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!