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:



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.

Chile 2017: First round

Chile has presidential and congressional elections 19 November. Unfortunately, an article at AS/COA does something that is far too common in media coverage of Latin American elections: It ignores the congressional elections.

That is especially unfortunate in this case, as this year’s elections in Chile are particularly interesting due to changes in the electoral systems for both houses of congress. (Details in a previous planting.)

The presidential election requires the leading candidate to obtain 50%+1 of the valid votes cast in Sunday’s first round. Otherwise, the top two advance to a runoff, which will take place on the 17th of December.This is the electoral system known as “two-round majority” or “majority runoff.”

As for the congressional electoral system, it remains open-list PR with D’Hondt divisors, as has been the case since the current democratic regime was established in the late 1980s. However, the seat product for the Chamber of Deputies has been increased moderately. Previously, it was 240 (120 assembly seats times 2 per district), which is a highly restrictive system. Now it will be 852.5 (155 seats times a new mean of 5.5 per district). That is only modestly proportional, but still a substantial increase. (For the central importance of the seat product, see Votes from Seats.)

The Senate seat product is also being increased, but only half that chamber is elected at a time, so the new system will not be fully implemented till four years hence.

The new systems (both houses) will create more political space both for minor parties and alliances that currently have few or no seats, and for the representation of more of the member parties in the alliances that already are a hallmark of the Chilean party system’s adaptation to the more restrictive system that has been in place. In the sense of being a system of open alliance lists, it is essentially the same allocation formula as in Finland and Brazil. The crucial difference is district magnitude–formerly two (the second lowest possible!) and now to be increased, although still well short of what those other two countries have–and, in comparison to Brazil, with a much smaller assembly size.

As shown in a table of polling trends for the presidential election (first link), there is more of a contest for second place and thus entry into the runoff than there is for first place. Former president Sebastián Piñera is leading but not likely to clear 50% of the valid vote. Two leftist candidates are vying to face him in the expected runoff.

It might not seem obvious, but the congressional electoral-system changes could be influencing presidential competition. In fact, that is one of the findings of Votes from Seats: We can predict the average trend in the “effective” number of presidential candidates from the assembly seat product. (This is in contrast to conventional “coattails” arguments that claim we can understand assembly-election fragmentation only by knowing how many viable presidential candidates there are.)

In the past in Chile, there was strong pressure for parties to coalesce in order to be viable participants in the highly restrictive congressional electoral system. While parties in a common alliance for assembly seats could run separate presidential candidates–see the 2005 case of unusual alliance behavior on the right–usually they would not. (And the 2005 case did not work out that well for the right, at least in the Chamber.)

Now, the pressure to join forces for assembly elections is reduced, which should be expected to push up the number of viable contenders for presidential-runoff slots as well. The candidates vying for that second slot are Beatriz Sánchez, backed by an alliance called the Broad Front (Humanist Party, Liberal Party, Green Ecologists, and others), and Alejandro Guiller, backed by Fuerza Mayoría (including the Socialist Party of the outgoing incumbent, Michelle Bachelet, as well as the Communists, Democrats, and others). Which one will make it, and how will it affect the left’s combined chances of blocking a victory for Piñera in the runoff? And how will the candidates help (or not) their alliances’ electoral process in the new congressional election?

Brazil electoral rules changes: Will they make a difference?

Brazil has passed some changes to its electoral rules, according to the Economist. The changes mainly concern rules outside the “electoral system” in the way Taagepera and I delimit that term in Votes from Seats. That is, despite various proposals under discussion in recent years in Brazil, the assembly size, district magnitude, and allocation formula all remain unchanged. Instead, rules changes are focused on financing provisions and attempts to regulate pre-election coalitions. The concerns in Brazil are over the excessive fragmentation of the Congress, which is blamed on incentives to corruption resulting from the open-list, highly proportional, system in place.

In this post, I want to consider the extent to which Brazil’s existing extreme fragmentation is expected, or not, based on its electoral system. Knowing the answer to this question can help us understand if changes to electoral rules, outside the core system features, might make a difference.

The following graph is an authors’ original of one that appears in the book as Figure 14.3. It shows the number of parties winning at least one seat in each district of Brazil’s and two similar electoral systems: Chile and Finland. Each of these electoral systems is D’Hondt, open list, with rules explicitly permitting lists to be presented by multiparty alliances. In each system, all seats are allocated in districts, via applying the D’Hondt divisors to the total votes won by each list. The emphasis is important, as the electoral system does not operate on parties, it operates on lists. Sometimes a list is a party list, but in these countries it is common for it to be an alliance list. In such cases, the electoral system does not shape the number of parties, except indirectly. The number of parties winning will be dependent on how many winning candidates on the various lists happen to be branded by different parties. At the extreme, every candidate could be from a different party, even if they were elected from just a few lists (or one list, as happens in some Chilean districts, electing just two seats). This could mean that the number of parties–as distinct from the number of lists–winning seats is “unpredictable”. This graph shows that is not the case–there is still a predictable average pattern.

