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 (NS), effective number of vote-earning parties (NV), 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 Party2018 Bloc2022 Party2022 Bloc
NS4.322.905.582.40
NV5.103.366.623.44
D2 (%)3.985.027.3011.74

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 NS=(MS)1/6, and using the numbers reported earlier for effective seat product, we should expect the 2018 system to yield NS=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.

yearD2NvNs
19920.04652.642.227
19950.041372.9482.541
19980.06413.2242.508
20010.047014.2663.494
20040.038283.8123.265

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 (NS) sometimes being higher than the effective number of vote-earning parties (NV), 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.

St Kitts and Nevis 2000–Crazy result

Given my sudden fascination with small assemblies, I was poking around in election results from St Kitts and Nevis, a Caribbean sovereign state with a population of just over 52,000. With 11 elected members, its assembly certainly counts as small. The 2000 election is really something. Look at the national result:

PartyCodeVotes% votesCandidatesSeats
St. Kitts and Nevis Labour PartySKNLP11,76253.85%88
People’s Action MovementPAM6,46829.61%80
Concerned Citizens MovementCCM1,9018.70%32
Nevis Reformation PartyNRP1,7107.83%31
Total Valid Votes21,841100%2211
Source: St Kitts and Nevis Election Center, Caribbean Elections.

The second largest party got no seats, while two parties with less than 10% each won a seat or two. This is a first-past-the-post system. The problem the PAM had was it came in second in all eight seats it contested, i.e., every district on the island of St. Christopher (none were close). The advantage the CCM and NRP had is they run only on the island of Nevis, which has three district. Here are the district results.

ConstituencyRegistered votersSKNALPPAMCCMNRPValid Votes
St Christopher #14,5191,7881,1492,937
St Christopher #25,6522,0111,5073,518
St Christopher #32,5961,2353771,612
St Christopher #42,4301,0137351,748
St Christopher #52,3288697691,638
St Christopher #62,5711,6131191,732
St Christopher #72,8741,4414791,920
St Christopher #84,3251,7921,3333,125
Nevis #92,9248087961,604
Nevis #101,517555184739
Nevis #112,4305387301,268
Total34,16611,7626,4681,9011,71021,841
Source: Same as for first table.

Note that there is some pretty serious malapportionment here, as well. Nevis constituencies have many fewer voters than St. Christopher constituencies. In fact, the three Nevis districts together have only about 1.2 times the population of the most populous St. Christopher district.

So what should we have according to the Seat Product Model? The seat product is 11 (magnitude of 1, times assembly size of 11), so the effective number of seat-winning parties should be 1.49. In this election it was actually 1.75. That’s actually not a terrible miss! But in most elections it has been considerably higher than that–as high as 3.90 in 2015. So just for fun, a quick look at that one:

PartyVotesvotes% votesCandidates
St. Kitts and Nevis Labour PartySKNLP11,89739.27%83
People’s Action MovementPAM8,45227.90%64
People’s Labour PartyPLP2,7238.99%21
Concerned Citizens MovementCCM3,95113.04%32
Nevis Reformation PartyNRP3,27610.81%31
Total Valid Votes30,299100%2211
(Last column is seats won, but the heading did not copy over.)

This time, the PAM benefitted greatly! It is in a clear second place in votes, yet won a plurality of seats. Not a majority, however. According to Wikipedia, there were alliances. But even at the alliance level, there was a plurality reversal: “The outgoing coalition (SKNLP and NRP) secured 50.08% of votes but got only 4 seats, the winning coalition (PAM, PLP and CCM) won 7 seats with only 49.92% of votes.” Oh, cool: Another case of pre-electoral alliances! The effective number of alliances was just 1.86.

And at the district level:

ConstituencyRegistered VotersSKNLPPAMPLPCCMNRPValid Votes
St. Christopher #15,0361,7271,7313,458
St. Christopher #24,7401,7581,6603,418
St. Christopher #33,2651,3481,0762,424
St. Christopher #43,1661,2161,2522,468
St. Christopher #53,1078841,2452,129
St. Christopher #62,8231,9692002,169
St. Christopher #73,1918671,6472,514
St. Christopher #85,7532,1282,3644,492
Nevis #96,1272,0331,7153,748
Nevis #101,3937543061,060
Nevis #113,5841,1641,2552,419
Total42,18511,8978,4522,7233,9513,27630,299

We might not expect regionalism in such a small country, with a small assembly. But the party preferences of the two islands obviously are genuinely different (and the PLP is “regional” in that it contested only two districts on St. Christopher); yet the parties aggregate into alliances for purposes of national politics.

