Chile 2017: Meet your new seat product

As discussed previously, Chile has changed its electoral system for assembly elections (and for senate). The seat product (mean district magnitude times assembly size) was increased substantially. Now that the 2017 Chilean election results are in, did the result come close to the Seat Product Model (SPM) predictions?

The old seat product was 240 (2 x 120). The new seat product is 852.5 (5.5 x 155). This should yield a substantially more fragmented assembly, according to the SPM (see Votes from Seats for details).

I will use the effective number of parties (seats and votes) based on alliances. The reason for this choice is that it is a list PR system, and the electoral system works on the lists, taking their votes in each district and determining each list’s seats. Lists are open, and typically presented by pre-election alliances, and the candidates on a list typically come from different parties. But the question of which parties win the seats is entirely a matter of the intra-list distribution of preference votes (the lists are open), and not an effect of the electoral system’s operation on the entities that it actually processes through seat-allocations formula–the lists. However, I will include the calculation by sub-alliance parties, too, for comparison purposes.

The predicted values with the new system, for effective number of seat-winning lists (NS) and effective number of vote-earning lists (NV), given a seat product of 825.5, are:

NS=3.08 (SPM, new system)

NV=3.45 (SPM, new system).

The actual result, by alliance lists, was:

NS=3.09

NV=4.02.

So the Chamber of Deputies is almost exactly as fragmented as the SPM predicts! In the very first election under the new system! The voting result is somewhat more fragmented than expected, but not wide of the mark (about 14%). It is not too surprising that the votes are more off the prediction than the seats; voters have no experience with the new system to draw on. However, the electoral system resulted in an assembly party system (or more accurately, alliance system) fully consisted with its expected “mechanical” effect. The SPM for NS is derived from the constraints of the number of seats in the average district and the total number of seats, whereas the SPM for NV makes a potentially hazardous assumption about how many “pertinent” losers will win substantial votes. We can hardly ask for better adjustment to new rules than what we get in the NS result! (And really, that Nresult is not too shabby, either.)

Now, if we go by sub-alliance parties, the system seems utterly fragmented. We get NS=7.59 and NV=10.60. These results really are meaningless, however, from the standpoint of assessing how the electoral system constrains outcomes. These numbers should be used only if we are specifically interested in the behavior of parties within alliances, but not for more typical inter-party (inter-list) electoral-system analysis. It is a list system, so in systems where lists and “parties” are not the same thing, it is important to use the former.

To put this in context, we should compare the results under the former system. First of all, what was expected from the former system?

NS=2.49 (SPM, old system)

NV=2.90 (SPM, old system).

Here is the table of results, for which I include Np, the effective number of presidential candidates, as well as NV and Ns on both alliance lists and sub-alliance parties.

By alliance By sub-list party
year NS NV NP NS (sub) NV (sub)
1993 1.95 2.24 2.47 4.86 6.55
1997 2.06 2.54 2.47 5.02 6.95
2001 2.03 2.33 2.19 5.94 6.57
2005 2.02 2.36 3.01 5.59 6.58
2009 2.17 2.56 3.07 5.65 7.32
mean 2.05 2.41 2.64 5.41 6.79

We see that the old party (alliance) system was really much more de-fragmented than it should have been, given the electoral system. The party and alliance leaders, and the voters, seem to have enjoyed their newfound relative lack of mechanical constraints in 2017!

Can the SPM also predict NP? In Votes from Seats, we claim that it can. We offer a model that extends form NV  to NP; given that we also claim to be able to predict NV from the seat product (and show that this is possible on a wide range of elections), then we can also connect NP to the seat product. We offer this prediction of NP from the seat product as a counterweight to standard “coattails” arguments that assume presidential candidacies shape assembly fragmentation. Our argument is the reverse: assembly voting, and the electoral system that indirectly constraints it, shapes presidential fragmentation.

There are two caveats, however. The first is that NP is far removed from, and least constrained by, assembly electoral systems, so the fit is not expected to be great (and is not). Second, we saw above that NV in this first Chilean election under the new rules was itself more distant from the prediction than NS was.

Under the old system, we would have predicted Np=2.40, so the actual mean for 1993-2009 was not far off (2.64). Under the new system, the SPM predicts 2.62. In the first round election just held, NP=4.17. That is a good deal more fragmented than expected, and we might not expect future elections to feature such a weak first candidate (37% of the vote). It is unusual to have NP>NV, although in the book we show that Chile is one of the countries where it has happened a few times before. Even the less constraining electoral system did not end this unusual pattern, at least in 2017.

In fact, that the assembly electoral system resulted in the expected value of NS, even though NP was so high, is pretty good evidence that it was not coattails driving the assembly election. Otherwise, Ns should have overshot the prediction to some degree. Yet it did not.

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=(MS)1/6
and
s1=(MS)-1/8.

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.