France 2022: Assessing the honeymoon election and towards a model of the impact of election timing on the president’s party’s seats

Was the French 2022 honeymoon election one that defies the usual impact of such election timing? Not to offer a spoiler, but the answer is yes and no.

Back around the time of the presidential runoff, I restated what I often say about elections for assembly held shortly after a presidential election: they are not an opportunity for the voters to “check” the president they have just chosen; presidential and semi-presidential systems just do not work that way. Well, usually. It seems hard to escape the notion that voters did just that–by holding Emmanuel Macron’s allies in Ensemble to less than a majority of seats, and by delivering bigger than expected seat totals to the Mélenchon-led united left (Nupes) and even to Le Pen’s National Rally (RN).

There will not be cohabitation, which was what I really meant in the French context when saying that honeymoon elections were not an opportunity to check the president. The results have not offered up any conceivable assembly majority that would impose its own choice for premier on Macron. I was also generally careful to say that I thought Macron’s allies would win a majority of seats, or close to it. They are relatively close, but considerably farther away that I expected, on about 42%. So, how does this outcome compare to honeymoon elections generally?

I have prepared an updated version of a graph I have shared before. An earlier version appears in Votes from Seats, as Figure 12.2. The x-axis is elapsed time, E, defined as the share of the period between presidential elections at which the assembly election occurs. The y-axis is the presidential seat ratio, RP, calculated by dividing the vote share of the party (or pre-electoral alliance) supporting the president by the president’s own vote share in the first or sole round. The diagonal line is a regression best fit on the nonconcurrent elections (those with E>0), and is RP=1.2–0.7E.

I added the France 2022 data point and label a little larger than the others, to call attention to it. The most notable thing is that this is the only case of a really extreme honeymoon–defined loosely as those with E<.05 but E>0–to have a value of RP<1.00. So in that sense, it is a poor performance. There are other honeymoons for which E≤0.1 that are below RP=1.00, including Chile 1965 and Poland 2001. In the Chilean case, the result obtains simply because the right did not present its own presidential candidate, but ran separately in the congressional election. Although this post is focused on honeymoon and other nonconcurrent elections, I also added labels to the two cases of concurrent elections (E=0) that have unusually low presidential vote ratios. Note that on average, RP in concurrent elections tends to be a bit below 1.00, as a combination of strategic voting and small-party abstention from the presidential contest leads assembly voting to be more fragmented than presidential voting, hence lowering RP. However, in very early term elections, the president’s party/alliance almost always gains. So France 2022 is unusual, but not a massive outlier. In fact, in terms of distance from the regression line, it is about equivalent to France 1997 or El Salvador 2006 (labelled).

We see that the 2022 election also features the lowest RP of any of France’s six honeymoon elections to date. The 2002 election (Chirac) produced an especially huge boost, whereas the 2017 election, when Macron had just been elected the first time, is almost on the regression line. (The regression does not include elections after 2015 because the dataset was collected around then; I added these more recent ones to the graph directly.) I also want to call attention to Volodomyr Zelenskyy’s 2019 honeymoon result in Ukraine for Servants of the People, as it is also among the most extreme honeymoon vote surges recorded anywhere as expected, perhaps aided by how uninstitutionalized that country’s party system has been. (If I wanted to be provocative, I’d say that factor also has been present in France, given frequent realignments on the right, the emergence of Macron, etc.)

(As an aside, I was somewhat surprised that an outlier, the one case of E>0.6 to have RP>1 is the French late-midterm election of 1986. This is remembered as the election that produced the first cohabitation of the French Fifth Republic. But the vote share of the Socialists was still considerably higher than Mitterrand’s own vote share in the presidential first round of 1981, when the Communists had presented their own candidate.1)

So much for the votes. I was wondering what happens if we look at seats? Strangely I had never done this before (at least with this dataset). This graph has as its y-axis the seat share of the president’s party (or alliance) divided by the president’s own first or sole-round votes, which I will call RPs. The x-axis is the same. In addition to plotting a best fit line, the diagonal, I also added the 95% confidence intervals from the regression estimates to this graph. There is also a lowess (local regression) plotted as the very thin grey line. Note how flat it is for a long portion of the term, a fact related to a point I will come to at the end (and also suggesting a more complex than linear fit may be more accurate, but I want to keep it simple for now).

