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 (N_S0), the effective number of seat-winning lists (N_S), the effective number of vote-earning lists (N_V), 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:

N_S0: –0.215

N_S: –0.098

N_V: –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 N_V and v₁ is the difference significant (N_V 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 N_V 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 N_S 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.

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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