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?

Chilean electoral reform

The electoral reform in Chile has been approved. As is to be expected in such processes, the final version is a bit different than what had been proposed back in 2013 when we first discussed the Chilean electoral reform.

The size of the Chamber of Deputies will be increased from 120 to 155, and the chamber will be redistricted to have 28 districts (currently there are 60). This means a mean magnitude of 5.5; the range will be 3-8. This is a very substantial change from the current system, in which all districts elect just two.

The Senate is also being increased in size from 38 elected members to 50. The fifteen regions will constitute electoral districts, leading to an average district magnitude of 3.3 (range of 2-5).

The D’Hondt method is retained, as are the open lists.

There will be a gender quota concerning nominations: neither men nor women can constitute more than 60% of the candidates on a list.

The first link above offers detail (in Spanish) about the debates and votes on specific provision, as well as which communes will be in which chamber district, and the district magnitudes for both chambers.

Visualizing the impact of two-seat districts

In response to my post about the two-seat districts in Burkina Faso, David Altman (a leading scholar on Chilean and comparative politics) contacted me to say I was not quite right in my contention that the Chilean experience showed that two-seat districts systematically advantage the second party or bloc. Fair enough. I made my point utterly without nuance–as if the second list was always advantaged more than the first–and I elided the distinction between national and district-level effects.

David showed me a graph he had generated in which it is clear that, on average, there is little difference between the vote-seat gap for the main center-left alliance and that of the right-wing alliance; in fact, the gap tended to be slightly higher for the center-left. It is the right that has been consistently second in nationwide votes, so the data seemed to challenge my “systematic” claim.

In the Burkina Faso post, I went over a number of examples from the district level in that country where there was a large advantage in terms of the translation of votes into seats for the second party. I do not think David and I disagree about the district-level effects. But what about the national?

For reasons Taagepera and Laakso* first emphasized in 1980, the best way to visualize how electoral systems treat parties (or alliances) is not by using the difference between seat and vote shares for each party, but by the advantage ratio, A:

    A=(percent seats)/(percent votes).

This is the approach I will use here. The first graph simply plots the distribution of A values in the Chilean elections from 1989 to 2013 (Chamber of Deputies only), using a kernel density plot. It also marks the arithmetic means with vertical dashed lines.

Chile Adv ratios kdens

Of course, with only seven elections, we should be cautious in interpreting how “systematic” the effect is. Yet the trend is clear: the right-wing alliance (referred to in the graph as “Alianza” and shown in blue) has a notable tendency to have higher advantage ratios than has the center-left (“Concertación”).** Yet in every election the Alianza has been second in nationwide votes, albeit by widely varying margins.

The second graph shows the advantage ratio against the nationwide gap in votes between the two parties (Concertación vote share minus Alianza vote share), with each election labelled.

Chile A vs vote gap

Note that as the gap grows, there is a tendency of the Alianza’s advantage ratio to increase. There is actually a small such tendency for the Concertación, too, although it is much closer to a flat line. More importantly, we would normally expect that as the top two parties/alliances grow farther apart in votes, the first one would gain more in seat share. Yet what the Chilean pattern shows us is that the second one gains more, relative to its vote share, as the gap grows. This is not something we would expect under any other district magnitude (except maybe M=4) under any proportional (or semi-proportional) allocation rule. It is this “relative to its vote share” point that I meant to convey. Two-seat districts are a good way to get the second force more over-representation than that of the first force.

If we turn to individual elections, we see that Alianza data point is higher than that for the Concertación in 1989, 1993, and 2005, all years in which the Alianza was more than ten percentage points behind the Concertación, plus in 2009 when the two alliances were almost even in votes. On the other hand, the large vote gap for the Concertación in two elections, 1997 and 2013, resulted in a higher advantage ratio for the Concertación. In 2013 I assume that has to do with the center-left having expanded its electoral reach by incorporating new parties and rebranding its list as Nueva Mayoría. I am not sure what the explanation is in 1997; the gap was large that year, but as the data plot shows, not unusually so.

I find it interesting that the worst year for the Concertación, by this standard, was 2005, which I had noted at the time as being unusual in having a bloc of parties compete against each other in the first round of the presidential elections while remaining united on legislative lists–the Alianza’s two main component parties had separate presidential candidates. The result in the legislative races was their best advantage ratio since the first democratic election of 1989.

It looks to me like two-seat districts in Chile have indeed generated a systematic greater advantage to the second alliance over the first, even if the effect is tempered by other features of specific elections.

* Rein Taagepera and Markku Laakso, “Proportionality Profiles of West European Electoral Systems,” European Journal of Political Research 8 (1980):423-46; see also Rein Taagepera and Matthew S. Shugart, Seats and Votes: The Effects and Determinants of Electoral Systems (Yale University Press, 1989), in particular chapter 7.