The thick dotted curve shows the predicted pattern. It says that the number of sub-alliance winning parties (again, whether winning on their own list or via having a winning candidate on a list in which they were one of two or more alliance partners) is the district magnitude, raised to an exponent designated “k”. You will need to read the book to see the derivation of k. I will give only the short version: k is the “embeddedness” factor, and captures the share of the total assembly seats that are elected in a given district. If a district elects all the seats in the entire assembly (as in Israel or the Netherlands), k=0.5 for reasons explained in the book (and also in Taagepera and Shugart 1993). When a district elects a smaller and smaller share of the total assembly, k increases and can be slightly over 1.00 when M=1 and the assembly is very large (as in the UK). What the embeddedness factor captures is the extent to which national politics enters the district level and makes district politics more competitive than it would be predicted to be, were there no extra-district politics. Specific to the case of Brazil, it tells us that we can expect higher fragmentation of the party system because of the electoral system–both the fact that the allocation rule is one of open alliance lists and that there are many large-magnitude districts embedded in a very large assembly.

What we notice is that the predicted curve, showing the expected number of parties winning at least one seat (on its own or on an alliance list) equalling Mk, fits the overall data cloud well. This is a deductively derived logical model, not a post-hoc data fit. The fit of the logical model to the data is confirmed by a regression test. However, the data plot also shows that Brazil’s very largest districts (with magnitude greater than 20 and up to 70) are even higher than the model predicts. So, for example, with M=55, we expect around nine parties to win seats. (The k formula here yields roughly 0.55, and so 55.55=9.1.) Yet Brazil’s actual districts in this very high-magnitude range all have more than nine parties, and sometimes more than twelve, represented.

Why is fragmentation so high? Without the logical model developed for these systems, we might have just said, well, they have high district magnitude. Maybe we would also have invoked country-specific features, and just said, “it’s Brazil”. Such statements about high M and Brazilian particularity remain valid, but what the model lets us see is that even if Brazil’s very largest districts “conformed” to the model–as indeed its more modest-sized ones do, on average–it would still be very fragmented. So, about those reforms…

The new electoral law amendment, according to the Economist, “outlaws election alliances among parties that do not share a programme.” That might be helpful, if it can be enforced, by eliminating alliances of pure seat-winning convenience. The amendments also impose a threshold (1.5% of the national vote or seats won in at least nine states)–not for winning seats at all, but for getting public campaign financing and and free television and radio time. That might matter more. (This ‘threshold’ rises to 3% by 2030.)

Perhaps it is the existing freedom to form alliances regardless of programmatic commitment with one’s partners and the promiscuous financing/publicity rules that cause some of Brazil’s districts to be above the predicted value. However, even if that is what is causing Brazil’s largest district’s to overshoot their expected number of seat-winning parties, the amount of fragmentation after these reforms would still be very high. In other words, Brazilians are likely to be disappointed by the impact of these reforms. The model says so!

If Brazilians wanted changes to make a more dramatic impact on fragmentation, what could they do? One thing would be to abolish alliance lists altogether. The lighter gray line in the graph above shows the expected number of lists to win at least one seat for a given district magnitude. It is equal to the square root of M. In the book we show that we do not need k for this; embeddedness does not push up the number of lists, on average, beyond the square root of M. If lists and parties are the same thing, as in many PR systems, then the number of parties winning at the district level is not systematically affected by extra-district politics. Other outputs of the party system are affected, the book shows: the size of the largest parties (both votes and seats) is systematically reduced, and the “effective” number of parties (again, both for votes and seats) systematically increased, by the extent of the district’s embeddnedness. The number of lists or party-lists is not. However, as shown here, the number of parties including those who win through alliance partnerships, is pushed up–systematically, in that it can be modeled.

Elsewhere in the book we show that the number of lists winning seats in Brazilian districts is consistent with the model (square root of M)–again, on average. So Brazil’s electoral system functions as expected–it turns list votes into list seats in a way consistent with PR systems worldwide. It also systematically increases the total number of parties through its alliance feature. Get rid of alliances, and the number of winning parties would surely drop (though probably not all the way to the square root of M, because at least some of these small parties could survive independently).

Of course, Brazil could do more dramatic things still, like redistrict to have smaller district magnitudes. But if the changes made this year, in advance of the 2018 elections, are the best Congress can enact, it is highly unlikely they could have done something that drastic! Given what was passed, perhaps the number of parties will come down–to the predicted value. That would still be a lot of parties!


Votes from Seats is published!

Available from Cambridge University Press. (Also available in Kindle format for only $15.90!)

(Please note that this post is a “sticky”; scroll down for new content.)

Take the number of seats in a representative assembly and the number of seats in districts through which this assembly is elected. From just these two numbers, the authors of Votes from Seats show that it is possible to deduce the number of parties in the assembly and in the electorate, as well as the size of the largest party. Inside parties, the vote distributions of individual candidates likewise follow predictable patterns. Four laws of party seats and votes are constructed by logic and tested, using scientific approaches rare in social sciences. Both complex and simple electoral systems are covered, and the book offers a set of ‘best practices’ for electoral system design. The ability to predict so much from so little, and to apply to countries worldwide, is an advance in the systematic analysis of a core institutional feature found in any democracy, and points the way towards making social sciences more predictive.