Brazil’s open list is (a little bit of) a hybrid now

Brazil is a classic case of open-list proportional representation (OLPR): lists win seats in proportion to their collective votes in a district (state), but candidates within the list are ordered solely according to preference votes obtained as individuals. These rules can result in individual candidates elected with very small preference-vote totals.

For the most recent Brazilian election, a new provision has gone into force. There is now a threshold on preference votes that candidates must obtain to be elected. This means that, in a very technical sense, a hybrid element has been brought into the Brazilian system. However, the provision is not the usual hybrid seen in “preferential list” systems, whereby seats not filled on preference votes are filled instead according to a party’s (or coalition’s) pre-determined rank. That hybrid format is what is typically called a flexible list or a semi-open list. However, Brazilian lists remain unranked, except via the preference votes.

Rather, in Brazil, a list that has an insufficient number of candidates with above-threshold preference votes forfeits those seats to other lists in the district. The threshold is set at 10% of the electoral quota, which is a Hare quota (1/M, where M is district magnitude).

This provision changed the allocation of 8 seats. Given a Chamber of Deputies with over 500 seats, we should not exaggerate the significance of the change, although of course, some other parties might have adjusted either their nomination behavior or their “intra-party vote management” practices (defined below) to avoid being hit by the threshold.

The Chamber’s website has an article regarding the seat shifts, and a table with the details (in Portuguese). The PSL, which is the party of the likely next president, Jairo Bolsonaro, won 7 fewer seats than it would have without the threshold. All these seats were in São Paulo, which is the highest-magnitude district in Brazil (M=70). The threshold there is thus 0.143% of the votes cast in the state. The Novo list in Rio Grande do Sul (M=31) also lost 1 seat due to the intra-list threshold. (Novo, meaning “New”, is a small liberal party.)

In São Paulo, the seven PSL candidates who were not eligible to take seats the list otherwise would have won had vote totals ranging from 19,731 to 25,908. They were replaced by candidates on six different lists with preference votes ranging from 56,033 to 92,257, suggesting the replacements had, on average, about three times the votes of the forfeiting candidates. (The party that picked up two of these seats was the Democrats.) In Rio Grande do Sul, the seat Novo forfeited would have been won by a candidate with 11,003 votes, but was instead filled by a candidate the Brazilian Labor Party (PTB, not to be confused with the PT of Lula) who had 69,904 votes, a preference-vote total 6.35 times greater than that of the forfeiting candidate.

As is clear from the vote totals of those who lost under this provision and those who gained, if the intention was to prevent candidates with marginal personal followings from riding in on the “coattails” of strong list-pullers (whose popularity increases the votes of the collective list), then the reformers can declare “mission accomplished”.

I am personally quite excited by this provision, which I had missed when summarizing minor changes made to the electoral law in 2017, because I once wrote up a proposal for just such a hybrid. It is in some text that was going to be part of one of the chapters in Votes from Seats, but Rein Taagepera and I decided it was not directly germane to the book and left it out. The chapter it would have been part of compares OLPR to the single non-transferable vote (SNTV) with respect to vote shares of first and last winners, and regarding the extent to which parties do (or do not) manage their intra-party competition.

Managing intra-party competition refers to parties doing one or both of: (1) restricting the number of candidates nominated, or (2) intervening in the campaign in an effort to shift votes from non-viable candidates to viable ones.

Under SNTV, these intra-party competition-management practices are critical because the total number of seats a party (or set of cooperating parties) can elect is entirely dependent on how many individual candidates it has whose votes are in the top-M vote totals in the district. Under OLPR, parties have no incentive to do this, if their goal is simply to maximize list seats–a list under OLPR can never displace seats to another list due to having “too many” candidates or having the candidates’ vote totals be widely unequal. (Parties may have other reasons to care about which candidates win, and multiple parties running in alliance face an SNTV-like conundrum in that they are competing with one another inside the list to get their candidates into the top s, where s is the number of seats won by the list. But these are separate problems, and the latter is a problem covered in Votes from Seats).

The proposal I drafted was a hybrid of OLPR and SNTV (unlike flexible lists, which are a hybrid of OLPR and closed-list PR). A threshold would be set on preference votes, and if a list won more seats, via application of the inter-list allocation rule, than it had candidates over the threshold, it would forfeit these seats. Any such forfeited seats would go into an “SNTV pool” to be be won by the otherwise unelected candidates with the highest preference-vote totals, independent of which list they had run on. My intention in devising this proposal was to encourage parties to be more active in managing their intra-party competition–taking some aspects of SNTV as beneficial–in order to make victory by candidates with marginal personal popularity less likely. (I would have set the threshold a little higher than 10% of a Hare quota.)