** The right has run under different names in different elections. I am using “Alianza”; the center-left changed names from Concertación to Nueva Mayoría in 2013.


The data, by year (pardon the plain text formatting):

year Conc_votes Alianz_votes A_Conc A_Alian
1989 .515 .342 1.116505 1.169591
1993 .554 .367 1.052948 1.135331
1997 .505 .363 1.138614 1.078972
2001 .479 .443 1.078636 1.072235
2005 .518 .387 1.045689 1.162791
2009 .444 .435 1.06982 1.111111
2013 .477 .362 1.17051 1.127993
Mean .4988571 .3855714 1.096103 1.122575

Chile’s election, 2013

Chileans went to the polls today in a general election (president and congress).

As of this time of posting, the count has just begun. I will update this space when there is more known. In the meantime, the profile of the three leading presidential candidates reads like a novel–and not only because the author is Ariel Dorfman.

Electoral reform advances in Chile

Both houses of the Chilean legislature have passed legislation to increase the size of both chambers and scrap the current electoral system.

The assembly size changes are modest. Chile currently has one of the smallest first chambers, relative to population, of any democratic country (see graph). The planned change from 120 to 134 will redress this only slightly. The Senate will go from its current 38 members to 44.

The current electoral system for both houses tends to be referred to by the rather uninformative name, “binomial” system. It is open-list PR in two-seat districts, using the D’Hondt formula. D’Hondt is probably the most common PR formula, but of course it isn’t very proportional when your district magnitude is two. It does, however, tend to over-represent the second largest list, usually the conservatives, and this was its intention. (Aside: I met someone in the US government in about 1988 who had served as an advisor to the Chilean government, and he said the goal of the system then being designed was, in his words, “to screw the left”. Interesting that it is a conservative government that is finally moving ahead with changes.)

The article does not make clear what the new system will be. Presumably PR with higher and variable magnitude. Or maybe the same M=2 districts but with the additional seats being for a national compensation tier. If anyone has details on either the planned new system or the politics behind it, please comment.

The new system will not be in place until the 2017 elections.

(H/t to Chris, in an earlier thread on the topic; yes, they’ve been talking about this for a while.)

Electoral reform in Chile?

Proposals to change the electoral system in Chile are again on the table, writes Mariano Montes (in Spanish). With the first post-dictatorship presidency from the center-right (who is currently very popular), the previous veto by the right may be overcome. The center-left Concertacion has never liked the current electoral system, which was originally designed to over under-represent them at the expense of the right.

The proposals would be to increase the size of each chamber, and simultaneously permit presidential reelection. These moves would require a constitutional amendment. With larger chambers, the district magnitudes would be increased, resulting in a more proportional system.

The current system actually is a proportional formula, continuing the pre-dictatorship system of open-list PR with D’Hondt allocation. What has made it mostly unrepresentative of political forces other than those grouped into the two big pre-electoral coalitions is that all districts currently have a magnitude of two. Rather awkwardly and imprecisely, this system has come to be known as the “binomial” system.

I am always somewhat amused by criticisms of the system that refer to its making possible districts in which one winning candidate has fewer votes than another who loses. Of course, this is precisely the sense in which it is not a “nominal” (or nomial?) system. Were it a nominal system, by definition, the two candidates with the most votes would be the winners in each district. Nominal systems are those in which votes are cast for candidates by name, rather than being first pooled by party or coalition affiliation. Nominal systems are top-M systems (where M is the district magnitude).

Chile’s system, by contrast, is a list system. That means the first criterion is the votes cast collectively for the candidates on each list. Then the open nature of the lists kicks in, where candidate vote totals matter. Rather than being a top-M system, at this stage it is a top-s system, where s is the number of seats each list has won. Obviously, when M=2, s can take only the values of 0, 1, or 2.

Given that it is D’Hondt, the list with the most votes will win two seats only if it doubles the vote total of the runner-up list. This is how all D’Hondt systems work, and D’Hondt is the most common of proportional allocation methods for list systems (open or closed). The difference is that most list-proportional systems that use D’Hondt have M>2 for most of their districts, and so the process continues beyond determining whether the largest list has more or less than twice the votes of the next list. But in any open-list system, it is always possible (in fact, typical) that some candidates who win seats are not in the top M. They merely must be in the top s of their own party’s or electoral coalition’s list.

It would make a lot of sense if Chile would revert to the pre-dictatorship system of larger districts, and thus greater proportionality. The current system over-represents the two largest list, but over-represents the one that is second in votes to a greater degree than the one with the most votes (because the second one often has many fewer votes in a district, but not only half as many). It also makes sense to expand the size of the chambers; Chile’s Chamber of Deputies is very under-sized, relative to its population (see the graph at a planting from more than five years ago on reapportionment in the USA).

Maybe Chile will finally have a more proportional electoral system. But, please, let’s not call the resulting system with its higher magnitudes a multinomial system!

Thanks to Greg Weeks for the tip.