Germany electoral system change

Note: This is a revised version of an older post (originally 15 Jan. this year). The electoral system changes changes (with some modifications) have now been passed. Rather than make a new planting I am just re-upping this older one, as the comment thread has continued to grow with useful information. I particularly recommend a new comment by Thomas D for good detail. In addition, see the post by Verfassungblog for background and Twitter thread by Heinz Brandenburg which has both background and excellent detail on the final version. (The Verfassungblog post refers to an earlier version of the draft; in the finally passed version the 3-districts alternative threshold is indeed being abolished.) The law is sure to be challenged before the Constitutional Court, and some or all if it may fail the constitutional test. As Thomas notes, the law could be a mortal threat to the CSU as we know it, as well as to the Linke. And it certainly means no more “personal constituency mandate” and thus is not a mixed-member system.

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[original post, edited] The parties in Germany’s current governing coalition have agreed a package of reforms to the electoral system. The proposal keeps the size of the Bundestag at 598 and eliminates Überhangmandate and “balance” seats.

For details, see first comment. This is a big deal. I’d understand this proposal as Germany abolishing MMP (and Verfassungblog and Brandenburg–linked above) agree. It is not a mixed-member system if it’s possible for a candidate with the most votes in a nominal district not to win the seat.

Could Nigeria’s presidential election require a runoff?

On 25 February, Nigeria holds its elections for president, house, and senate. The country uses single-seat plurality elections, but with an important qualification in the case of the federal presidency. The winner of that contest must have not only a nationwide plurality of votes, but also meet a “distribution” requirement: earn at least a quarter of the vote in at least two thirds of the federal entities (consisting of 36 states and a capital territory).

If the first-round plurality candidate fails to meet the distribution qualification, then there is a runoff. The two candidates in a runoff would be the plurality candidate and the other candidate who wins the most states with a majority of the vote. Note that if there are three or more serious candidates, with regional bases, the runoff opponent might not be the one with the second highest votes in the first round.

Nigeria this year has precisely the situation that could lead to a runoff and possibly not with the top-two candidates: There are at least three candidates who might be considered “serious” and all exhibit Nigeria’s typical tendency towards regional concentration of support. See Africa Elects. Nigeria has not previously had a runoff.

Polling is apparently sparse, but shows Peter Obi of the Labour Party (LP) in the lead–some recent polls show him far ahead. I am not sure how reliable Nigerian polls are, let alone whether they effectively capture state-by-state trends. The next two candidates after Obi appear close in polling: Bola Tinubu (All Progressive Congress, APC) and Atiku Abubakar (Peoples Democratic Party, PDP). A fourth candidate, Rabiu Kwankwaso of the New Nigeria Peoples Party (NNPP) also has regionally concentrated support. Given the distribution requirement, even a candidate with little chance of winning might deprive a more nationally popular candidate of 25% of the vote in some states or of a majority in enough states to affect runoff qualifications should there be a second round.

The APC is the incumbent president’s party, and the PDP has provided the winning ticket in various past elections (including its presidential candidate this year as vice president in the past). Obi was the PDP’s vice presidential candidate in the last national election, in 2019, with Abubakar at the top of the ticket.

As far as congress is concerned, at the 2019 election the APC won 202 seats and the PDP 126 in the House of Representatives, which has 360 seats. In the 109-seat Senate, the APC won 63 and the PDP 44. It seems likely that this year’s results will be more fragmented, but given the use of single-seat plurality in both houses, obviously it depends entirely on the parties’ relative regional concentration in the voting.

Nigeria uses a pure presidential system.

The Ranked Choice Voting Elections of 2022 in Alaska and Maine

Maine, which became in 2018 the first state in the U.S. to adopt Ranked Choice Voting (RCV) for federal elections, was joined last year by Alaska, where RCV was rolled out as well for state elections. Moreover, in 2022 RCV tabulations were carried out in both states for races in which no candidate won an absolute majority of first preferences (no RCV counts took place in 2020, as all federal races in Maine were decided on the first count). However, the Alaskan implementation of RCV, while broadly similar to that of Maine, has a number of differences which influenced the outcome of the election in the former.

Maine

In many respects, the U.S. House of Representatives election in Maine’s CD-2 was a rerun of the 2018 race. Congressman Jared Golden ran again as the Democratic nominee in the district, while Republicans nominated Bruce Poliquin, who had represented the district from 2015 to 2019, when he lost the seat to Golden. Meanwhile, Tiffany Bond ran again as an independent candidate. As in 2018, no candidate won an overall majority of first preferences, and Golden won once more after Bond was eliminated and her second preferences (along with those of voters who backed write-in nominees) were redistributed among the remaining two candidates.

That said, there were a number of differences with respect to 2018.  In 2022, Golden outpolled Poliquin in the first preference count, and went on to win the second count and the election by a larger margin than in 2018, when he narrowly beat Poliquin in a come-from-behind victory. Moreover, Golden won not only an absolute majority of valid second count votes but also of all votes cast, including blank, exhausted and invalid ballots. In addition, a narrow 50.3% majority of CD-2 voters casting valid ballots in the first count ranked at least two candidates (77.7% among Bond voters, 64.3% among Golden voters and 31.1% among Poliquin voters – largely in line with the respective 2018 figures for the same candidates). And It should be noted as well that by 2022 Poliquin accepted the validity of RCV, which he had unsuccessfully challenged in court four years earlier.

That said, the 2022 election results in CD-2 revealed some disconcerting patterns. In the first count, overvoted ballots, invalidated by voters indicating a first preference (or second preference with a skipped first preference) for over one candidate more than doubled since 2018, from 435 to 1,020, although they remained a small fraction (0.3%) of all votes cast. At the same time, while ballots with just one candidate ranked were fewer than those with at least two candidates with valid rankings, the number of ballots with one candidate assigned all rankings grew exponentially, from 7,706 in 2018 to 54,610, of which a large majority (42,985) were cast for Bruce Poliquin. However, voting in that manner is wrong, as clearly spelled out by how-to-vote instructions, which indicate that duplicate rankings have no bearing in the election outcome:  in the cited cases only the first preference would be counted as a vote for the indicated candidate, and the increased frequency of such ballots would seem to indicate that many CD-2 voters still don’t understand the workings of RCV.

Alaska

Ballot Measure 2, narrowly approved by Alaskan voters in a 2020 referendum, not only introduced RCV for federal as well as state executive and legislative offices, but also replaced the existing partisan primaries with a non-partisan blanket primary, in which the top four candidates – chosen by plurality voting – advanced to the general election.

The rules governing RCV counts in Alaska are largely identical to those of Maine, except that Alaska appears to treat differently ballots with duplicate rankings for candidates. Specifically, it’s impossible to replicate from cast vote record data the results of successive RCV rounds in the official reports issued by Alaska’s Division of Elections unless lower duplicate rankings are treated as skipped, which results in a small number of ballots deemed exhausted on account of two or more consecutive skipped rankings.

The new arrangements had an early debut in the summer of 2022, when a special election was held to fill the state’s at-large U.S. House seat, vacant since the sudden death earlier that year of Don Young, who had represented Alaska in Congress for nearly fifty years. In the blanket primary the top four candidates in decreasing order of votes were former Alaska governor and vice-presidential nominee Sarah Palin (Republican); Nick Begich (Republican); Al Gross (Independent); and Mary Peltola (Democratic). However, Gross subsequently withdrew from the race and endorsed Peltola, a former state representative.

Although Peltola placed a distant fourth in the special blanket primary, she went on to secure a first preference count plurality in the August special election, ahead of Palin and Begich, and narrowly defeat Palin after Begich was eliminated and his second preferences were transferred. A majority of Begich first preference voters chose Palin as their second preference, but a substantial number either chose Peltola or exhausted their ballots, indicating no preference for either of the two remaining candidates, which in turn prevented Palin from overcoming Peltola’s first preference lead. However, Begich would have prevailed over Peltola in the final round of counting had he managed to outpoll Palin in the first preference count.

Peltola, Palin and Begich also qualified for the general election in the regular blanket primary held in August alongside the special election. They were joined by Libertarian Chris Bye, who came in fifth place, but was allowed to take part in the election following the withdrawal of Tara Sweeney, who placed fourth in the race. In the general election, Peltola won the largest number of first preferences votes once again, just short of an absolute majority, securing an expanded lead over both Palin and Begich, who once more arrived second and third. Peltola won a decisive victory over Palin in the final round of voting, in which Begich was eliminated, and would have also defeated the latter by a substantial margin if he had managed to win more first preference votes than Palin.

Meanwhile, in the blanket primary for the U.S. Senate contest, incumbent Senator Lisa Murkowski, a moderate Republican, topped the poll, followed by Kelly Tshibaka, a conservative Republican, and Patricia Chesbro, a Democrat. Buzz Kelley, a Republican who came in fourth place, subsequently withdrew from the race and endorsed Tshibaka, but remained on the ballot. In the general election Murkowski narrowly outpolled Tshibaka in the first preference count, and went on to win a clear majority in the final count, following the elimination of Chesbro and the transfer of her second preferences.