The malapportionment is still noteworthy–look at the small population of Nevis 10. However, one of the other two districts is now the most populous in the country, quite unlike in 2000.

Final point: Its population may be small, but according to the cube root law St Kitts and Nevis should have an assembly more than three times what it actually has: 37. If they were proportional to registered voters, Nevis would be allotted nine of those 37 seats. It currently has 3 of the 11, so 27%, so quite close to its population share, unlike in 2000 when it was overrepresented. Making the seats allocated by island more easily fit population balance in itself would be a good argument for increasing assembly size, but an even better argument would be making anomalous results like the two elections shown here less likely–even if they insist on sticking with FPTP.

Kosovo 2021: A single-district electoral system that violates the rank-size principle

In the previous planting asking whether free-list PR violated my own definition of a “simple system, I mentioned the criterion of avoiding violation of the rank-size principle in allocation of seats to votes within district (see footnote 2). I later happened upon a major example of violation of the rank-size principle: Kosovo in 2021!

It is a single district of 120 seats, but per Wikipedia:

The Assembly had [under the Constitutional Framework] 120 members elected for a three-year term: 100 members elected by proportional representation, and 20 members representing national minorities (10 Serbian, 4 Roma, Ashkali and Egyptian, 3 Bosniak, 2 Turkish and 1 Gorani). Under the new Constitution of 2008, the guaranteed seats for Serbs and other minorities remains the same, but in addition they may gain extra seats according to their share of the vote.

The result of this is that there are parties with as much as 2.5% of the votes but no seats (there is also a 5% legal threshold for non-ethnic parties), and parties with as little as 0.14% who have seats when somewhat larger ethnic parties do not. For instance, the United Roma Party of Kosovo has a seat with 1,208 votes while the Innovative Turkish Party, which I presume is an “ethnic” party, with 1,243 votes, has none. That would be because the two set-aside Turkish seats were won by the Turkish Democratic Party of Kosovo, which had almost 6,500 votes (0.75%).

Perhaps it is not a “single district” and we should think of each ethnic group’s set-aside representation as a distinct district in addition to the general constituency. But that is certainly not how I generally understand “district.” In any case, there is nothing “simple” about the provision or its impact on outcomes, particularly regarding the rank-size criterion.

In addition, these provisions result in the odd case of a party with a majority of the vote not getting a majority of the seats, which is certainly unusual for a proportional representation system!

Is free-list PR a “simple” electoral system?

This seems like a trick question. Of course, free-list has all sorts of complex features. In such a system, the typical rules are that any voter may cast up to M votes (M being the district magnitude) for individual candidates, even across different lists (panachage). A vote for any candidate on a list counts as a vote for that list for purposes of determining proportional seat allocation across lists, as well as for the candidate in competition among other candidates on that list.

However, this system handles votes and seats for lists just like any other list-PR system: It is designed to allocate seats to lists first, and only then to candidates. It thus is “simple” on the inter-party dimension, unlike SNTV or MNTV or STV (where candidate votes do not count towards aggregate party vote totals and seats are allocated based only on candidate votes).

My general definition of a “simple” electoral system is one that is a single-tier, single-round, party-vote system. The free-list could be said to violate that last part of the definition, in that “party vote” maybe should mean a single party vote per voter. My instinct is to keep free list in, because it remains “simple” in terms of how it processes the votes across lists. But I could be convinced otherwise, given that effectively every voter can vote for more than one list–a “dividual vote” in Gallagher’s terms.1

In Votes from Seats, Taagepera and I kept at least three free-list systems in our dataset: Honduras (since 2005), Luxembourg, and Switzerland. The issue came back to my mind because of my consideration of including some smaller countries and non-independent territories in a dataset for some further analysis of key questions. One of the smaller countries that could be added to the data is Liechtenstein, which I believe uses a free-list PR system. My gut says “yes, include” but now I wonder if we already violated our own criteria2 in having those free-list systems in the prior analysis. To be clear, none of our results would be changed if we had dropped them.3 It is just a matter of consistency of criteria.