The article on the Chamber website is not clear on the precise rule now used in Brazil for deciding on the replacement candidates. In any case, it certainly has a similar effect to my proposal. (From a comment by Manuel at the earlier thread, it seems the forfeited seats are assigned proportionally rather than SNTV-like.) I can’t claim credit, as there is no way any Brazilian official saw my unpublished proposal. But I am pleased that some such a provision has been adopted somewhere.

Thanks to Dr. Kristin Wylie (on Twitter) for calling my attention to this article.

16 thoughts on “Brazil’s open list is (a little bit of) a hybrid now

  1. As usual, Manuel is several steps ahead of me! He already called our attention to this change at the earlier thread on the election. I had not yet read his comment when I posted this entry.

  2. Credit also goes to Tom, who noticed the SNTV-style implications of the new provision.

    Now, concerning the allocation of Chamber seats under the revised system, I refer you to pages 88 and 90-93 of the Electoral Justice official results report for the state of Rio Grande do Sul, available in PDF format here. In page 88 there’s “Anexo IV – Cálculo do QE e QP,” that is the statewide calculation of the “Quociente Eleitoral” or Q.E. i.e. the Hare quota, and the “Quociente Partidário” or (Q.P.), namely the single party or coalition seats obtained by full Hare quotas. On the “QUOCIENTE ELEITORAL (Q.E.)” section we have (A) the number of Chamber seats; (B) the number of nominal i.e. candidate votes; (C) the number of party votes; (D) the number of valid votes (the sum of candidate and party votes); (E) the Q.E. calculation, equal to (D) / (A), or valid votes divided by number of seats; and the 10% of Hare quota performance threshold. With 5,845,077 valid votes and 31 seats, this yields a Q.E. or Hare quota of 188,551 and a ten percent performance threshold of 18,855.1. Blank and invalid ballots have no bearing on these calculations, but notice the large numbers (596,391 and 394,398), relative to the number of valid votes.

    Then, on the “QUOCIENTE PARTIDÁRIO (Q.P.)” section we have the single parties or coalitions; their number of candidate, party and valid votes (D); their Q.P., defined as (D)/(E), or valid votes divided by the Hare quota, disregarding fractions; the number of candidates reaching the 10% of quota performance threshold; and the number of seats filled. Notice that NOVO was entitled to two seats, but because it had just one candidate reaching the performance threshold, it filled just one seat; the remaining parties and coalitions had a number of filled seats equal to their Q.P., that is the number of seats obtained by full Hare quotas, as they had enough candidates attaining the performance threshold.

    With 24 seats filled up to this point, the remaining seven seats are determined by the procedure detailed on pages 90-93, under “Anexo V – Cálculo de distribuição de sobras”, that is the distribution of remainder (seats) calculation. There you’ll find the following formula:

    MÉDIA = votos válidos (nominais + legenda) / (Q.P. obtidas + vagas média obtidas + 1)

    which translates to

    Average = Valid votes (i.e. candidate + party) / (Hare quota seats + seats by average + 1)

    that is, the standard D’Hondt rule average calculation; notice that Hare quota seat totals do not factor in candidates below the threshold. Immediately below the formula, there are several iterations of the (largest) average calculations, each one listing the parties or coalitions; their candidate, party and valid vote totals; the number of Hare quota seats (“Q.P. obtidas”) and filled seats (“Q.P. Preench.”); the number of obtained and filled seats by largest averages (“Vagas média obtidas” and “Vagas média Preench.”); the number of unelected candidates so far with at least 10% of the Hare quota; and the result of the average computation. Notice as well that on the first iteration, the average for Novo is 145796.66666666666666, which is equal to the number of valid votes obtained by the party (437,390) divided by three, that is its two Hare quota seats plus one. The largest average in this first iteration – indicated by an asterisk to its right – went to the PSOL / PCB coalition, which obtained one seat and filled it as well, since it had one candidate satisfying the performance clause requirement.

    In the second iteration, the valid vote total for the PSOL / PCB coalition is divided by two (one obtained seat plus one), and a new largest average was determined. Because NOVO forfeited one seat on account of the 10% of quota threshold, twenty-four seats were filled on the initial stage instead of twenty-five, and there were seven iterations of this procedure instead of six. In the additional, final iteration the PSDB / PTB / PRB / REDE / PP coalition had the largest average and filled the last seat, for a total of nine. This seat went to the coalition candidate with the ninth largest vote total, who belonged to PTB. Coincidentally, without the performance clause in place, he would have been the losing candidate with the largest vote total. Nevertheless, the procedure leaves it clear that forfeited seats due to the performance threshold are determined by application of the D’Hondt rule until all seats are duly filled, while keeping separate counters for seats obtained under the regular D’Hondt rule, and seats actually filled in accordance with the performance clause.