Although RCV was also implemented for state elections in Alaska, in the gubernatorial election incumbent Mike Dunleavy, a conservative Republican, won an absolute majority of first preferences and consequently no RCV tabulation was carried out for that contest; nonetheless, the cast vote record data furnished by Alaska’s Division of Elections includes the rankings for the gubernatorial race.

In the special election 72.4% of voters casting a valid ballot indicated preferences for at least two candidates, but in the general election the figure dropped to 66.7% (64.3% in the U.S. Senate contest and 66.9% in the gubernatorial race). However, unlike in Maine’s CD-2 in either 2018 or 2022, all U.S. House, Senate and gubernatorial candidates had a majority of first preference voters casting their ballots in that manner, with Kelly Tshibaka having the lowest share (55.9%) and Nick Begich the highest (80.6%) among major party statewide candidates.  Interestingly enough, among Peltola first preference voters that figure dropped from 72.8% in the special election to 58.1% in the general election, while among Palin voters it increased slightly between both events, from 64.7% to 69%. In fact, preference combination statistics – available in State of Maine 2018 / 2022 and State of Alaska 2022 Ranked Choice Voting (RCV) Election Data – indicate that in the general election voters who ranked Peltola first and skipped all other rankings constituted the largest single group (52,732) for the U.S. House contest.

While both Palin and Tshibaka conceded defeat in their respective races, both cited RCV as a major factor in the adverse outcomes. That said, it’s by no means certain either would have prevailed under the arrangements previously in place in Alaska. Both might have won traditional partisan primaries, but Palin’s evident unpopularity among many Begich voters would have remained a liability under plurality voting in the special election and particularly the general election. Meanwhile, Senator Murkowski might have opted to run as a write-in candidate had she lost the GOP nomination in a traditional primary, and possibly prevail as such in the election, as she did back in 2010. Moreover, in the case of the U.S. House contest it’s worth noting that in recent years the late Don Young had been re-elected by noticeably reduced percentage margins – down to mid-to-high single digits – which suggested the seat might have become very competitive even under plurality voting once he was no longer the GOP nominee.

Nonetheless, Peltola’s upset victory in the special election reinforced the view among many Republicans that RCV is designed to deliver an unfair partisan advantage to Democrats, and that perception is likely to foment resistance to its adoption in other states. In addition, it’s not clear that the success under RCV of Republican candidates like Gov. Mike Dunleavy in Alaska or Sen. Susan Collins in Maine will help to dispel that notion (all the more so since both won outright in first preference counts, where the absence of RCV tabulations might lead some voters to erroneously assume such victories were achieved under plurality voting). Even so, in 2022 Nevada voted to switch to RCV, although that change won’t become final until confirmed by voters in a second referendum, scheduled to be held in 2024.

Finally, some early RCV advocates in the U.S. have since moved on to push for the adoption of other electoral systems such as party-list proportional representation. However, at the present time such proposals have yet to gain any traction, and what momentum exists for electoral reform appears to be in favor of RCV.

Belize to correct its egregious malapportionment

The Supreme Court of Belize has brokered a consent order that will lead to a redistricting to correct the country’s extremely high malapportionment.

Co-Counsel Michelle Trapp stated that [Sean P.] Trende’s report, among other things, found at the time it was written, only five of Belize’s 31 electoral divisions met the international standard deviation of registered voters, generally between five to 15 percent with allocation made for sparsely populated areas.

Trende’s report itself indicates some districts have around five times the voters as some others.

The country has had some lopsided results in the past, including 2020 when a party with almost 60% of the votes won 26 of the 31 seats. Of course, FPTP in a very small assembly will tend to do that, but presumably it has been exacerbated by the malapportionment. (By the cube root law, Belize would be expected to have around 75 seats in total given its population.) Several other elections have been similarly lopsided.

Farther back, it even had a majority reversal. In FPTP systems, plurality reversals happen from time to time–defined as when the party with the plurality of votes does not win the plurality of seats–but majority reversals are rather unusual. Yet in 1993 the People’s United Party won 52.1% of the vote but only 13 of the 29 seats parliament then consisted of. The UDP-NABR alliance won the other 16 seats, despite just 48.7% of the vote.

Looking at the 2020 election at district level, I see one constituency, Ft. George, that had only around 1,500 votes cast (and the PUP nabbed with just 983) while Stann Creek West has over 7,600 votes cast and several others have more than 6,000. There is another around the voter base of Ft. George, as well as several in the mid two thousands or around three thousand. So it is indeed severely malapportioned.

The 1993 majority reversal did not take place under malapportionment this severe, but it was substantial. At that time Stann Creek West was among the relatively lower-population districts (just over 2,000 votes cast) while a few other districts had over 3,000. There were others with only around 1,500. So the problem is not new, but has got worse. And there seem to have been some really significant internal population shifts in the past thirty years. Fortunately, this will be corrected. They still should increase the size of their assembly, too–or adopt some sort of PR. But at least they will improve their small-assembly FPTP.

Finally, now that I’ve poked around Wikipedia pages on Belize constituencies a bit, I want to go see the Belize City Swing Bridge, one end of which is in Ft. George constituency, and which requires four operators to manually crank it.

Coordination failure under nationwide PR: Manufactured majority in Israel 2022

The votes are not yet final from the 1 November 2022 Israeli general election, but the outcome is quite clear. The right-wing bloc of parties supporting current opposition leader Benjamin Netanyahu will have won a manufactured majority. Media are calculating the bloc’s combined seats at 65 out of 120. Yet the bloc currently has just 48.1% of the votes.* That is actually lower than the clear majority of the vote they got in April, 2019, yet at that election the result was deadlock while this one will produce a majority coalition government. What explains the difference? Coordination.

The reason for the manufactured majority in this election, despite a nationwide proportional representation electoral system, is coordination failure. The strategic choices of political leaders and voters in both the left and the Arab political camps have made Netanyahu’s impending return to government possible. On the left, Labor has barely cleared the 3.25% legal threshold, with 3.56% as of now (around 20:30 Israel time), while Meretz is below, at 3.19% (and its percentage has declined in recent hours as more votes are counted*). Even if–as appears unlikely–Meretz ultimately clears, and thus wins 4 seats instead of zero, it would not drop the right below 61 seats. For that to happen, it would also be necessary that all three Arab lists in this election cleared the threshold. But Balad is sitting on only 3.03%, so that looks at least as unlikely.

Had Balad stayed in alliance with the remnant Joint List (i.e., Hadash-Tal, which won 3.93%) and had Meretz either won just enough to clear the threshold or formed an alliance list with Labor, as Interim PM Yair Lapid openly encouraged, the additional seats won by these camps surely would have blocked Netanyahu from winning. Then there either would have been some unexpected coalition possibilities emerging, or another election next spring, with Lapid of the Yesh Atid party remaining Prime Minister during that time (and until a new government eventually formed). Thus it is hard to exaggerate just how much the left and Arab political camps blew it–assuming blocking the return of Netanyahu was important to them. (Frankly, I doubt Balad’s leaders care, although many of their voters must, and leftist leaders and voters alike surely do.)

I should add here that the third piece of the former Joint List, Ra’am, which backed the outgoing government, cleared the threshold easily with the highest vote percentage of any of the three Arab lists (4.34%). This appears to be vindication for leader Mansour Abbas’s consistent message over the last two years of normalizing Arab participation in national governance; in 2021 Ra’am had 3.79%. I will count this as one piece of good news from the election.

In some respects, this year’s outcome is a mirror image of the first of this recent run of frequent elections, in April 2019. In that first of two elections in 2019, the right suffered a coordination failure when New Right fell just below the threshold, with 3.22% of the vote. In that election, the combined right-wing vote was 55.4% if we include Yisrael Beiteinu or 51.44% if we do not. But the non-Likud, non-Haredi right was splintered: Union of Right-Wing Parties (3.70), Kulanu (3.54), New Right (3.22), and Zehut (2.74). Thus the right bloc had only 60 seats, or with Yisrael Beiteinu (4.01% of the vote) included, 65. Had New Right cleared the threshold, the combination without YB would have been 61 or 62, depriving YB leader Avigdor Lieberman of the pivotal position. (It was only after the election that he earnestly said no to the coalitions with Haredi parties that he had willingly been part of up to a few months before.) Thus coordination failure on the right probably prevented a right-Haredi government from forming in 2019, and kicked off the four-election cycle of deadlock and attempted “unity” governments.

In this year’s election, coordination on the right returned in a big way. The non-Likud, non-Haredi right was almost entirely consolidated on one list, that of Religious Zionism, which won 10.31% of the vote and probably 14 seats. There will be much consternation and condemnation over the prominent role that RZ leaders Bezalel Smotrich and Itamar Ben Gvir will play in the likely new government. Much of it will be deserved. They are genuine extremists. However, it will be portrayed as a far-right surge when it really only is the non-Likud, non-Haredi electorate converging on its only viable option. Consider that in the 2021 election, RZ won 6 seats (5.12% of the vote) and Yamina won 7 seats (6.21% of the vote). That is 13 seats and just over 11% of the vote. This time the remaining option will have actually lost vote share while picking up (apparently) one seat. It is not a far-right surge, it is a right-wing coordination success. To these votes we could also add Jewish Home, now led by Ayalet Shaked, which won 1.16% of the votes–far below the threshold, but suggesting the combined vote share for this more-rightwing-than-Likud flavor of politics basically did not change.