The regression line here is very close to RPs=1.5–E, which is a wonderfully elegant formula! It says that at a midterm election, a president’s party’s seat share would be, all else equal, the same as his or her own vote share half a term earlier. At a truly extreme honeymoon election–imagine one held the day after the president was elected, but with the result known–the seat share would be about 1.5 times the president’s vote share. At an extreme counter-honeymoon it would drop to around 0.5. So where did Macron’s Ensemble come out in the election just concluded? His RPs=1.52! So the party actually did about what the average trend says to expect. It was his 2017 surge that was higher than we perhaps should have expected (although, again, not as high as Chirac’s in 2002).

The result in the second figure is obviously holding constant the electoral system, so it should be taken with a grain of salt, given the importance of variation in electoral systems in shaping the size of the largest party (which is usually the president’s party, at least until we get to midterms and beyond).

What I find particularly elegant about the equation is its suggestion that midterm elections are no-effect elections, in terms of seat share for the president’s party. This was presumably what major party leaders were going for in the Dominican Republic when they shifted to the world’s only ever case (to my knowledge) of an all-midterm cycle. Both president and congress were elected to four-year terms, each at the halfway point of the other. (Actual outcomes during were not always no-effect, though on average they were close2; they have since changed back to their former concurrent elections.) This may seem a surprise to readers who know the American system and its infamous midterm decline, but actually the midterm-election median in the US is 0.969. In an almost pure two-party system, anything below 1.00 might look bad, and be both politically consequential and also somewhat over-interpreted. But 0.969 is not really that much below 1.00! Okay I am cheating just a little by reporting the median. The mean is 0.943; it is brought down by a few major “shellackings” like 2010 (0.891), although 1990 was worse (0.719, in this case because G.H.W. Bush had won such a big landslide of his own).3

In concurrent elections, the regression suggests also that on average, RPs is around 1.00. For the US, the median is 0.979, and the mean is 1.009. Note how it is higher than the midterm average, but perhaps not as much as one might expect.4

At this point, both these equations are just empirical regression best fits, not logical models. There is logic behind the general effects of electoral cycles on a presidential party’s performance, but not a logical basis for the specific parameters observed. I would very much like to have such a logical basis, but I have not hit upon it. Yet.

(Considerably nerdier and some rather half-baked stuff the rest of the way.) Such a logical model may be closer now that there is a simple and elegant empirical connection between presidential votes and seats. Seat shares are more directly connected to parameters of the electoral system than votes shares are–even vote shares for assembly parties, but vote shares for presidential candidates are a good deal more remote from the assembly electoral system. Nonetheless, in Votes from Seats we do derive a predictive formula for the effective number of presidential candidates, based on the assembly’s seat product. A regression reported in the book confirms its plausibility, but with rather low R2. From that formula one could get an expected relationship for the leading presidential candidate’s vote total, vp. It would be vp = 2–3/8[(MS)1/4 +1]–1/4. We already have, for the seat share of the largest party, s1=(MS)–1/8. It so happens that these return the same value at around MS=175. Expectations of vp<s1 or s1<vp would then depend on whether MS (mean district magnitude times assembly size) is higher or lower than 175; for most presidential systems it is a good deal higher (the median in this sample of elections, including semi-presidential, is 480). Tying this observation to the one about midterm elections (E=0.5) yielding actual (not predicted) sp=vp and accepting for simplification that the president’s party seat share (sp) is also the largest party seat share, at least in elections that are not after the midterm, might be a path towards a model. But that may take a while yet. Below I will copy a table of what the formulas for vp and s1 yield at various values of seat product, MS, for simple systems. These values of s1 are without regard to elapsed time when the assembly election takes place.

