously does not change anything of substance.)

Early polling had him short of this (not even 25% just before the presidential first round), but predictably, SoP has been rising in the polls ever since Zelensky took office. The party almost certainly will beat this projection, and may even have an electoral majority. If short of 50% of votes, the party still looks likely to win a parliamentary majority, given the electoral system (discussed below).

A bigger boost than average (where the average across systems with nonconcurrent elections is what my projections are based on) is to be expected in a context like Ukraine, in which the party system is so weak. That is, poorly institutionalized party systems would tend to exaggerate the normal electoral cycle effect. The effect will be only further enhanced by low turnout, as opponents of the new president have little left in the way of viable political parties to rally behind. Thus a performance in the range of the mid-40s to over 50% of the vote would not be a surprise.

As for the electoral system and election itself, Ukraine is using again (for now, at least) its mixed-member majoritarian (MMM) system. It consists of 225 single-seat districts, decided by plurality, and 225 closed-list proportional representation seats, in a single nationwide district. The two components are in “parallel”, meaning seats won by any given party in districts and seats won from party lists are simply summed; there is no compensatory process (as with MMP). There is a 5% threshold on the list component; quite a few small opposition parties may waste votes below this bar. Due to parts of the country being under Russian occupation, only 199 single-seat contests will take place.

In some past MMM elections in Ukraine, a large share of the single-seat districts have been won by independents or minor parties, whereas the national parties (such as they are) have, obviously, dominated the nationwide list seats. It is probably quite likely that this rather extreme honeymoon election will result in most of the seats in both components being won by “Servants.”

On that theme, a tweet by Bermet Talant makes the following points (and also has some nice polling-place photos) based on conversations with voters in Kyiv:

• Ppl vote for leaders. Few know other candidates on party lists, even top5

• Servant of the People = Zelensky. Bscly, ppl vote for him again

• In single-member districts, ppl vote for a party too, not candidate

This is, of course, as expected. It is a completely new party. Many voters will be wanting to support the new president who created the party. The identity of candidates will not matter, either on party lists (where at least the top ones might be known in a more conventional party) or in the districts (where the vote is cast for a candidate). The single-seat districts themselves are referred to as the “twilight zone” of Ukrainian elections in a fascinating overview of the candidates and contests in the district component published in the Kyiv Post. These contests attract “shady candidates” many of whom are “largely unknown”. If a given election lacks a strong national focal point, it would tend to favor independents and local notables. In an election with an exceptionally strong focal point–as in a honeymoon election, more or less by definition–that will benefit whoever has the “Servant of the People” endorsement.

The timing of the election, and the likely dominance of an entirely new pro-Zelenskyy party, really is presidentialization at its very “finest”.

I am just going to quote myself, in the final paragraph of an earlier post about Macron’s honeymoon election, as it totally applies here, too: “All of the above should serve as a reminder of two things: (1) the purpose of the upcoming election is to ratify the new executive’s direction, not to be a second chance for an alternative vision; (2) the honeymoon electoral cycle matters.”

Expect the new Verkhovna Rada to be Servants of Zelenskyy.

Did Greece just have a normal election?

The Greek general election of July, 2019, may have been about as “normal” as they get. After the country’s period of crisis–economic and political–things seem to have settled down. The incumbent party, Syriza (“Radical Left”), which saw the country through the crisis got booted out, and the old conservative New Democracy got voted in.

Of course, around here when we refer to an election as “normal” it means it conforms to the Seat Product Model (SPM). Applying the SPM to an electoral system as complex as that of Greece is not straightforward. However, based on some calculations I did from breaking the system down to its component parts (an approach I always advocate in the face of complexity), it seems we have a result that conforms to a plausible interpretation of its “expectation”.

The basics of the electoral system are as follows: there are 300 seats, of which 50 are an automatic bonus to the party with a plurality of the vote, while the remainder are allocated as if there were one nationwide district. The “as if” is key here. In fact, there are 59 districts. In other words, the district magnitudes in which the election plays out for voters and candidates are quite small. There are 12 seats in a nationwide compensatory tier [EDIT: see below], so we have 288 basic-tier seats for a mean district magnitude of around 4. (I am not going to go into all the further details of this very complex system, as these will suffice for present purposes; Election Resources has a great detailed summary of the oft-changed Greek electoral system.)

To check my understanding that the system is as if nationwide PR for 250 seats, plus 50 for the plurality party, I offer the following table based on the official results. Note that there are two columns for percent of seats, one based on 250 and the other based on the full 300. For the largest party, ND, the “% seats out of 250” is based on 108 seats, because we are not including the 50 bonus seats in this column.

Party % votes seats % seats out of 250 % seats out of 300
Nea Dimokratia 39.9 158 43.2 52.7
Syriza 31.5 86 34.4 28.7
Kin.Al 8.1 22 8.8 7.3
KKE 5.3 15 6.0 5.0
Elliniki Lysi 3.7 10 4.0 3.6
Mera25 3.4 9 3.6 3.0
14 others 8.1 0 0.0 0.0

We can see that the seat percentages out of 250 are close to the vote percentages, as we would expect if the system acts as if it were nationwide PR (not counting the bonus). More to the point, we would expect all parties, even the smallest that win seats, to be over-represented somewhat, due to the nationwide threshold. That is indeed what we see. Over 8% of the votes were wasted on parties that failed to clear the threshold. The largest of these, Laikos Syndesmos, had 2.93%. The threshold is 3%. No other party had even 1.5%.