It is quite striking how much of the movement from utter coordination failure on the right in 2019 to smashing coordination success in 2022 is the story of Naftali Bennet and Ayalet Shaked and their supporters. Their gambit in 2019 was that there was political space for a strongly right-wing option that is less tied to the old religious Zionist parties, represented at the time by the Jewish Home alliance (in which both were prominent figures and Netanyahu coalition partners). But for a very small number of votes, they could have been vindicated, but instead the last three and a half years turned this on its head, with the list of Religious Zionism commandeering this segment of the vote in 2022. On the way here, Bennet and, more reluctantly, Shaked tried another gambit, teaming up with Yesh Atid, Labor, Meretz, Ra’am, and Yisrael Beiteinu (among others) on the “change” government. Bennet was at the time leader of Yamina, which did not even run in this election. We could say it was hardly a party at all, in terms of the disciplined outfit we’d expect of a party providing the prime minister, as it did for the initial period of the government formed in 2021. It only shed members of Knesset and voters from the moment it announced the coalition. And now its voters have a home and a government, in the form of the most hardline party to have entered any of Netanyahu’s cabinets to date.

As for the left, Labor and Meretz refused to forge an alliance. This is understandable, but also blew up on them in a big way. They had run on an alliance list in the March, 2020, election and won only 7 seats and less than 6% of the votes. Compare that to 11 seats (and over 9% of the vote) in September, 2019, for their separate lists and then in 2021, 13 seats (and combined 10.7% of votes) for their again separate lists. Thus they have reason to believe that together they are worth less than the sum of their parts–conditional on their two separate parts clearing the threshold! In this election they combine for only 6.75% of votes and 4 seats–8 if Meretz ultimately squeaks over the threshold as now seems unlikely. It was a gamble, and it looks to have failed.

There are already recriminations against Lapid for not properly “managing” the center-left bloc (see under “cannibalistic pig“). But he tried to encourage a Labor-Meretz alliance and was rebuffed. I am not in position to say whether he could have done more to prevent center-left voters from choosing him over his threshold-challenged partners. It seems to me that’s not really the bigger party leader’s job, even though it was obviously in his interests that both win seats. Once the Labor and Meretz leaders concluded they could clear the threshold running alone, it was incumbent on them to deliver their votes.

Frankly, it seems that Labor and Meretz are yesterday’s news, and they should either merge or fold. The future of the center-left is Yesh Atid. Over seven elections in just under a decade, Yesh Atid has proven it is not just another centrist flash in the pan, but a serious option with staying power and organization. It is, nonetheless, unlikely ever to be the head of a center-left/Arab government. As the 2021 experience shows, you need a party of the right to cross over and make that a majority (or you’d need Ra’am or some other cooperation-minded Arab party to supplant Hadash-Tal and Balad). It is not clear where another right-wing splinter could come from; it won’t be from the right of Likud, and there just isn’t a “soft right” anymore to its immediate left. Maybe after Netanyahu finally leaves the scene there will be. The future of the center-left is thus probably mainly as a potential coalition partner to a post-Netanyahu Likud, and it would be better for it to be one strong partner than to be fragmented into Yesh Atid and two minnows farther to the left (if they both could clear again in a future contest), plus whatever becomes of Benny Gantz’s Blue and White. (The latter is the real “soft right” in the current party system, but is already firmly tied to the center-left as of now.)

Many supporters of proportional representation in the US, Canada, and elsewhere speak as if PR means no need for strategic electoral behavior. The Israeli experience of 2019 through 2022 shows the folly of such belief. Coordination is still important, especially if there are any significant contra-proportional features to the PR system. And usually there are–sometimes in the form of moderate district magnitude, and sometimes–as in Israel–in the form of a moderately high legal threshold, despite nationwide PR. The right had the coordination this time that it lacked in 2019, whereas the left and Arab sectors in this election did not. And thus a bloc will have the parliamentary majority and government despite not having won a majority of the vote.

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Update: With around 99% counted, it is now 64 seats (53.3%) on 48.4% of the vote. Meretz shrank farther from the threshold and is at 3.16%.

The output indicators for Italy 2022: Yes, MMM in a smaller assembly really mattered

In the pre-election planting I pointed out how much more disproportional Italy’s electoral system would be, given the substantial reduction in assembly size. The current allocation rules and balance between single-seat districts and list-PR seats remained unchanged since 2018, but the assembly size was cut from 630 to 400. (Here I will be referring only to the Chamber of Deputies.) The system is mixed-member majoritarian (MMM).

Assuming I calculated things correctly–and I think I did, but the party vs. bloc calculations can be a little confusing, so caveats apply–here is how the change mattered.

I will report effective number of seat-winning parties (N_S), effective number of vote-earning parties (N_V), and deviation from proportionality (D₂, the Gallagher index also known as the Least Squares Index). I will report both by individual party and by pre-electoral bloc. I believe that for an electoral system like this, the bloc figures are more meaningful, but here you have both and can decide which one works for your analytic purposes.

	2018 Party	2018 Bloc	2022 Party	2022 Bloc
NS	4.32	2.90	5.58	2.40
NV	5.10	3.36	6.62	3.44
D2 (%)	3.98	5.02	7.30	11.74

The change is pretty dramatic. Taking that last line first–disproportionality–we see an increase at the bloc level from around five percent to nearly twelve percent. The 2018 bloc-level figure is a level just below what we might see in a moderately proportional system like Estonia (5.3% in 2019) or Spain (5.37% in 2016) or Luxembourg (5.20% in 2013). The 2022 bloc-level figure is closer to what we might find with a majoritarian system, such as Canada (11.3% in 1988) or the UK (11.8% in 2019) or to take a “brotherly” MMM example, Japan (11.5% in 2000). Thus the increase is quite consistent with how I characterized the system in the previous post, as having changed from an effective seat product just over 900 (consistent with moderate PR) to one of 650 (the same as the value for the UK) solely due to assembly-size reduction.

The effective number of seat-winning blocs is certainly in the ballpark of expectations under a majoritarian system, with 2.90 in 2018 and a drop to 2.40 in 2022 when the assembly size reduction makes it even more majoritarian. The reduction in 2022 occurs in spite of a slightly increased fragmentation of the vote, even at the bloc level (from 3.36 to 3.44). That is, of course, why the disproportionality is so high in 2022.

The bottom line result is that the center-right bloc obtained 59.3% of the seats on 43.8% of votes–a classic majoritarian outcome. In 2018, for comparison, it had 42.1% of the seats on 37.0% of the votes. Its votes grew by 6.8 percentage points, but its seats by 17.2. Some of that is due to the bigger gap between the top two two blocs this time around, which in turn was a product of the center-left’s less complete alliance formation, but a lot of it is the lower number of single-seat districts resulting from the cut in the Chamber size.

Based on the seat product model, by which we expect N_S=(MS)^1/6, and using the numbers reported earlier for effective seat product, we should expect the 2018 system to yield N_S=3.12 and the 2022 system to yield 2.94 (based on effective seat products of 920 and 650, respectively). These are “politics blind” expectations, based solely on the systems’ fundamental design features–district magnitude of the basic tier and the sizes of the tiers that comprise the assembly. We can see that in both elections the actual outcome by blocs was a little less fragmented than these expected values, but not to any extraordinary degree. The calculation of effective seat product for these complex systems gets their impact on the assembly party system about right.

As I mentioned, I do think these indicators are more meaningful when calculated on party level for a system like this. The parties within a bloc coordinate nominations in the single-seat districts, and the contest over who will form the post-election government takes place between blocs. Thus the blocs are the meaningful units. On the other hand, nothing commits the parties within a bloc to continuing to work together, and they agree that the votes for list will determine which one gets the prime ministerial post if the bloc wins a majority. The parties thus remain relevant and competitive actors, too. The outcome at party level was a little less “blocky” overall this time, with more parties gaining significant vote and seat shares despite being outside a bloc.¹ But even at the party level, what is likely to matter most–at least in the short run–is that the largest party within the largest bloc has a majority of its bloc’s seats (119 of 237 for the Brothers), despite only 26% of the overall vote for parties.²

All in all, the the key take-home outcome is that the MMM system strongly rewarded the parties that had coalesced to form the biggest bloc, and the largest party within that bloc. That is just as we would expect MMM to do, particularly with such a reduction in assembly size.

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1. Five Star was in this category both elections. In 2018 it won 32.7% of votes and 36% of seats. This time it dropped to 15.4% of votes and 13% of seats. In addition, Action–Italia Viva in this election had 7.8% of votes and 5.3% of seats. More to the point, the three biggest blocs (counting Five Star as one of the “blocs”) had 92.5% of the votes in 2018 but just 85.4% in 2022.
2. Quite different from 2018 when the League had just 47% of its bloc’s seats–which were in any case not a majority of the Chamber. The League’s party vote in 2018 was 17.4%.

Italy 2022

Italy votes in general elections today. The Brothers of Italy is expected to be the largest party, in a pre-electoral alliance with the League and Forza Italia that may end up with a substantial majority of seats in both houses.