Questions like this always nag comparative analysis, or science more generally. What things are part of the set being analyzed? It is not always clear-cut.

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  1. Note that there is no question regarding standard open-list PR: Even if there are multiple candidate preference votes cast per voter, as in Peru, only a single list vote is registered per voter.
  2. In fact, on p. 31 of Votes from Seats, we say “Only categorical ballots and a single round of voting are simple, by our definition.” A free-list ballot is dividual and thus not categorical. However, the reason we give for limiting the coverage to categorical ballots is that “other ballot formats… may violate a basic criterion for simplicity in the translation of votes into seats: the rank-size principle” (emphasis in original). For example, the party with the most aggregate votes in a district may not have the most seats allocated in the district (or at least tied for most with the second-most voted party). This violation of the rank-size principle can occur with SNTV, STV, and MNTV, but as noted above it can’t occur in free-list PR (per my understanding, anyway). I note that in a later work, Party Personnel, my coauthors and I seem to adopt a stricter definition. On p. 53 of that book, we say that simple means “a voter votes once, and this vote counts for the entire party list of candidates.” Yet the conceptual point there is somewhat different, in that we are referring to “simple vote” not simple electoral system, and we remove open-list PR from the standard of simple vote because they permit differentiation of candidates within a list in the same district. But as for the vote counting for the entire list, free list still meets that part of the criterion. (A reminder that “voting system” is not a synonym for “electoral system”!)
  3. Although I did not think of this possible issue with free lists at the time, I definitely ran robustness-check regressions with Switzerland dropped. I did so mainly because of its multiparty alliance feature, which also is a complex feature for reasons discussed in the book (mainly with reference to Finland and Chile). Doing so did not affect the results, so we left the case in. There are not enough elections from the other free-list cases, nor are they observably different on our outcomes of interest, that they could affect results. (Switzerland is observably different–far more fragmented than expected for its seat product, and that seems to be mostly due to alliances, even above the impact of its ethnic fragmentation–see p. 269 of Votes from Seats. But the inclusion or exclusion fo the case is immaterial for the overall results.)

Small assemblies in non-independent territories

I am going to do a little crowd-sourcing here. What do people think is a reasonable way to define “autonomous enough” to include a territory in a set of small assemblies worthy of comparative analysis alongside independent nations with small assemblies?

That is, there are various countries with very small assemblies that are recognized as independent states, such as St. Kitts and Nevis (assembly of 11 seats) or Antigua & Barbuda (17). Like the two just mentioned, most of the small-assembly independent states that are also democracies with small assemblies are in one world region (Caribbean) and use one type of electoral system (FPTP).

Now suppose one wanted to branch out and include small territories that were either not in the Caribbean or used PR. Suppose further that one did not want to include obviously fully dependent territories that just happen to hold elections for an internal legislative council. Where would one draw the line?

For instance, are the Faroe Islands and Greenland “autonomous enough” to include? What about Aruba and Curaçao? These use PR systems, and the first two are not Caribbean. Or the Cook Islands, with is FPTP but non-Caribbean?

One would need a reasonable standard for autonomy. I sort of feel the places I just named might qualify, but I do not know why I feel that way. And I do not want the can of worms opened whereby I’d be asked–legitimately–why did you exclude Turks and Caicos (for example)? (Other than, well, I already had enough FPTP Caribbean cases.)

The smallest currently included independent country in my related datasets seems to be St. Kitts & Nevis (pop 54k). One of the territories I mentioned is much smaller than that (Cook Islands only 15k), but others are of the same order as St. Kitts (like Faroe Islands and Greenland, 53-55k). I probably have a floor somewhere on population–which might well exclude Cook Islands–but my current query is for a reasonable standard on what is sufficiently self-governing to be comparable to small independent states for purposes of analyzing their assemblies and electoral systems.

What do readers of this site think?