Table of expected values of presidential vote shares (pv) and largest assembly party seat share (s1)

MSpvs1ratio_s1_pv
10.651.001.54
100.600.751.26
250.570.671.16
500.560.611.10
1000.540.561.04
1500.530.531.01
1750.520.521.00
2000.520.520.99
2250.520.510.98
2560.510.500.97
3000.510.490.96
5000.500.460.92
10000.480.420.88
100000.420.320.75
250000.400.280.70
500000.390.260.67
1000000.370.240.64
2000000.350.220.61
Note how we would expect president’s parties to have a seat share greater than the president’s own vote share at low MS due to system disproportionality, but higher as MS increases beyond 175, presumably because of strategic behavior being different around the majoritarian presidential election and the more permissive assembly electoral system. The smallest MS observed in this dataset for a (semi-)presidential system is 124 (Sierra Leone, 2002, 2007). The largest is 202,500 (Ukraine, 2006, 2007). For nonconcurrent elections, the minimum MS is 240 (Chile, 1997, 2001).

Footnotes

  1. Also, Mitterand himself had finished second in the first round, with 25.9% of the votes (the incumbent, Giscard, had 28.3%). The Communist candidate had 15.4%. In the 1986 election, Socialists won 31% of the votes, for RP=1.2. (I am not counting the Communists as part of Mitterrand’s alliance by then, as he had fired the Communist ministers that were in his initial cabinet.)
  2. The values for RPs in these Dominican elections were: 0.587 in 1998, 0.975 in 2002, 0.945 in 2006, and 1.067 in 2010. So other than that first run, if the no-effect was what they wanted, they basically got it.
  3. [Added, 21 June.] I somehow forgot that my first publication on this topic, in the APSR in 1995, also used seats as its outcome of interest–but it was change in seat percentage for the president’s party from the prior assembly election (with president’s vote share as a control). Looking back on that pub, I see that my regression there would agree with my updated analysis here in suggesting that midterm elections, all else constant, are no-effect elections. The regression line clearly passes very near the change=0, E=0.5 point in the article’s Figure 1. And, yes, in that article I commented on this as a “particularly striking feature” (p. 332).
  4. The way I set up the regression, its constant term would be the RPs when E=0, a concurrent election. This constant is actually 0.95, but its 95% confidence interval includes 1.00 (it is 0.844–1.057). The coefficient on the nonconcurrent dummy is 0.552, from which I get the approximation, 1.5, in the equation in the second figure (summing this coefficient and the constant). The coefficient on E is –1.072. R2=0.215.

France 2022 fourth round (legislative runoffs)

Sunday is the final round of the four-round French election–two rounds for president, two for National Assembly. Thus the legislative runoffs are now upon us. Although we have the unusual case of a honeymoon election in which the leader of an opposition alliance is proclaiming he is running for prime minister, probably the only real question in the results is whether the just-reelected President Macron gets a assembly majority or not. (See earlier planting for discussion of such points.)

In advance of the runoffs, I been poking around in the statements (profession de foi) that candidates make available. It’s a great resource for anyone wanting study patterns in the way the candidates and parties/alliances communicate. I am not about to look at this systematically, but I note a few stark differences in presentation. (Most of the following is based on a comment by me at the earlier post, but with some elaboration.)

Every candidate for an assembly seat runs with a substitute, who would replace the the originally elected member were the latter to vacate the seat for any reason (including becoming a cabinet minister). Thus, in effect, France has two-person (closed) lists for each single-seat district. The replacement is typically, although not always, featured on the statement (and, from photos I have seen, in campaign signs). But there is considerable variation in how they are presented.

Also, as typifies highly presidentialized parties (or, given that this includes major opposition parties, too, leader-ized?) as France has, almost every candidate is featured next to the presidential candidate in whose alliance the assembly candidate was running.