The electoral system is similar to that used in 2018 in that it is mixed-member majoritarian despite having just over 60% of seats elected in the party-list proportional component of the system. In an important sense, however, this year’s version is even more majoritarian–the size of both chambers has been reduced substantially. Other things equal–as they are–a smaller assembly is less proportional (or “permissive” to small parties). And when you combine a relatively majoritarian system with a smaller assembly, you get a more majoritarian system overall. The new Chamber of Deputies, at 400 seats, is closer to the cube root law expectation for a country the size of Italy, but nonetheless the impact would be to favor more substantially than before the largest party or pre-electoral alliance, relative to the 2018 system which had a Chamber size of 630. The size of the Senate has been reduced correspondingly from 315 to 200 seats.

How is the system mixed-member majoritarian (MMM) and not mixed-member proportional (MMP)? This question has been asked before. The answer is straightforward: the seats a party wins in the list component are simply added on to those that it wins in the nominal component (single-seat districts decided by plurality). There is no compensation mechanism, not even a partial one like in the 1994–2001 version Italy used.¹ There is a single vote, but whether voters can split their votes between nominal and list components has no bearing on the classification, which depends entirely on whether the list seats are allocated so as to compensate for deviations from proportionality arising from the district results (as under MMP) or not (as with “parallel” allocation under MMM).

The results from 2018, aggregated by pre-election alliances that coordinate nominations in the single-seat districts, certainly made this clear. The center-right alliance combined for 37% of the votes. This alliance won 42% of the seats, which is not terribly disproportional. However, we have to remember that more than three fifths of the seats are elected by PR. The nature of the system can be seen by looking at the detailed breakdown. The alliance won 111 nominal seats (out of 232, for 47.8%). Thus they were over-represented in this component of the system, as expected from single-seat plurality. If the list component were compensatory, as under MMP, the share of list seats won by this alliance should have been lower than its share of the vote. Yet it won 39.1% of them (111 of 386). It should have ended up with somewhere around 233 seats were these seats compensatory, but instead won 265 (including 3 seats for Italians overseas).

If we take the largest opposition force, the dynamic is even clearer. This was Five Star, which ran on its own, not as a part of any pre-electoral alliance. It won 32.7% of the vote, and 93 of the 232 nominal seats. That is 40%, so it is also slightly overrepresented in this component. To this it added 133 list seats, which is 34.5%, ending up with 227 seats total (including 1 abroad), or 36.0%. That the system was MMM becomes clearer still if we consider the second largest opposition alliance, the center-left. It had 22.9% of the vote, and won 28 nominal seats. This is only 12.1% of these seats–sever underrepresentation, as expected for a third party under single-seat plurality. Its list seat total was 88, which is 22.8% of the list component. Yes, 22.8%, so it got near-perfect proportional representation. However, it got this proportional result only in the list seats themselves. Overall, due to the punishment in the nominal seats, it was underrepresented, ending up with 122 seats (including 6 from Italians abroad), which is 19.4%. It was not severely underrepresented in the final result because–again–the list component is so large. However, were the system MMP they should have had approximately 110 list seats instead of just 88, in order to make their overall seats proportional to list votes. And, as already covered, the other alliances and parties would have had their list seats cut somewhat due to a compensation mechanism, if it were MMP. Thus the system is MMM, albeit with a large list component. I should also add that when I say “list votes” I mean votes aggregated from the nominal contests, given there is only a single fused ballot and not separate list and nominal votes (as there are in the MMM systems of Japan and Lithuania, or in the MMP systems of Germany and New Zealand).

Because polling for today’s election shows the Brothers of Italy in the lead and the combined center-right alliance clearing 40% of the vote while the second place center-left alliance looks to be under 30%, the system likely would provide a substantially larger boost to the center-right this time around than last, even if the rules were unchanged. However, assembly size is a core defining characteristic of an electoral system. If the rules for how seats are allocated are unchanged, and the balance in an MMM system between nominal and list seats is also unchanged, the key variable in how majoritarian it will be overall is assembly size. As already noted, both houses are half as large in the 2022 system as they were in 2018. This change promises a further boost to the winning alliance. There are only 147 single-seat contests in the Chamber of Deputies this time (around as many as in the Australian House of Representatives) and only 74 in the Italian Senate (about as many as in Liberia’s first chamber), it will be even more “work” for the list-PR component allocation to offset, despite its size relative to the nominal, given it is non-compensatory.

In terms of effective seat product, my estimations have it at 920 in the 2018 election. The goal behind the effective seat product is to allow us a rough approximation of what simple electoral system a given complex system is most similar to, in terms of its impact on the party system. Simple, single-tier systems with seat products in the 900–1000 ballpark include Luxembourg (900) and Greenland (961). The former has an assembly about ten percent the size of Italy’s in 2018, yet in terms of impact of the party system, the design of Italy’s system made it more like the simple PR system for the 60-seat assembly of Luxembourg than like other assemblies with 600+ seats and PR allocation (e.g., Germany’s effective seat product is currently around 1800 and Italy’s under its old PR system prior to the early 1990s was around 9800). As for Greenland, they get an effective seat product of 961 from an assembly of only 31 seats by allocating in a single territory-wide district. In other words, while Italy 2018 was a system of MMM, the large assembly and large share of seats allocated in the list component make the Chamber system of 2018 similar to a small-assembly PR system. But what about 2022?

The calculation of the effective seat product for the new Chamber of Deputies system would be around 650. In other words, roughly the same effect on a party system as Britain’s FPTP system, despite the election of over three fifths of deputies in a PR component. This is a fairly substantial reduction. It is based on the “as if” calculation of (1) an MMP system with same parameters as Italy’s new system, which would be an effective seat product of around 2860, and (2) a FPTP system of the actual size of Italy’s nominal component (147). For MMM, we take the geometric average of these two values, which is (rounded) about 650. This is very slightly less restrictive than the MMM system that was in use from 1994 to 2011 (for which the effective seat product could be said to have been around 660). Applying the same procedure to the Senate electoral system of 2022 would yield an effective seat product of around 370, implying roughly the same impact on the party system as the FPTP system of the Canadian House of Commons has.

In conclusion, Italy now has the most restrictive and thus plurality-favoring electoral system it has had in the post-WWII era.² Despite still having a fragmented multiparty system in which parties enter pre-electoral alliances, it has an electoral system that is more like FPTP in the UK (in the case of the Chamber) or Canada (in the case of Italy’s Senate) than like a PR or MMP system. If the largest alliance clears 40% of the votes, as expected, it should obtain a substantial bonus in seats, due to the relatively majoritarian design of the system.

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Notes

1. That system was also MMM. It was often mis-classified in various sources as MMP. The misunderstanding was somewhat more justifiable than for the current one, because of the partial compensation mechanism, which was based on adjusting party-list votes according to nominal seat performance (rather than allocating list seats with regard to nominal seats won as is done under MMP). Even with the partial-compensation mechanism, that former system also should be classified as MMM.
2. All of Italy’s post-war electoral systems have been complex in one way or another. Above I mentioned that the system in use as of the early 1990s had an effective seat product around 9800. That was a remainder-pooling PR system and Italy has not used a PR system since then. The mixed-member system put in place in 1994 had an effective seat product around 660. The bonus-adjusted system from 2006 through 2013 comes out to around 1325 (but this is a more challenging system to estimate because of its unusual features). In all cases, these numbers refer only to the Chamber. Also, the calculation of effective seat product for the 1994–2001 system does not take the partial compensation mechanism into account. Perhaps it should, which would increase the effective seat product of that former system to some (small) degree. However, it is not clear how one would carry out such an adjustment, given the unusual nature of the mechanism. I do not think it is necessary or worthwhile to attempt.

Angola 2022: What (effective) seat product and impact on the outcome?

Earlier this week, in trying to understand the Angolan electoral system, I was unsure whether the allocation of the national list seats was compensatory, or in parallel to the provincial district results. In the comments, Miguel was kind enough to quote the relevant sections of the electoral law, confirming that allocation is parallel.

The results show the ruling MPLA won 51% of the vote and the main opposition UNITA 44%. I will take these as given, and not speculate on whether they are the “real” vote totals or a product of “electoral alchemy.” Rather, I am interested in whether the translation of these votes into seats suggests the MPLA chose a system that would benefit it considerably, or not.

The MPLA has won 124 of the 220 seats. That is 56.3% of the seats, for an advantage ratio (%seats/%votes) of 1.10. How does this compare with an “average” electoral system? I checked my dataset, restricting it to “simple” systems, even though Angola’s is not simple, and to those that are not FPTP or other M=1. The average across 377 such elections is… 1.12.

In other words, if the MPLA was trying to give itself a considerable seat advantage from this electoral system design, it kind of failed.

There is certainly one aspect of the electoral system design that looks like “rigging” via the rules: The provincial tier is highly malapportioned. The 18 provinces vary widely in population, yet each elects five members. See the images with preliminary vote totals in another comment from Miguel or see the CNE site, which also includes seats now. Given the use of D’Hondt at this level and the ample margins in rural provinces, the MPLA won 4-1 in several districts (and 5-0 in one)¹ and 3-2 in all others aside from the three where UNITA was ahead. (UNITA won 4-1 in Cabinda.)

