Netherlands, compared to the Seat Product expectation

The recent election in the Netherlands was noteworthy for its high fragmentation. But was it higher than we should expect, given an extremely proportional electoral system? If so, how much higher?

Fortunately, from Taagepera’s Seat Product Model, we have a baseline against which to compare any given election. For “simple” electoral systems–those with a single tier of allocation and a basic PR formula (or FPTP)–we expect:


NS is the effective number of seat-winning parties, whereas s1 is the seat share of the largest party. MS is the seat product, defined as the mean district magnitude, times the assembly size. The derivation of these models for expectations may be found in Taagepera (2007), and is also summarized in Li and Shugart (2016) and my forthcoming book with Taagepera, Votes from Seats.

Two important points about these models: (1) They are not mere regression estimates, bur rather are derived deductively; (2) On average, they are remarkably accurate. For long-term European democracies, the mean ratio of actual NS to the model expectation is 1.007; for s1 it is 1.074. (They are not substantially less accurate for other regions or younger democracies, but given the topic of this post, the longer-run European democracies are the most relevant comparison set. The ratios reported are based on 219 individual elections.)

For the Netherlands, with a single nationwide district, MS=150*150=22,500. This means we should expect, on average, in an electoral system like that of the Netherlands, that NS=5.31 and the largest party has 28.6% of the seats (s1=0.286). In other words, we should expect the Dutch party system to be quite fragmented.

In the graphs below, we compare the actual values in each election since 1945 to the Seat Product expectation.

First, for NS.

Now, for s1.

Strikingly, both values are well off the expectation now and have been in some other recent elections–but not so much as recently as 2012 or 2006. The 2017 election appears to be a continuation or acceleration a trend, but that trend has been somewhat irregular. Note, however, a bit farther back in the past there were elections in which NS was much lower than expected, and s1 much higher–in other words, when fragmentation was less than expected. (Note to readers: On 31 March I revised this paragraph to better reflect the recent trends shown in the graph.)

Over the entire period, the mean effective number of seat-winning parties has been 5.08, and the mean largest seat share has been 0.29. In other words, the Netherlands has not been exceptional in its long-term averages, given its extremely high seat product.

A key question is whether fragmentation will again come back closer to expectation. This is not a question the Seat Product Model can answer. But note that if we had been running this test in about 1986, I might have said, “will the Dutch electoral system ever again fragment, like we’d expect?” Sometimes things even out, sometimes they don’t.

Obviously, the fragmentation inn 2017 is far higher, relative to the baseline than it was during the previous (and brief) fragmenting around 1970. Perhaps that means the Dutch party system has entered a new phase from which there is no turning back. The very high proportionality of the system means it can sustain this level of fragmentation without anyone being seriously under-represented. On the other hand, one might want to be careful about assuming recent trends can’t reverse themselves. Parties could merge, or voters could tire of voting for small parties that are only bit players in policy-making.

The value of the Seat Product Model is it lets us go beyond simply saying “the Netherlands uses PR, so fragmentation is no surprise” or, alternatively, “fragmentation is out of control in the Netherlands”. It lets us say just how much the fragmentation in the Netherlands is out of whack with expectation. In 2017, the precise answer is that NS is 1.62 times the expectation, while s1 is 77% of expectation. That degree of divergence from the expectation is almost at the 99th percentile for NS among European countries; the divergence for s1 is at about the 18th percentile.

Will actual and expected values again converge in the Netherlands? Stick around for a few more elections and see.

Netherlands 2017 open thread

I hope to have something to say about the recent election in the Netherlands. But so far have not. But maybe you do. Here is your chance!

We can talk about the election result itself, or the coalition negotiations, which should be pretty interesting.

(Part of the reason for not having a post yet is that I made this election one of the themes for my students’ final exam earlier this week. And now that means exams and papers must be graded, grades assigned, etc.)