For example, in Bouches-du-Rhône no. 4, the candidate from Nupes features the principal and the substitute prominently, side by side. The national leader, in this case “candidate for premier” Mélenchon, is shown towards the bottom of the first page. This is the reverse of what seems to be the norm for candidates of Ensemble or RN, where the candidate is pictured (photo-shopped, more to the point) next to the leader, with the substitute in a smaller photo on a later page.

For instance, see the Ensemble candidate in the same district.

See this one for a candidate of RN (Bouches-du-Rhône no. 1). Unlike most that I have seen for candidates in other parties, this does not talk about the candidate or the district at all. It just tells what the RN party program is. It also does not mention the substitute. Instead, a picture of the main candidate with Le Pen and also (strangely) a picture of the party president, Jordan Barella. The main message comes through clearly in all caps at the top: “La seule opposition à Macron” (the only opposition to Macron).

Here is another RN candidate statement that is marginally less party-centric than that one. In Hérault no. 7, it is a little more specific to the local context, not in the sense of any mention of district issues, but in calling out the “extreme left” opponent in the district who must be stopped. The Nupes candidate in the same district has a statement that looks like the other Nupes one I mentioned before (and with minor variation, all those from Nupes that I have seen). It has the substitute depicted side-by-side with the principle and featured more prominently than the national leader, while still making room for a photo of Mélenchon at the bottom of the first page. It also has at the very top, “Face au RN, pas d’abstention”–a call not to abstain, given the contest is against the RN. Otherwise, it is mostly oriented around the national program of the alliance.

In general, the Ensemble statements seem to say the most about the candidates themselves, with information on their career on the second page, often along with some words about the district’s needs. Maybe this is to be expected for the alliance that has already won the presidency, and now wants to show how the majority Macron is seeking would be in tune with local voters’ needs. The other two main forces, RN and Nupes, on the other hand, need to emphasize how they seek to counter the president’s national policy priorities. The candidates in Nupes and RN most certainly are not cultivating a personal vote or a local vote on their statements–or rather on the subset of statements I saw.

I actually did find one from Ensemble that did not show a photo of Macron at all, although it does say “presidential majority” at the bottom of the front page. Instead, it shows the principal candidate and the substitute standing side-by-side in a park. This district is one of the three-way runoffs, Dordogne no. 3 (first round: NUPES 24%, Ensemble 23%, RN 22%), and the second page of the statement has a large block of text denouncing the “extremes” represented by the other two runoff candidates’ national programs. It still saved plenty of locally targeted information about priorities.

We can probably draw some conclusions from these patterns–if they are indeed patterns–about the priorities of the parties and alliances, in terms of local vs. national emphasis, as well as how important the leader is to the vote-seeking strategy. I looked at dozens, and while I can’t claim they were representative of the wider set of districts, it seems they just might be.

Israel’s stable coalition

Yes, you read the headline correctly. Ever since the current broad-yet-narrow coalition government in Israel was formed, it has been something of a sport for various journalists covering Israeli politics to predict its early demise. I cautioned otherwise at the time. [Note: see UPDATE at very bottom of post, 16 June]

It may be that the coalition really is in its death throes, even as it has only just passed the one-year mark of its planned three-year term. I have lost count of the number of individual members of coalition parties who have announced a “strike” or a “freeze” whereby they stop voting with the coalition for a period of time to try to get some measure they favor passed (or something they oppose stopped). Most of them have made clear that they would not defect to the opposition or vote to call an early election. But some (I think three dating back to the original investiture vote) have outright defected. The coalition fell to a 60-60 deadlock with the opposition when Idit SIlman (Yamina), coalition whip, went over to the opposition in April. More recently, there was one member from Meretz (the left-most flank of the coalition), Ghana Rinawe Zoabi, who announced she was leaving–bringing it to 59–but then walked it back a few days later after mayors of Arab towns persuaded her to stay. The most recent defector is Nir Orbach from Prime Minister Naftali Bennet’s Yamina Party, who has said “I am not part of the coalition,” putting it back, apparently, at 59 active members (where “active” might include, at any given time, one or two on “strike” of some presumably temporary sort ).