What undermines the MPLA’s own advantage considerably is the nationwide list component, which constitutes just under three fifths of all the seats (and uses Hare quota and largest remainders). If the MPLA had really wanted to create a system to advantage itself, it could have done so by making this tier smaller, or by various other designs.

I do note that UNITA is somewhat underrepresented. Its 90 seats is 40.9%. Given 44% of the votes, its advantage ratio is 0.928. Across a subset of electoral systems fitting the criteria I referred to above, this is quite low. In fact, the average for second parties is 1.075. (Subset because my dataset does not currently have second party shares for all elections; there are 147 elections here.)

In this sense, the electoral system’s design did indeed punish the main opposition. So if this was the MPLA goal, mission accomplished. The malapportionment must be a main cause of this, combined with the parallel (non-compensatory) allocation of the national seats. It should be noted as well, however, that with only two big parties, if one is overrepresented even a little bit (as the MPLA was), the second will probably be more underrepresented than would be the case in a multiparty system more typical of PR electoral systems.

Interestingly, much of the disadvantage to UNITA went to the advantage of smaller parties instead of to MPLA. There were three other parties, each of which won 2 seats. Two seats is 0.91% of the assembly; these parties had from 1.14% to 1.02% of the votes apiece. These small parties won only in the national district, where the only threshold was that a party could not win a seat by remainder unless it had already won a seat.² Given that the national district is 130 seats, it could easily have supported even more parties than the five that won at least 2 seats. The largest party to win no seats had 0.75%. A simple quota for this district would be 0.769%, so this party was below the weak threshold anyway.

The effective numbers of parties were 2.20 by votes and 2.06 by seats–note not much difference there.³ The deviation from proportionality (Gallagher’s “least squares index”) was 4.44%. The latter figure, using again my set of simple non-FPTP systems, is not much different from average (4.87%). So all in all, despite the unusual electoral system, it is not a terribly remarkable result in terms of election indices.

As far as the effective seat product is concerned, for a parallel system I have found the satisfactory method is to take the geometric mean of what we would get if the basic tier were the entire system and what we would get if the system were compensatory. The seat product of the basic tier of this system is straightforward: district magnitude of 5, times tier size of 90 gives us 450. The formula for compensatory based on these parameters (an update and slight modification of a method I have shown here before) would yield an effective seat product of 3844. But because it is actually parallel, we take the geometric average of these values, which is 1315.

An effective seat product of 1315 is in the general range of the simple seat product Norway had (1297) before it adopted a small compensatory tier after 1985, or Peru’s in 1980 or 1985 (1296), and also not much smaller than Switzerland’s (1540).⁴

The disproportionality we should expect from an effective seat product of of 1315 would be around three percent; the actual 4.4% is thus not too much higher. The seat share of the largest party in this election is about 1.4 times expectation⁵ from such a seat product and the effective number of seat-winning parties is about 0.62 the expectation. Obviously, this is due to MPLA political dominance. Or perhaps due to unfair vote reporting. That I can’t say. What I can say is that, despite a fairly unusual combination of extreme malapportionment in one tier and a greater than 50% parallel national tier, the impact this electoral system had on the seat allocation and disproportionality was not anything too out of the ordinary.

Finally, an interesting question but one I will not attempt to answer is whether, had UNITA won a narrow plurality of the nationwide vote, could the MPLA have retained a plurality or even majority of the assembly seats? Given the malapportionment and parallel allocation, I will say maybe. However, once again, I will point out that if they had wanted to ensure they could “win by losing,” the design they came up with was perhaps a little too “fair” to really be in their best (presumed to be anti-democratic) interest. On the other hand, if they are open to a gradual transition to democracy, and perhaps losing a fair election in five or ten years’ time, the system isn’t too bad. It plays to the MPLA’s regional strength yet does not overrepresent it greatly, and it creates space for the opposition, both UNITA and other parties, to operate.

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Notes

1. MPLA won 4-1 in Cuanza Sul, Moxico, Namibe, Huíla, and Cuando Cubango. It won 5-0 in Cunene (where the votes split 82.9%–14.4%). It is really striking that most of these strong MPLA districts are in the south, where UNITA was most present in the civil war. Meanwhile, the UNITA pluralities are Luanda (the capital and largest by far), Cabinda (the non-contiguous oil-rich enclave in the far north which has had a separatist movement) and Zaire (also in the northwest).
2. It is not clear to me if this means a party could have won a provincial seat and thus been eligible for a remainder seat in the national district, or it had to have won a quota of nationwide votes. In any case, as all provincial seats were won by MPLA or UNITA, this detail would not have affected the results of this election.
3. If I knew nothing other than that the effective number of vote-earning parties in some election was 2.2, I would expect the effective number of seat-winning parties to be around 1.72, based on logically derived, and empirically supported, formulas in Votes from Seats.
4. By comparison, if we used the “as if compensatory” estimate of 3844, we would be in roughly the range of single-tier systems like Finland (3076 in 2019) or another former Portuguese colony, East Timor (4225). Indonesia is also in this seat-product neighborhood (4134), as was the French PR system of 1986 (3174).
5. A ratio of actual to expected of 1.38 is near the 90th percentile for over a thousand elections, simple and complex, in the dataset (and would be about the same if I looked at just the simple non-FPTP subset).

At-Large Legislative Contests in the 2020 Puerto Rico General Election

While most seats in both houses of the Legislative Assembly of Puerto Rico are chosen by plurality (single-seat districts in the House, two-seat districts in the Senate), there are 11 seats in each body – out of a total of 27 in the Senate and 51 in the House of Representatives – that are filled on an at-large basis, by Single Non-Transferable Vote (SNTV). The 2020 election in the U.S. Commonwealth was notable not only for the fact that candidates from five parties secured at-large representation (along with a sitting independent senator), but also for the unexpectedly poor showing of the largest opposition party, the pro-Commonwealth Popular Democratic Party (PPD) in the at-large legislative races.

To be certain, the outcome of the election was nothing short of a political earthquake, with both the ruling, pro-statehood New Progressive Party (PNP) and PPD polling their worst results ever: 33.24% and 31.75% of the valid votes for governor, for a combined share of 64.99%. Meanwhile, the island’s perennial third party, the left-wing Puerto Rican Independence Party (PIP) shot up from 2.13% in 2016 to 13.58%, but the new Citizens’ Victory Movement (MVC) – ideologically diverse but broadly left-liberal – outdid PIP with 13.95%. Another new party, the Christian-conservative Project Dignity (PD) won 6.80%.

Despite their respective setbacks, the two major parties continued to monopolize between themselves all legislative district seats (MVC narrowly lost a House race in San Juan to PNP), with PPD securing a majority of these in both houses despite polling fewer votes than PNP, due to latter’s concentration of votes in the San Juan metropolitan area. So why did PPD fail to do as well in the at-large legislative races? The answer lies in the workings of the at-large representation system in Puerto Rico, known in Spanish as representación por acumulación.

Specifically, since politics in Puerto Rico evolved into a two-party system in 1968, following 28 years of PPD dominance, the two major parties have nominated six at-large candidates each for both the Senate and the House of Representatives in every election (from 1952 to 1968 PPD nominated seven at-large candidates to each legislative body). In order to guarantee each candidate has an equal chance of being elected, parties vary the order in which candidates are listed on the ballot in each of the island’s electoral districts – precintos in Spanish – 110 in total since 2012 (to be increased to 114 in 2024); parties assign candidates a set of electoral districts known as a legislative bloc – bloque legislativo in Spanish – in which they are placed at the top of their respective party lists, and as such automatically receive straight votes cast for their party, which have constituted the majority of ballots in every election; party ticket votes with votes cast for other at-large candidates from the same party are considered split votes. (See sample ballot.)

From 1972 to 2012, PNP and PPD elected four to six at-large candidates each in both the Senate and the House. Nonetheless, over the years an increasing number of voters cast either split ballots or bypassed party tickets altogether and voted for candidates only – in Spanish voto por candidatura – and PIP, which nominated single at-large candidates for each body from 1984 onward, was able to tap into that vote to secure seats for its at-large candidates in nearly every election during that period (the party won no at-large seats in 2008 and only a Senate at-large mandate in 2012). Even so, as recently as the 2012 election 81.27% of valid legislative ballots were straight votes, and the overall impact of split/candidacy votes was comparatively limited.

However, in 2016 split/candidacy voting soared from 18.73% to 35.62% of the legislative ballot valid vote, and the main beneficiary was José Vargas-Vidot, who became Puerto Rico’s first-ever independent candidate to win a legislative seat, securing a Senate at-large mandate and topping the poll as well. In fact, his vote total was made up entirely of split/candidacy ballots, since no provision is made to cast a straight vote for an independent candidate, and his victory reduced PPD to three at-large Senate seats (with PIP winning one and PNP the remaining six).

