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!


21 thoughts on “Brazil electoral rules changes: Will they make a difference?

  1. With a pure open-list system, where a vote for the list has no effect on the ranking (rather than being a vote for the rankings in the list itself), the value of belonging to a party is devalued, isn’t it? I thought I had read that Brazilian reformers wanted to allow voters to vote for the list as ranked. Wouldn’t that strengthen the party, and therefore provide more incentive against extreme fragmentation? Or has that idea fallen off the radar screen? Or is my memory mistaken?

    • To be clear, there is no party ranking to allow the voter to vote for. There is not even, strictly speaking, a list presented to voters. You vote by entering the name or number of the candidate or party you want to vote for. Party votes are actually list votes, and have no bearing on the intraparty allocation (among either candidates or sub-alliance parties). Many (most?) voters probably have no idea with which other parties the one they vote for is pooling votes.

      There was a discussion of moving to a closed-list system. It is actually hard to predict how it would work in Brazil. Party organizations are so weak, for the most part, that it is not clear who benefits from getting the authority over ranking. So many parties, as they currently exist, are empty shells. I see no reason to believe that Brazil would get “strong parties” simply by moving to a closed list. Or even a flexible list.

      The best thing they could do (were I to be asked) would be to drastically cut district magnitude. Then the list type is relatively less consequential. But that was not discussed, to my knowledge, and is probably a non-starter.

      (Various forms of mixed-member system have been discussed, but it has not gone far. I doubt MMP makes much sense for Brazil, either.)

      • What about Finnish-style quasi-list? If everyone had to vote for a candidate, at least it would raise the bar a little higher for candidates, wouldn’t it?

      • Well, both Finland and Brazil are in that graph and others in Votes from Seats. It seems it does not make much difference, even though I agree that, theoretically, it should.

        The rate of voting solely for a party label in Brazil is pretty low, although I do not have figures readily available.

      • Finnish-style quasi-list now has fans in Canada, where Prince Edward Island voters voted a year ago (the Liberal government was not happy and invented a turnout requirement after the fact, as an excuse not to honour the vote), for MMP, in a variation where you must vote for a regional candidate. I was particularly pleased with their sample ballot, which contains a one-line explanation of MMP: “A vote for a candidate counts as a vote for that candidate’s party. This vote helps elect Island-wide MLAs for top-up seats.”

  2. I wonder if there exists a simple answer to every problem/feature in open-list PR. We know the classic open-list PR turns the intra-party competition into SNTV. And we also know STV is like a cousin system to SNTV that is almost always technically superior. So I think allowing a voter who votes for a list to rank the candidates in the list and distribute the seats to its winners by STV is a logically sound path that is worth exploring. I think it could also be used to replace the hodgepodge of methods that attempt to balance list rank and voter preference in most semi-open/flexible list systems.

      • Hmm, maybe I didn’t make it too clear. What I imagine is that the way the seats distribute to different lists is completely identical to a (non-panachage) party list system: a voter votes for one list and one list only. And a list wins X number of seats according to this vote total, by D’Hondt or whatever. But after voting for a list, the voter unlocks the ability to rank candidates in that one list and that list only, such that STV counting is only among candidates in that list, to determine who wins these X seats. And other lists will have their own separate STV counting with different X and quotas among their candidates. That is what I mean when I say it changes the intra-party dynamics from SNTV to STV.

      • Just to be absolutely clear, “voting for a list” and “ranking the candidates in that list” is done together while the voter is at the voting booth that one time.

      • John, this is exactly what was used with the D’Hondt-STV hybrid used in the Australian Capital Territory’s inaugural election, along with various other features too tiresome and stupid to expand upon. While it’s true that STV is indeed superior to SNTV for *interparty* contexts, the main problem with SNTV (the requirement it places upon large parties to balance their vote, and the anomalies caused if they do not do so) is present to a far smaller extent in an intraparty contest, where there is no great issue of distortion if candidates fail to balance their vote.

        While it may be somewhat annoying to a faction in a party if they have to balance their vote, I hardly see why that justifies such a substantial increase in the technical complexity of a system (and a faction so concerned about their representation should probably form their own party anyway).

    • While I’d probably use STV for anything if I could, I think many people may see this as a reasonable objection: It is more complicated than any form of non-ranked list voting.

      To me it seems:
      1. Vote one guy, most votes wins
      2. Vote one guy, if no one gets enough we’ll do it again
      3. Vote one guy or one party; if your guy doesn’t get in, you’ll still help his party
      4. Vote one guy or one party, if your guy wins enough votes, he’ll jump the queue
      5. Rank some or all of the candidates and math decides who wins

      Is what the average Joe on the Street sees unless he is being told who to vote for or someone is trying to push a tactical vote

  3. A key theme of the chapters of Votes from Seats that are concerned with the intraparty (intra-list) dimension is that the parties that operate within open alliance lists are subject to the same “SNTV” pressures as in pure SNTV. That is, the small parties need to concentrate their votes on whatever number of candidates they can reasonably elect–usually one–and the large parties have to guard against their smaller partners poaching seats if their own vote is too dispersed.

    Given the large M, which means that the larger alliances can win several seats and have dozens or even over a hundred candidates, the challenges are immense. Nonetheless, parties are pretty good at managing their vote, and tend to win about the number of seats they have collective vote totals to elect.

    With magnitude and the number of candidates (even just within any given list) so high, STV seems totally unworkable.

    • “Over a hundred candidates” I thought the biggest M in the Congress of Deputies is only 70. Perhaps that’s one thing they could fix, in addition to cutting down overall M, as logically it makes no sense to nominate more candidates than there are available seats. I imagine the biggest resistance to these reforms is the small parties themselves refusing to pass them in Congress.

      • The biggest M is indeed 70, but lists that are presented by alliances can present many more than M candidates. I do not recall the exact amount, but I think it is 1.5M.

  4. STV works well with a district magnitude much lower than an open list PR system. The minimum district magnitude for both systems 3, but the max for STV 9, and open party list 25.

    Why doesn’t Brazil try a 1 vote MMP system?

  5. “The best thing they could do (were I to be asked) would be to drastically cut district magnitude.”

    That is it. The electoral districts are the states, and a single state, Sao Paulo, has over 20% of the population.

    Go to either STV, additional member/ MMP, single member districts, or semi-proportional with single member districts with some members elected by nationwide open list. Really only STV or abandoning proportionality would get rid of the shell parties.

    • That’s a very strange conclusion. They could lower district magnitude and not have to change anything else, and they’ll get fewer parties. Nothing inherent in MMP or STV that gets to that end, though STV is certainly associated with smaller M in practice. But as I’m saying, M is the only thing they need to change. BTW they should obviously also get rid of the maximum and minimum number of seats allocated to states and just have no malapportionment at all in the Chamber of Deputies, but that’s a whole other story.

  6. Pingback: Chile 2017: First round | Fruits and Votes

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