    As in the case of Sao Paulo, the exact same distribution of seats could have been obtained by first allocating all seats by the D’Hondt rule; determining that NOVO was entitled to just one seat (instead of two); and then repeating the procedure for the remaining thirty seats among the remaining parties and coalitions, disregarding NOVO’s votes and single mandate.

    • I can also confirm that in Sao Paulo the Chamber seats forfeited by PSL – awarded to other single parties and coalitions by the D’Hondt rule as previously noted – were in turn assigned to the unelected candidates within those parties or coalitions with the highest vote totals. Had the seven seats in question been allocated strictly by number of candidate votes, the first three seats (2 DEM, 1 PSB) would have gone to the same candidates who were elected under the existing rules, but candidates from PSDB, PP, DEM and PSD with 86,042, 85,381, 83,400 and 81,160 votes, respectively would have filled the last four seats, displacing candidates from SOLIDARIEDADE, PR, PC do B and PODE with lower vote totals ranging from 56,033 to 75,613.

      In other words, under the traditional D’Hondt method the seven seats forfeited by PSL were filled by the single parties and coalitions with quotients ranked 71 to 75 and 77 to 78; the 76th quotient belonged to PSL, but was disregarded precisely because the party did not qualify for further seats as a result of the ten percent of quota performance threshold.

    • And very quickly, the previously described procedure for allocating Chamber seats with the 10% performance threshold in place is confirmed by TSE Resolution No. 23,554 of 2017, available in Portuguese here. Meanwhile, I now have detailed 2018 Senate and Chamber of Deputies election results on my website’s Brazil page. Incidentally, they were quickly picked up by the English- and Spanish-language Wikipedias, in the case of the Senate within hours of having published them. Meanwhile, the Portuguese-language Wikipedia cites mostly but not always identical Chamber figures from a Brazilian news media source, but having verified my numbers several times, it’s possible that the differences stem from an oversight on their part, namely that they might have mistakenly included votes for disqualified candidates, deemed void by TSE and reported separately from those for the remaining candidates. That said, TSE has made it quite clear that the published results are subject to review, and I’ll be re-checking all figures ahead of the runoff vote.

  3. What electoral system would make Brazil’s party system less fragmented and caused the vanity parties to united? Would Brazil had been better for it’s Presidential election using the Irish STV to elect it’s President?

  4. A switch to STV could entail a potential logistics problem, namely that Brazil relies on electronic voting, but any STV count would have to be carried out on a centralized basis, and with reprogrammed machines (or even a new electronic voting system). This was already an issue with Maine’s Democratic gubernatorial primary under RCV earlier this year, and it would be even more so – much more so – in a country with close to 150 million registered voters, spread over a land mass the size of the contiguous 48 states of the U.S, and with an 80% voter turnout rate.

    It’s been said that unlike the Spanish colonies in the Americas, which went their separate ways after gaining independence from Spain, the Brazilian colonies went the opposite way, uniting into a single nation. However, while linguistically homogeneous, during the first republican era of 1891-1930, the federal government was weak and states had a good deal of freedom, to the point some called their governors “presidents” and even had diplomatic relations with foreign countries. That hasn’t been the case since then, but I don’t think it’s an exaggeration to say that the states and regions of Brazil still dance to their own tune, and for that and other reasons the country has not been able to develop a stable national party system, other than for the two-party system that existed during the military governments of 1964-85, which is nevertheless regarded as an artificial construct. At the present time this can be seen in the contrasting outcomes between the presidential election – where Bolsonaro’s large 46% plurality compares favorably to the level of support for Hitler and NSDAP in the German presidential and parliamentary elections of 1932-33 – and the legislative election, where the 11.7% share of the vote for PSL in the Chamber of Deputies poll is not too different from the results polled by AfD in the Bundestag election last year (or for that matter last Sunday’s Landtag election in Bavaria).

    Nevertheless, if Bolsonaro ends up winning as polls suggest he will, I’m not sure if the 30-party carnival that has become Brazil’s party system will last for long. Bolsonaro’s longing for the 1964-85 regime makes me think that he will try to simplify the party system, perhaps not down to two parties but to the limited multi-party system in place by 1982. All the same, I don’t rule out he might attempt a self-coup, not least because he has indicated in the past he would; even if he doesn’t, the prospects for the survival of Brazilian democracy as we have known it appear dire. I reiterate, be afraid. Be very afraid.

    • I would think that Brazil needs a higher electoral threshold of at least 15% in each multi-member district, and a lower district magnitude, no multiple member district higher than 25 members perhaps, the lower house needs to increase in size to reduce the over-representation of rural states, perhaps 10% of the lower house has a national tier to ensure national proportionality with the threshold set at 5%, perhaps this will reduce the amount of parties in Brazil.