Although PNP returned to power in the 2016 election, the party polled its worst result up to that point in the gubernatorial election, and PPD its second-worst, with the major parties’ combined share of valid votes declining from 95.56% in 2012 to 80.67%. Meanwhile, independent candidate Alexandra Lúgaro won a respectable 11.13% of the vote, and went on to found MVC in 2019. By then, the marked decline of PPD in 2016, along with the emergence of Lúgaro’s new party and the success of the Vargas Vidot independent candidacy called into question the wisdom of nominating six at-large candidates in 2020, when five might have a better chance of securing election. To that end, a proposal was made to the party leadership, which however was rejected after a former but still highly influential party leader spoke against it, insisting that “too much was in play,” that nominating five at-large candidates instead of six could be perceived as an admission of weakness, and prevent the party from winning an overall majority in either or both houses of the Legislative Assembly.

(In the interests of full disclosure, I should note I collaborated in the proposal calling for the nomination of five PPD at-large candidates, and was present at the party leadership meeting in which it was discussed and turned down.)

As it was, MVC anticipated it would fare at least as well as Lúgaro did in her independent gubernatorial run in 2016, and nominated two at-large candidates for both legislative bodies, using Lúgaro’s 2016 vote as the basis for the corresponding legislative blocs. Meanwhile, PNP and PPD ran their usual six-candidate slates for both the Senate and the House, PIP and PD nominated single candidates for both houses, and Sen. Vargas-Vidot ran for re-election. However, although every MVC, PIP and PD at-large candidate as well as Sen. Vargas-Vidot was successful in the 2020 election, PNP only won four at-large seats in the Senate and five in the House, while PPD won just two at-large seats in both houses, as detailed in the following table (full results are available on my Elections in Puerto Rico website):

	House		Senate
Party	%	Seats	%	Seats
PNP	33.84	5	33.37	4
PPD	36.03	2	31.27	2
PIP	10.56	1	11.29	1
MVC	12.83	2	10.99	2
PD	6.73	1	7.33	1
Ind.	–	–	5.76	1

In both the Senate and House at-large races, the combined percentages obtained by all six PPD candidates – 31.27% in the Senate and 36.03% in the House suggested that while securing six of eleven seats might not have been a realistic goal, the party should have done better than winning just two seats (18.18%) in each case. However, an additional complication was that PPD candidates fared quite unevenly, although it should be noted these disparities weren’t due to the makeup of the PPD legislative blocs; instead, the large number of split/candidacy votes – which increased to 40.15% of all valid legislative ballots in 2020 – made the legislative bloc arrangements far less meaningful, as many voters backed candidates who weren’t assigned the top spot in their electoral districts. The uneven performance of PPD at-large candidates on account of split/candidacy votes was particularly evident in the House of Representatives, as shown in the following table:

Candidate	Straight	Split/Cand.	Total
Héctor Ferrer	48,750	93,100	141,850
Jesús Manuel Ortiz-González	52,591	19,359	71,950
Enid Monge	52,031	6,474	58,505
Keyliz Méndez-Torres	48,416	8,827	57,243
Yaramary Torres	48,348	6,774	55,122
Gabriel López-Arrieta	45,817	4,838	50,655

In fact, Ferrer polled 73,213 votes outside his assigned legislative bloc – a figure which by itself exceeded the vote totals of the remaining five PPD House at-large candidates.

Among PPD Senate at-large candidates, the split/candidacy vote total disparities weren’t as marked, but even then the two winning candidates had the largest totals on that column:

Candidate	Straight	Split/Cand.	Total
Juan Zaragoza-Gómez	52,591	21,218	73,809
José Luis Dalmau-Santiago	52,031	19,865	71,896
Aníbal José (Jossie) Torres	45,817	15,385	61,202
Brenda López-De-Arrarás	48,348	11,613	59,961
Ada Álvarez-Conde	48,750	8,470	57,220
Luis Vega-Ramos	48,416	6,234	54,650

Another factor at play is that many voters don’t understand the workings of SNTV, and for one reason or another cast their votes under the incorrect assumption they can vote for up to six candidates in each legislative body – as if it were a Multiple Non-Transferable Vote (MNTV) election – instead of only one. Ballot design might be at play, as at-large races are the only instance in which the number of nominations doesn’t go hand in hand with the maximum number of votes a voter may cast, but the fact is that both PNP and PPD actually use MNTV in their internal party primaries to choose at-large nominees, and many voters – sometimes including even seasoned political analysts – mistakenly assume that system is also in place for general elections, ballot instructions to the contrary notwithstanding.

The introduction in 2016 of vote counting machines providing detailed overvote and undervote statistics highlighted the confusion surrounding the way in which at-large legislators are chosen. Specifically, although overvoting in at-large legislative races, while somewhat reduced in 2020 (due to the efforts of how-to-vote campaigns from civic groups), is still significantly higher than in district races chosen by plurality voting, where it remains negligible (even though the vote counting machines are supposed to warn the voter about overvoting and undervoting). Besides overvoting, some PNP or PPD voters back third-party or independent at-large candidates under the assumption they are giving just one of six votes to such candidates, with the remaining five votes they think they have (but really don’t) going to the rest of their preferred party slate, when in fact they are giving their sole vote to a candidate outside their party.

Another issue in at-large legislative races is the so-called invasion of electoral districts, in which major party at-large candidates actively campaign for votes in electoral districts that don’t belong to their assigned legislative bloc, fully aware they are taking away votes from fellow party candidates. Suffice it to say this is a very sensitive matter, and there’s no information to confirm whether or not it took place in 2020.

It should also be noted that the 2020 general election in Puerto Rico was carried out under a new electoral law imposed unilaterally by PNP just months before the election, over the objections of opposition parties. One of the more controversial provisions of the law granted the ruling party near-absolute control of the Elections Commission, which had been run on a power-sharing basis among registered parties since a major reform in 1983 (following the disastrous 1980 election, in which the Elections Commission had been under PNP’s full control as well). While there were few issues with in-person polling, either election day or advanced, the tally of the bulk of advance/absentee votes in special polling station 77, mainly domicile and mail-in votes, accounting for about one-eight of all ballots, proved to be extremely problematic from the beginning, not least because its ten-fold expansion under the new electoral law overwhelmed the agency. To this day the exact number of voters requesting advance ballots in 2020 remains unknown, the results of polling station 77 are riddled with discrepancies – often quite significant – in every electoral district, and some believe the cited issues might have adversely affected PPD in the at-large contests. However, PNP leaders insist there is nothing wrong with the electoral law, and to date have resisted attempts to reform it ahead of the 2024 general election.

At any rate, the decision by PPD leaders to nominate six at-large candidates in 2020 for both houses proved to be a monumental blunder, which had the effect of exposing the very weakness that party leaders desperately wanted to conceal; in practical terms it resulted in a Senate in which no party had overall control of a legislative body for the first time since 1940; PPD won a plurality of Senate seats and an overall majority of one in the House.

But would PPD have been better off by nominating five at-large candidates instead of six? According to a Senate-only, post-election simulation I ran with five candidates, the answer is affirmative: at least four candidates, and possibly all five would have been elected. Even so, it’s by no means certain PPD will nominate in 2024 five at-large candidates instead of six, not least because many party leaders remain in denial about the major changes in voting trends that took place in 2016 and 2020, insisting they are nothing more than a transient phenomenon. That said, it’s worth remembering that in Spain it took several years for PP and (to a lesser degree) PSOE leaders to finally come to terms with a similar shift away from two-party dominance after 2015.

Finally, from time to time some PNP and PPD leaders have called for the elimination of at-large legislative seats, thus resulting in a Legislative Assembly elected in its entirety by plurality in districts. However, such calls appear to be motivated by a desire to get rid of independent and third-party legislators; that such a move could backfire in future elections in which either PNP or PPD, or both might no longer be major parties appears not to have been considered at all. And while leaders of both parties might scoff at such prospects in the here and now, they cannot be ruled out altogether in the long run, all the more so since as a result of their steady decline the two major parties appear to be increasingly dependent on the support of old voters, much like CDU/CSU and SPD in Germany’s 2021 Bundestag election. In fact, in the 2020 general election PNP and PPD won between themselves 87.71% of the advance/absentee vote in the gubernatorial race, 85% of which came from voters aged 60 or older; but among the younger election day voters they polled just 60.68% between themselves. All the same, doing away with the at-large legislative seats would require amending the Constitution of Puerto Rico, and for the time being it does not appear such an amendment – which would have to be approved by voters in a binding referendum – will be forthcoming.

Election indicators in Taiwan, SNTV era

I noticed that the always handy Election Indices file maintained by Michael Gallagher on his Electoral Systems page did not include Taiwan’s SNTV era of competitive elections (1992-2004). I needed the indicators for something I am working on. It just so happened that I had the candidate-level data for those years (thanks to Nathan Batto sharing them some years ago for another project). So I set out to calculate some key indices. In the off chance anyone needs them, here they are.

In the table below, “D2” is Gallagher’s “least squares” index of disproportionality (as a share, rather than percentage), “Nv” is the effective number of vote-earning parties, and “Ns” is the effective number of seat-winning parties.

year	D2	Nv	Ns
1992	0.0465	2.64	2.227
1995	0.04137	2.948	2.541
1998	0.0641	3.224	2.508
2001	0.04701	4.266	3.494
2004	0.03828	3.812	3.265

I calculated these by considering every independent candidate–and there are many of them, although not many won seats–as a separate “party.” This is the only really proper way to do these indices–especially for a purely nominal system like SNTV–if one has the data at candidate level, and in the absence of any information as to groups of these candidates being de-facto parties.