The question is whether a government can survive when it has 61 or more announced opponents in the 120-member Knesset. A majority opposed means it is done, right? Well, not necessarily. Israel has a full constructive vote of no confidence. This means a government can’t be voted out by a parliamentary majority unless that majority is simultaneously electing a replacement government. There is almost no prospect of this happening, as it would require the Joint List (of mostly Arab parties) to be willing not just to passively tolerate a Likud-led (and, yes, Bibi Netanyahu) government, but actively vote for its installation. This is almost impossible to imagine, so in this limited sense, the government may actually be stable.

We are talking about Israel, a country whose politics are notably unpredictable, so there are other scenarios that can’t be entirely ruled out. Maybe at least two of Blue & White (Benny Gantz, 8 seats) or New Hope (Gideon Saar, 6) or Yisrael Beteinu (Avigdor Liberman, 7) will surrender their current ministerial posts and vote for a new coalition with Likud as a partner if not leader. Each has as at least as many seats as the Joint List (6), and if the two bigger of these parties defected, they could then form a majority without either the Islamist Ra’am party (4 seats), which backs the current coalition, or the ultra-nationalist Religious Zionist party. All three of the lists I mentioned as hypothetical defectors from the current ministerial team have been burned in the recent past by Netanyahu; it also means Liberman has to join up again with the Haredi parties, which would be a big backtrack from a position he’s held firm on since 2019. So it is hard to see what they gain by enabling his return to power. Never say never, but it seems unlikely. That suggests that indeed, at least as far as no-confidence votes are concerned, the coalition is still stable, and could remain so even if suffered another defector or two.

Stable in terms of remaining in power. Of course, it can’t pass legislation if the opposition unites against it. But that is a big “if.” Just this week, the first reading of a tax measure passed against the coalition’s declared position, but it was only 51–50. In other words, while the government may have trouble mustering a majority, it is not a sure thing for the opposition, either–even on a bill sponsored by a member of Likud. Then there is always the possibility of a selective member or two from outside the coalition voting with the government on specific bills. The government may not be able to pursue its most ambitious legislative agenda, but it probably can pass bills here and there (as well as continue executing laws already passed in a way favorable to its agendas to the extent permitted).

The bigger obstacle is the next budget. This is the one way a government can fall without losing a constructive vote of no confidence. The next budget bill must be passed in March, 2023. This vote, however, does not require 61 members of Knesset. More yes than no is sufficient. So that is a somewhat easier obstacle for the government, although by no means an easy one.

The final way–and the most likely way–that it could be forced out is if the Knesset votes to set an early election. This requires 61 votes, but it can be a negative coalition (i.e., we don’t want this Knesset and government to continue), rather than the positive vote (here’s a new government we are putting in now) like the constructive vote of no confidence. Orbach, the most recent defector from Yamina, stated in his announcement that, while he was leaving the coalition, he would not vote for early elections. He said instead that he would work to form an alternative government from within the current Knesset. We have already been over why that is not likely. At least as of now, it does not seem that there are 61 votes for an early election.1

Thus, unless the government simply resigns, it may continue on, despite its current difficulties. The constructive vote of no confidence really does enhance the potential for “separation of powers” (or better, separation of purpose) whereby the assembly majority opposes the government but does not have the means to replace it–in this case, because it does not agree on what the replacement should be (and does not favor going to elections).

So it may seem strange to call the Israeli coalition “stable” in its current situation. But if “stable” simply means that it can survive, then it is stable unless there are multiple further individual defections or a surprise change of heart by two or three of the party leaders who made this government possible in the first place. There are certainly other ways we might define whether a government is “stable” but by this criterion, and at this moment, it’s stable.

