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.

The datasets for Votes from Seats

I have neglected to publish a link that has been available since December–the article announcing the datasets used in Votes from Seats (national and district) was published in Research & Politics (open access).

Citation:

Cory L. Struthers, Yuhui Li, Matthew S. Shugart, “Introducing new multilevel datasets: Party systems at the district and national levels” (December 20, 2018). https://doi.org/10.1177/2053168018813508

The abstract:

For decades, datasets on national-level elections have contributed to knowledge on what shapes national party systems. More recently, datasets on elections at the district level have advanced research on subnational party competition. Yet, to our knowledge, no publicly accessible dataset with observations of the party system at both national and district levels exists, limiting the ease with which cross-level comparisons can be made. To fill this gap, we release two corresponding datasets, the National Level Party Systems dataset and the District Level Party Systems dataset, where the unit of analysis is the party system within either the national or district jurisdiction. More than 50 elections in the two datasets are overlapping, meaning they include observations for a single election at both the district and national levels. In addition to conventional measures such as the effective number of parties, we also include underutilized variables, such as the size of the largest party, list type, and the vote shares for presidential candidates in corresponding elections.

The datasets themselves can be accessed directly at Dataverse.

Is AV just FPTP on steroids?

In debates over electoral systems in Canada, one often hears, from otherwise pro-reform people, that a shift to the alternative vote would be worse than the status quo. It is easy to understand why this view might be held. The alternative vote (AV), also known as instant runoff (IRV), keeps the single-seat districts of a system like Canada’s current first-past-the-post (FPTP) system, but replaces the plurality election rule in each district with a ranked-ballot and a counting procedure aimed at producing a majority winner. (Plurality winners are still possible if, unlike in Australia, ranking all candidates is not mandatory. The point is that pluralities of first or sole-preference votes are not sufficient.)

Of course, the claim that AV would be FPTP on steroids implies that, were Canada to switch to AV, the current tendency towards inflated majorities for a party favored by less than half the voters would be even more intensified. This is plausible, inasmuch as AV should favor a center-positioned party. A noteworthy feature of the Canadian party system is the dominance, most of the time, by a centrist party. This is unusual in comparison with most other FPTP systems, notably the UK (I highly recommend Richard Johnston’s fascinating book on the topic). The party in question, the Liberal Party, would pick up many second preferences, mainly from the leftist New Democratic Party (NDP) and so, according to the “steroids” thesis, it would thus win many more seats than it does now. It might even become a “permanent majority”, able to win a parliamentary majority even if it is second in (first-preference) votes to the Conservatives (who thus win the majority or at least plurality of seats under FPTP). The “steroids” claim further implies that the NDP would win many fewer seats, and thus Canada would end up with more of a two-party system rather than the multiparty system it has under FPTP.

There is a strong plausibility to this claim. We can look to the UK, where AV was considered in a referendum. Simulations at the time showed that the Liberal Democrats would stand to benefit rather nicely from a change to AV. While the LibDems are a third party, heavily punished by the FPTP electoral system even when they have had 20% or so of the votes, what they have in common with the Canadian Liberals is their centrist placement. Thus, perhaps we have an iron law of AV: the centrist party gains in seats, whether or not it is already one of the two largest parties. An important caveat applies here: with the LibDems having fallen in support since their coalition with the Conservatives (2010-15), the assumptions they would gain from AV probably no longer apply.

On the other hand, we have the case of the Australian House of Representatives, which is elected by AV. There, a two-party system is even stronger in national politics than in the FPTP case of the UK, and far more so than in Canada. (When I say “two party” I am counting the Coalition as a party because it mostly operates as such in parliament and its distinct component parties seldom compete against one another in districts.)

It is not as if Australia has never had a center-positioned party. The Australian Democrats, for example, reached as high as 11.3% of the first-preference votes in 1990, but managed exactly zero seats (in what was then a 148-seat chamber). Thus being centrist is insufficient to gain from AV.

Nonetheless, the combination of centrism and largeness does imply that Canada’s Liberals would be richly rewarded by a change to AV. Or at least it seems that Justin Trudeau thought so. His campaign promised 2015 would be the last election under FPTP. While he did not say what would replace it, he’s previously said he likes a “ranked ballot” and he pulled the plug on an electoral-reform process when it was veering dangerously towards proportional representation.

Still, there are reasons to be somewhat skeptical, at least of the generalization of the Australian two-party experience. The reasons for my caution against the “steroids” view are two-fold: (1) the overlooked role of assembly size; (2) the ability of parties and voters to adapt.