Values for Ns and Nv for these elections can be found in Bormann and Golder (as “enpp1” and “enep1”, respectively). However, my Nv values are somewhat higher because the index values in Bormann and Golder’s dataset would have been estimated from aggregated votes of “others” (including “independents”). That is, they do not take all others/independents to be one party (as is sometimes erroneously done by others), but without the candidate-level data, any such estimate could fall short of the method I am using, based on complete data on every candidate’s votes and formal party affiliation, if any. My calculations for Ns match theirs for enpp1 almost exactly, as they should, given that relatively few independents won seats (43 over the 5 elections).

Hungary 2022 – how biased an electoral map?

Hungary’s 2022 election resulted in an overwhelming victory for the incumbent Fidesz party, led by Prime Minister Viktor Orban, against a broad opposition coalition, led by Peter Marki-Zay, comprised of liberals, social democrats and the nationalist Jobbik party. Orban’s twelve-year-long government has been the focus of international attention over its nationalist policies and weakening of democratic institutions.

One of the earliest initiatives of Orban’s government was a set of amendments to the electoral law in 2011. While Hungary retained a mixed-member system, the three-tier system introduced in 1989 was replaced with a two-tier system. The size of the legislature was cut drastically, from 386 to 199. This involved a redrawing of the single-seat districts, as the number of these districts fell from 176 to 106: the two-round system previously used for these seats was replaced by first-past-the-post.

The process of drawing new electoral boundaries and introducing a new electoral system represents an excellent opportunity for a governing political party to entrench its own advantages. Fidesz had a completely free hand in that process, owing to its two-thirds constitutional majority. So, what does the electoral system look like?

Based on the 2022 results, there is a clear negative relationship between Fidesz vote share and registration numbers. Interestingly, this is driven by very high registration in the electoral districts of suburban Pest county, which is the cluster on the right of the plot: Budapest, the opposition’s stronghold, has roughly average enrolment.

But what does this mean in terms of actual election results? In order to examine this, I simulated a set of uniform swings¹ between Fidesz and the Alliance for Hungary. The below plot shows seat totals in the single-seat districts at different vote shares for both the opposition alliance and Fidesz (vote shares for the other parties were kept constant).

The vertical line shows where the two parties tie – approximately 44% of the vote each, or a swing of 7.8% towards the opposition. At this level, Fidesz would win 56 single-seat districts to 50 in total for the opposition. In order to win a majority of the single-seat districts, the Alliance would need approximately 46% of the vote to 43% for Fidesz.

Of course, the list seats need to be taken into account. The below plot shows the number of total seats each party would have won with the same vote shares as in the prior plot. The vote share for the other parties is held constant, and I assume that the nationalist My Homeland party would have held onto its 5% of the vote and 6 seats, and that the German minority would have elected its single member under the special procedure for ethnic minority parties.

The effect of the list seats is fairly minor. A tied vote would give the Alliance 91 seats to 100 for Fidesz, the slimmest of absolute majorities. Fidesz loses this majority at a fractionally lower share of the vote. However, for the opposition to win a plurality, they need about the same 46-43 vote share as they need for a majority of the single-seat districts, and to win the 100 seats required for an absolute majority they need 47% of the vote to 42% for Fidesz.

How serious is this effect? How does it compare to other jurisdictions? One method which has received some use in the (inevitably US-centric) gerrymandering literature is the ‘efficiency gap’, which calculates the difference between the number of wasted votes for the two major parties, as a proportion of all votes. I calculate the efficiency gap at this election to be 5.2%, again ignoring votes for minor parties. According to the paper laying out the efficiency gap measure, this gives Hungary a map roughly as biased towards Fidesz as the maps in Minnesota or South Carolina were towards the Republican Party, or the map of California was towards the Democratic Party. Hungarian bias, however, does not seem to be as strong as that in North Carolina or Florida.

Hungary’s 2012 electoral map, then, provides Fidesz with a modest but meaningful electoral advantage, only slightly ameliorated by the list tier. Nonetheless, the opposition at this election achieved a vote share well short of what would be needed to win a majority. Unlike in Poland, the role of the electoral system in the installation of this government has been seemingly fairly minimal.

¹ Note that ‘swing’ is here defined as percentage points subtracted from Fidesz’s (or the opposition alliance’s) vote and added to the opposition alliance’s (or Fidesz’s) vote share. I believe this is the Australian definition, as opposed to a British one that (I think) averages the two figures.

Did Thailand’s parliament just vote to switch to MMP?

Via the Nation from Thailand, it seems that a joint sitting of parliament has voted to adopt mixed-member proportional representation (MMP) instead of a mixed-member majoritarian (MMM) system. The headline reads, “Parliament votes for party-list MP calculation method to be divided by 500.”

The meeting, which comprised senators and members of the House of Representatives, chose whether to divide the party-list MP calculation by 500 or by 100. The first choice won with 354 votes in favour, 162 votes against, 37 abstentions and four no votes.

The meeting rejected the use of 100 to calculate party-list seats, which is the current method, by 392 votes to 160, with 23 abstentions and two no votes.

This is a somewhat awkward way of stating the choice between MMP or MMM, but it works. Let’s take a couple of examples to demonstrate. Suppose there are 36 million valid votes, and there is a party with 6 million votes, or one sixth. If the division is by 500, then a simple quota for a seat is 72,000 votes. This party has 83 full quotas (6M/72k=83, discarding the fraction, 1/3). If instead the division is by 100, then a simple quota is 360,000 votes. Our hypothetical party with six million votes now has 16 quotas.

The first scenario logically implies MMP. The party might have won, let’s say, 30 nominal seats (single-seat district contests in which the plurality wins the seat). It is entitled to 83 seats. So it gets 53 list seats, to bring its nominal total of 30 up to its full share of 83 quotas out of 500. It is thus proportionally represented.

The second scenario logically implies MMM. Again, let’s say it has 30 single-seat wins. Its 16 quotas mean 16 list seats, which it will add to its 30, for a total of 46 seats. This is a little short of ten percent (9.2%, to be precise). It is under-rerepsented.

Note that in the first scenario, it has one sixth of the total 500 seats. In the second it has one sixth of the 100 list seats. This is precisely how MMP vs. MMM works.

Now let’s take a somewhat larger party, with nine million votes. If the division is by 500, it has 125 full quotas. The hypothetical vote total has been chosen to roughly reflect the For Thais Party (PPT) in 2019, which actually won 7.8 million votes. That made it second largest party in votes, but it won the most nominal seats, 136. So let’s give it in our hypothetical that number as well.¹ It is over-represented already! It is entitled to 125, based on full quotas with the denominator of 500. In other words, it has 11 overhangs. It will keep these, but it will get no list seats. Even though the system is MMP, the other parties that need compensation from the list seats will remain somewhat under-represented as a result.

If instead the division is by 100, this party has 25 full quotas. It thus wins a quarter of the 100 list seats, and adds these to its 136 nominal seats, for a total of 161. This is 32.2% of the total, under the hypothetical MMM system. It is over-represented, given it had 25% of the vote. It was also over-represented under MMP, as we saw in the outcome with division by 500. However, in that case, its seat percentage is 136/500=27.2%, which is much closer to its vote percentage than the MMM example.²

The Nation article concludes with this puzzling note:

However, Thammasat University public law specialist Prinya Thaewanarumitkul expressed concern on Facebook on Wednesday that the new formula would result in the number of list MPs exceeding the number allowed by the constitution.

No, it would not. Or, rather, it would not have to do so. The public law specialist seems to be assuming the overhangs would be compensated, by adding further list seats. But MMP does not necessarily do this, and if the list seats are restricted to 100, it will not generate more than 100 list seats for the simple reason that it can’t. The “extra” implied seats do not exist, and we simply reduce the total compensation potential when there are overhangs in the nominal tier. You keep 100 list seats, but the parties that have not already won at least their full quotas worth in the nominal tier get fewer of the list seats. This can be accomplished by recalculating the quota. In the scenario here, assuming those 11 overhangs for the party with nine million votes are the only overhangs the election produced, the quotas would be recalculated with a denominator of 500-11=489. Now parties get a list seats for each 73,619 votes they have earned (instead of 72,000). Our party with the six million votes is now entitled to 81 total (again, discarding fractions) rather than 83. And other parties–not considered in these illustrations–get similar reductions in what would have been their entitled final shares had there been no overhangs generated by parties that got over-represented due to success in the nominal tier.

In conclusion, it seems Thailand has chosen to shift to MMP. However, it will not be a highly proportional version of MMP, given that 20% of total seats in a compensation tier is on the small side. It is still MMP, and need not permit expansion of the list tier in order to so qualify.

I should also not that this was the second reading of the bill, not final passage.

____

Notes

1. In the 2019 election, there were 350 nominal seats and 150 list, but rather than weight the seats to totals out of 400 nominal seats, I will just go with the raw numbers of seats PPT won in 2019.

2. In all these scenarios, for simplicity, I have ignored remainder seats, which result from the fractions that are ignored after seats are assigned via full quotas.