      The Senate is fairly fragmented as well, perhaps adding a national tier and requiring 5% of the vote for parties to gain seats there.

      It isn’t hard to amend Brazil’s Constitution as it is oddly one of the only Federations that I can think of that requires no state approval or national double majority referendum to ratify.

      It doesn’t seem surprising consider the extreme economic inequality in the country that a candidate like Bolsonaro has done so very well, it is amazing that someone like him hasn’t come around sooner.

      I doubt any electoral system could stop someone like him or any form of populism as this is the sign of the times.

      Perhaps Brazil needs to emulate Portugal; the parent country to some degree in it’s electoral system. Portugal is fairly small, and not regionally fragmented.

  5. I’m super late on this (think I got here via the Ecuador post), but variations of this have been features of the Panamanian electoral system (at least its multi-member districts) since democracy was reestablished in 1990 (and perhaps before, but I’m unsure).

    In the 2019 edition: about two thirds of the districts, electing about one-third of the total number of MPs, elect their candidates using FPTP with electoral fusion. In the remaining third, electing from two to seven candidates, the following system is used:

    Each list consists of either a single party or a group of independents (called “libre postulación” in Panama). Lists may run as many candidates as there are seats.

    Voters can either vote for the party/list alone (“votar en plancha”) or else for as many candidates of their preference from a single list. They cannot vote on multiple lists. Each party may run a single candidate from another party on their list; this candidate is marked with an [R] on the ballot, and can only receive a remainder seat, not one of the party’s quota seats. The candidate is also on their main party’s list and can receive that party’s quota seats.

    Parties receive one seat for each complete Hare quota obtained, and that seat goes to their candidate with the most preference votes.
    Then, if there are seats remaining to distribute, parties which did not receive a full quota but did receive at least half a quota receive seats in descending order, until either all seats have been awarded or until all parties with at least half a quota receive a seat. Again, the seat goes to the candidate with the most preference votes.

    I’ve always had an issue with calling this “proportional” because a party with 1.99 quotas and a party with 0.5 quotas generally receive a seat each through this method.

    Any remaining seats are awarded by remainder by adding together the number of preference votes the candidate received across all party lists (their main party plus any allied parties on which they were listed with an [R]). The candidates with the most preference votes win, but each party/list can only receive a single remainder seat. I believe a candidate listed on multiple lists is considered the single remainder seat for their principal party, but I’m not sure. At the remainder stage, votes “en plancha” are essentially ignored. Many voters do not vote for all of their party’s candidates. This is due to strong personalism within the Panamanian system (despite having stable parties), and also to internal factionalism.

    How many preferences one can express and how the remainder are awarded has changed. In 2009, voters had the same choice (vote for one list en plancha, or vote for some/all the candidates on a single list), but the “one remainder seat per party” rule did not exist, so parties often had several candidates from other parties with [R]s on their lists, and generally the largest party won every remainder seat if any existed.

    In 2014, it was changed to “one person, one vote” where each voter expressed a vote for one candidate only. This often meant that the remainder seats went to the most popular candidates of minor parties, rather than the 3rd or 4th candidate of a major party (perhaps most similar to Brazil). District-level alliances were banned; to ally in a district, parties had to be in a national alliance. This was more to impact electoral fusion in the FPTP seats, but impacted how remainder candidates in MMDs could fuse across party lines as well. Additionally, several popular candidates with [R]s were elected as quota candidates; this essentially means those who voted for them on other party lists had wasted their vote.

    The similarities in the 2014 and 2019 systems to Brazil are that down-ballot candidates for major parties can lose their seats to more personally popular candidates from less popular parties. I personally am not a fan, and had always assumed the “more individually popular candidate from a smaller party gets a seat” characteristic to be a bug, not a feature, but this does make me reconsider somewhat.

    • The Panamanian system is very interesting. And odd.

      I had not really thought of the similarity to the new Brazilian rules, although I see the point that these provisions do something similar.

      • Transferable preferences? Or some sort of points system, like the former Finnish 1-2-3 system or Slovakia’s use of Borda for the minority seats (or of Austria and Iceland – if I understand the online systems properly – within lists)?

      • Transferable preferences, yes, identical to Australia. Perhaps the NYC mayoral election has led to some tremendous increase in salience for preferential voting throughout the Americas (given the current President of Brazil, I don’t know that this is necessarily the right time for electoral system innovation).

      • It’s somewhat unsurprising, given the prevalence of two-round systems and that AV elections generally replicate them at half the cost.

        It will be interesting to see if it makes the agenda of Chile’s new Constitutional Convention (whose Spanish name is actually Constitutional Convention and not Constituent Assembly because of a right-wing demand), although ironically this upcoming presidential election is the first where the two second-round candidates aren’t a foregone conclusion in advance.

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