Assembly size is the most important predictor of the size of the largest party, disproportionality, and the effective number of seat-winning parties in countries that use single-seat districts. (It is likely relatively less important when there are two rounds of voting, as in France, but still likely the most important factor.) This is a key conclusion of Votes from Seats. It is thus important not to overlook the fact that Australia has an assembly size considerably smaller than Canada’s. In the book, Taagepera and I show that Australia’s effective number of seat-winning parties and size of largest parliamentary party are almost what we would expect from its assembly size, even if FPTP were used. (See also this earlier post and its comment thread; how close it is to expectation depends on how we count what a “party” is.) The data are calculated over the 1949-2011 period, and the effective number of parties has been just 1.10 times the expectation from the Seat Product Model (which is based only on assembly size when single-seat districts are used). Similarly, the average largest party has been 93% of the expected size (averaging 50.5%  of seats when we would expect 54.2%).

Thus we do not need to invoke the alleged steroids aspect of AV to understand the dominance of two parties in Australia. But this does not mean it would not make a difference in Canada. Consider that the current effective number of parties and size of the largest party in that country, averaged over a similar period, are also just about what we should expect. The multipartism, including periodic minority governments, that characterize Canada are not surprising, when you use the Seat Product Model (SPM). They are surprising only if you think district magnitude is all that matters, and that FPTP is FPTP. But it isn’t! An electoral system using the FPTP electoral rule with an assembly of more than 300 seats is a different, and more multiparty-favoring, electoral system than one with 150 seats. Replace “FPTP” in that sentence with “AV” and it is surely still true.

But what about the centrist party, the Canadian Liberals? Surely AV would work differently in this context, and the Liberals would be a much more advantaged party. Right? Maybe. If so, then it would mean that the SPM would be overridden, at least partially, in Canada, and the largest party would be bigger than expected, for the assembly size, while the effective number of parties would be lower than expected. Of course, that’s possible! The SPM is devised for “simple” systems. AV is not simple, as we define that term. Maybe the SPM is just “lucky” that the one country to have used AV for a long time has the expected party system; or it is lucky that country has the “correct” assembly size to sustain two-party dominance. (Australia is the Lucky Country, after all, so if the SPM is going to get lucky somewhere, it might as well be Australia.)

This is where that other factor comes in. While no one has a crystal ball, I am going to go with the next best thing. I am going to say that the SPM is reliable enough that we can predict that, were Canada to have AV, it would have an effective number of parties around 2.6 and a largest party with around 48% of seats. In other words, just about where it has been for quite some time (adjusting for the House size having been a bit smaller in the past than it is now). Note these are averages, over many elections. Any one election might deviate–in either direction. I won’t claim that a first election using AV would not be really good for the Liberals! I am doubting that would be a new equilibrium. (Similarly, back in 2016 I said my inclination would not be to predict the effective number of parties to go down under AV.)

Parties and voters have a way of adapting to rules. Yes the Liberals are centrist, and yes the Conservatives are mostly alone on the right of the spectrum (albeit not quite as much now, heading into 2019, as in recent years). But that need not be an immutable fact of Canadian politics. Under AV, the Liberals might move leftward to attract NDP second preferences, the NDP center-ward to attract Liberal and even Conservative second preferences, the Conservatives also towards the center. It would be a different game! The Greens and other parties might be more viable in some districts than is currently the case, but also potentially less viable in others where they might win a plurality, but struggle to get lower ranked preferences. The point is, it could be fluid, and there is no reason to believe scenarios that have the largest party increasing in size (and being almost always the Liberals), and correspondingly the effective number of parties falling. With 338 or so districts, likely there would remain room for several parties, and periodic minority governments (and alternations between leading parties), just as the SPM predicts for a country with that assembly size and single-seat districts.

As I have noted before, it is the UK that is the surprising case. Its largest party tends to be far too large for that huge assembly (currently 650 seats), and its effective number of seat-winning parties is “too low”. Maybe it needs AV to realize its full potential, given that the simulations there showed the third party benefitting (at least when it was larger than it’s been in the two most recent elections).

Bottom line: I do not buy the “FPTP on steroids” characterization of AV. I can understand were it comes from, given the presence in Canada of a large centrist party. I just do not believe Liberal dominance would become entrenched. The large assembly and the diversity of the country’s politics (including its federal structure) both work against that.

I agree with electoral reformers that PR would be better for Canada than AV. I also happen to think it would be better for the Liberals! But would AV be worse than FPTP? Likely, it would not be as different as the “steroids” claim implies.