The French thresholds for runoff participation

This week is the inter-round period in the French two-round assembly elections. The first round was on 12 June. The French way of electing members of the National Assembly is not top-two majority-runoff, like the country’s presidential elections (or most elections in California). Rather, it is majority-plurality. That is, it is possible to have more than two candidates in the second round in any given single-seat district, and when this happens, the winner is the one with the most votes, even if it is less than 50%+1.

In any system within the broader family of two-round systems, there need to be threshold provisions for both (1) determining whether a runoff is required, and (2) determining who is eligible to participate. Under typical majority runoff, the provisions are (1) 50%+1 in the first round, or else (2) there must be a second round in which only the top two may participate.¹

France follows the same first provision–with a caveat that I will get to. A majority is required at the first round. If that does not occur, the rules are that any candidate with votes equivalent to at least 12.5% of the registered voters in the district may stand in the runoff. That is, an eighth of the electorate, not an eighth of the votes cast. This is an important distinction. There is a further twist on the runoff-participation rules: If there are not two candidates who clear the 12.5%-of-registered threshold, then the top two go to the runoff anyway.

Here are some examples. In the district of Paris no. 2, the Ensemble (pro-Macron) candidate had the first-round plurality, with 35.66%, followed by the candidate of Nupes (pro-Mélenchon) on 27.27%. The third candidate, from the Republicans (LR, traditional right) has 18.23%. So is it a three-way race? Non. This candidate’s votes are a mere 10.63% of the total registered voters. Hence it is a top-two runoff.

Then we have Paris no. 15. Here, the leading candidate (from Nupes) has 47.31% of the votes cast. Pretty close to a majority, but not good enough under criterion #1 (50%+1 or else runoff). However, no other candidate cleared 12.5% of the registered voters. So maybe a runoff is not required after all. Not so fast. There needs to be a runoff if the plurality candidate did not win a majority of votes cast. Thus the candidate with the second highest vote total (from a left party unaffiliated with Nupes) advance to a runoff despite having won only 9.44% of the registered electorate in the first round. (This candidate won 17.87% of votes cast, but for qualifying purposes, this is not even relevant.)

There is, as I mentioned, a caveat on the first criterion, that a majority in the first round obviates the need for a second. To be elected in the first round, the leading candidate’s vote total also must be greater than 25% of the registered electorate in the district. There is at one prominent case where this comes up in the current election–prominent because it involves a famous politician. The district is Pas-de-Calais-11. The leading candidate is Marine Le Pen (you’ve probably heard of her–leader of the National Rally (RN)). She won 53.96% of the votes. Good for her; she won a majority! However, her votes amount to just 22.52% of registered voters. As a result, she must face a second round against another Marine, Tondelier of Nupes, who qualifies despite a vote total that is only 9.79% of the registered electorate.

It would be strange to have a candidate win a majority in the first round and yet lose the runoff. It probably won’t happen. On the other hand, if the opposition to her could mobilize and vote for the Nupes Marine, it is theoretically possible. Looking at the rest of the field, we find an Ensemble candidate in third place with 5.15% of registered electorate and then no other candidate over 1.5%. It would be a tall order, needing a whole lot of abstainers to turn up. But the rules of the French two-round system create the opportunity.

I thank Giacomo Benedetto and Steven Verbank (both via Twitter) for the above examples and clarifications on rules.

Just for fun, I was clicking on districts somewhat randomly. (You can play the game, too, by going back a step or two in any of the links for the three examples above.) It seems that the low turnout might be responsible for quite a few districts being like the second example–a candidate qualifying for a runoff despite being below 12.5% of the electorate in the first round. I do not know how common this or a majority but not 25% of registered voters has been over the course of the Fifth Republic’s history (dating to 1958, with then exception of a list-PR system in 1986). It is also noteworthy that there are eight three-way runoffs this year (compared to just one in 2017). If anyone happens to have a list of them, please post in the comments.

Randomly, I will now mention a few cases that looked interesting to me. Yonne no. 1: The top three candidates (Nupes, RN, and LR) have vote percentages of 24.25, 23.92, and 22.61. Only the first one has more than 12.5% of registered, and the third narrowly missed it (having 11.50%). I have no idea how often a candidate might ever have won from third place in a three-way runoff in France. If there were to be such a case, this would seem to be a promising opportunity–a mainstream right candidate against the left and far right, who combine for less than a majority of votes cast. However, the LR candidate came up short of making it a three-way.

Another similar case is Moselle no. 5: Top three candidates from RN, LR and Ensemble, with vote percentages of 25.88%, 24.53%, and 23.48%. Tight three-way race. But third did not clear 12.5% of the registered electorate–in fact, the leader had only 10.35%–and so it can be only a two-way.

Another majority-but-runoff case in Bouches-du-Rhone no. 4: Nupes leader has 56.04% of votes cast, but only 21.36% of registered voters. So the second candidate, from Ensemble, who won won only 14.88% of votes (and 5.67% of the electorate) advances to a runoff.

I probably could do this all day. But I probably should not.

One more thing before I hit “publish.” This collection of candidate statements and photos for every candidate in every district is an incredible resource! It is interesting that many of them are pictured next to their party’s presidential candidate (did someone say presidentialization?), and I also like how some of them show a little photo of their replacement candidate. Every candidate is elected with a substitute, who takes the seat if the principal vacates it for any reason during the term. Such reasons include appointment to an executive post, as France does not allow simultaneous service in the assembly and executive.

1. Or sometimes–including French presidential elections–the top two remaining if one of the initial top two has bowed out for whatever reason.

Ontario 2022

Ontario’s election on 2 June saw another Progressive Conservative seat majority on barely over 40% of the votes. The party, led by provincial Premier Doug Ford, barely increased its vote percentage from 2018, when it won 40.2%; this time the tally is about 40.8% (pending final count). Its vote total actually went down, because it was the lowest turnout in the province’s history. Yet it will have 83 of the 124 seats, whereas in the 2018 election it won 76.

For those keeping the stats, that would be a bare two-thirds majority (66.9%), and an advantage ratio (%seats/%votes) of 1.64. That is very much on the high side, even by the standards of FPTP with multiparty systems.

The main shifts in vote percentages were among the two largest opposition parties. The Liberals improved from 19.4% to 23.9%. The payoff in seats was minimal: the party won 8 seats this time, 7 last time. The NDP performed especially badly, going from 33.3% of the vote in 2018 to 23.7%. However, even though the NDP’s votes are marginally behind the Liberals’, the NDP will continue to have more seats–a lot more–with 31 (down from 40 at the last election). Yes, FPTP in multiparty systems!

Ontario objectively needs to shift to a proportional system. It is not as if the province has not had the opportunity to do that before.

Kosovo electoral system note

In light of our previous discussion about how Kosovo’s electoral system challenges our usual notion of what a “district” is, this note from Michael Gallagher‘s Election Indices is interesting.

I am not sure Michael has made the correct choice here–minority representation provisions are part of the electoral system, after all–but I am also not sure this is incorrect. The system really is challenging to classify and quantify. I note in particular his decision to count its assembly size–and therefore, its district magnitude, given there are no district divisions unless we count the ethnic reservation/guarantee as separate “districts”–as 100 before 2014 but as the full 120 since then. Here, for reference, are the indices he reports in the main part of the document:

The unusual nature of the system is what results in the effective number of seat-winning parties (N_S) sometimes being higher than the effective number of vote-earning parties (N_V), something that is otherwise rare, and certainly should not happen in a single-district nationwide proportional system. As I noted in the earlier discussion, in 2021 it was even the case that a single party list won a majority of votes, but did not win a majority of the full 120 seats. Because I assume all legislators are equal, and that a government needs a majority of the 120, and not just the 100, I think it is incorrect to treat assembly size as not including the 20 ethnic representatives. Gallagher’s data from 2014 do include them, and I think that should be the case for the earlier years as well.

The question of how to calculate the indices is indeed a vexing one. Gallagher very helpfully explains his choices and what would change if we use a different assumption about what “counts.” This allows the researcher using his valuable resource the ability easily to make his or her own decision. But this researcher still is not sure which decision to make with respect to this system!

I am not comfortable with the idea of counting these various ethnic guarantees as additional “districts” even though I see the case for it (which Henry made in a comment to the previous planting). That lack of comfort is not solely because these “districts” overlay the main one. That is, after all, the case of the Maori districts in New Zealand (each of which encompasses the territory of several general electorates). For that matter, it is also the case with any two-tier system. Rather, the conceptual difficulty is that a given party list may win seats in either component of the system–the general 100 or the set-aside for their ethnic group–if they qualify for additional seats beyond their ethnic group’s reservation/guarantee.

However we conceptualize the system, I believe all these parties should be taken into account in calculating the effective number of parties (votes and seats). The question of whether we count them for deviation from proportionality is less clear to me.

I think I need to count this as a non-simple system (by the criteria used on Votes from Seats), giving us a unique case of what could be called a single nationwide district PR system that is nonetheless complex. For countries whose electoral system has just a few ethnic set-asides (like Colombia or Croatia), I tend to ignore the reserved seats when thinking of whether they are “simple” districted or national-district systems. But when such seats are a sixth of the total, they are clearly a complicating feature, as the unusual outcomes reveal.