It is clear that the system has worked in this election exactly as intended. The largest party has a majority of seats, due to the bonus, but even the percentages out of 300 are close to proportionality–far more than they would be if Greece tried to “manufacture” majorities via FPTP or two-round majority instead of “bonus-adjusted PR”.

The effective number of seat-winning parties (NS) is 2.70. It would have been 3.13 based on the indicated parties’ percentages of seats out of 250. So the bonus provision has reduced NS by 13.7%. (The effective number of vote-earning parties, NV, is 3.68, calculated on all the separate parties’ actual vote shares.)

But what about the SPM? With 288 seats in districts and 12 nationwide, we technically have a basic-tier seat product of 288 x 4 (total seats in the basic tier, times the mean magnitude). However, this includes the 50 bonus seats, which are actually assigned to districts, but clearly not allocated according to the rules that the SPM works on: they are just cream on top, not a product of seat allocation rules in the basic tier and certainly not due to compensation. So, what percentage of seats, excluding the bonus, are allocated in districts? That would be 288/300=0.96, which out of 250 yields a “shadow” basic-tier size of 240 (96% of 250). So our adjusted basic-tier seat product is 240 x 4=960.

In a “simple” system (no compensatory tier as well as no bonus), we would expect, based on the Seat Product Model formula, that the effective number of seat-winning parties would be NS=9601/6=3.14. We would expect the size of the largest party to be s1=960–1/8=0.424. Note that these are already really close to the values we see in the table for the 250-seats, pre-bonus, allocation, which are 3.13 and 0.432. I mean, really, we could hardly get more “normal”.

[Added, 14 July: The following paragraph and calculations are based on a misunderstanding. However, they do not greatly affect the substantive conclusions, as best I can tell. The system is two-tier PR, of the “remainder-pooling” variety. However, the 12 seats referred to as a nationwide tier are not the full number of compensatory seats. With remainder-pooling systems it is not always straightforward to know the precise number of seats that were allocated above the level of the basic tier. Nonetheless, the definition here of the basic tier seems correct to me, even if I got the nationwide portion wrong. Thanks to comments by JD and Manuel for calling my attention to this.]

Nonetheless, there is a nationwide compensation tier, and if we take that into account through the “extended” SPM, we would multiply the above expected values by 2.50.04=1.037, according to the formula explained in Votes from Seats. (The 0.04 is the share of seats in the upper, compensatory, tier; 100–0.96). This is obviously a minor detail in this system, because the upper tier is so small (again, not yet counting the bonus seats). Anyway, with this we get expected values of NS=1.037 x 3.14=3.26. We do not have a formula for the largest seat winning party (s1) in two-tier PR, but one can be determined arithmetically to lead to the following adjustment: s1=0.973 x 0.424=0.413. (This is based on applying to the extended SPM for Nthe formula, s1=NS–3/4, as documented in Votes from Seats [and its online appendix] as well as Taagepera (2007).) I believe these are the “right” figures for what we should expect the outputs of this system to be, on average and without taking election-specific politics into account, given this is not a “simple” (single-tier PR) system even before the bonus seats are taken into account.

Out of 250 seats, 41.3% is 103. The ND actually won 108 pre-bonus seats. The 50 bonus seats then would get the party to an expected 153, which would be 51.0%. It actually got 52.7%.

So, as we deconstruct the electoral system into its relatively simpler components, we get an impact on the party system that is expected to result in a bare-majority party. As for NS, values are generally around s1–4/3, which with s1=0.51, would be 2.45, which is somewhat lower than the actually observed 2.70. But perhaps the actual relationship of s1 to NS should be something between a “typical” party system with a largest party on 51% of the seats (2.45) and the party system we expect from 250 seats with Greece’s pre-bonus two-tier PR system (3.26). The geometric average of these two figures would be 2.82. The actual election yielded NS=2.70, which is pretty close. OK, so maybe the similarly of this value of NS to our “expectation” came out via luck. But it sure looks like as normal a result as we could expect from this electoral system.

Of course, in 2015, when there were two elections, the country was in crisis and the outcome was rather more fragmented than this. I am not sure when the 50-seat bonus was implemented; it used to be 40. So I am reluctant to go back to the pre-crisis elections and see if outcomes were “normal” before, or if this 2019 result is just a one-off.

For the record, in September, 2015, the largest party had 48.3% and NS=3.24; in January, 2015, the figures were 49.7% and 3.09. These are hardly dramatic differences from the expectations I derived above (51.0% and 2.82), but they are more fragmented (particularly in terms of higher NS albeit only marginally in terms of a lower s1). So, all in all, maybe the Greek electoral system is not as complex as I think it is, and all its elections fall within the range of normal for such a system. But this 2019 election seems normaler than most.

Finally, Israel has a totally normal election

[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.