  1. Another consideration here is that the coalition agreement provisions that were put into Basic Law (i.e., Israeli’s constitution in all but name) have stipulations about the interim period after an “alternating” government like the current one has its term ended early via the setting of elections. If there are at least three defectors from Bennet’s (right-wing) side of the government, Alternate PM Yair Lapid of Yesh Atid (center-left) automatically becomes PM. An election would be at least three months from the passage of the bill calling the election, and given that there is no guarantee that the election would result in a Knesset that could have a majority for a government (meaning potentially yet another election or elections, like 2019–21), those on the right voting for this option would be risking a signifiant period of time with PM Lapid. An Israeli government in this position is no mere caretaker. It is a government, period. I put all this in a footnote because I do not take it too seriously. The Knesset does not actually dissolve in the period between passage of a bill calling an election and the time the new Knesset is elected. It can still function. And these measures were passed by… 61 votes. Therefore, if 61 votes exist to call an election, 61 votes probably also exist to repeal the provisions and allow Bennet to remain as PM. Still, there would be some risk to right-wing politicians doing this, as they could not do these acts–call the election and repeal the provisions–simultaneously. So an agreement to do so could fall apart. But I’d think they could pull it off.
  2. UPDATE (intended to be part of the previous footnote but Word Press won’t allow a new paragraph here without putting a number in front of it): I just heard of a twist on all this that I wasn’t aware of, from Haviv Rettig Gur on the Times of Israel Daily Briefing podcast. The bill regulating legal matters in Judea and Samaria, which expires at the end of June—and which Likud and allies say they won’t vote for (even though expiration would be bad for some of their voters)—would get an automatic 6-month extension if the government falls before 30 June. Thus some members from the right of the coalition may want to pull the plug to save (temporarily) the status quo of the otherwise sunsetting legislation—even if it meant an interim PM Lapid. On the other hand, the polls aren’t great for the opposition and Netanyahu may not want to provoke an election now—“assessments are changing daily.” (This paragraph added 16 June, 6:30 a.m., PDT)

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.

France assembly 2022: Putting the prospects for NUPES in context

The first round of the French 2022 National Assembly election is on 12 June. As readers of this blog recognize, this is an extreme honeymoon election, owing to the short time that has elapsed since the presidential election. In that two-round contest in April, Emmanuel Macron was reelected, winning 27.9% of the vote in the first round and 58.6% in the runoff.

The runner-up in the presidential contest was Marine Le Pen of the extremist National Rally, with 23.2% in the first round and 41.5% in the runoff. In a close third place was the leftist Jean-Luc Mélenchon, with 22.0%. In the period since the runoff results were known, Mélenchon has led the formation of a left alliance known as the New Ecologic and Social People’s Union (NUPES). (See the series of very helpful comments from Wilf at an earlier post, where he shared news stories about the coalition bargaining as it was taking place.) Mélenchon has not been shy about his goal, proclaiming that he is running to be premier. If this happened, it could usher in a period of cohabitation, defined as president and premier from opposing parties and the president’s party not in the cabinet. (I say “could usher in” because there’s always the possibility Macron’s party would be in a cabinet headed by Mélenchon, although if the latter actually were premier–and especially if NUPES won a majority of seats–that would be rather unlikely.)

As readers of this space will know, I find such an outcome extremely unlikely. Honeymoon elections do not work that way. They are not a second chance for voters to “check” the president. They confirm the mandate the voters have just conferred on the new (or newly reelected) president. Or do they? Maybe this will be a special case. That is what I am setting out to explore in this post.

Regarding “normal” honeymoon elections, see the post on France that I wrote in 2017, just before the presidential runoff, suggesting that Macron’s then-new party would get around 29% of the vote, and be the largest party. It actually won almost exactly that, 28.2%, and given both allies and the majoritarian two-round electoral system, Macron ended up with a large assembly majority. See the graph in that post, which also appears in Votes from Seats, and shows how nearly all elections early in a presidential term result in rather significant surges for the president’s party. The graph shows something called “Presidential Ratio” graphed against “Elapsed Time.” The ratio, RP, is simply the vote share of the president’s party, divided by the president’s own (first or sole round) vote share in the preceding presidential election. The elapsed time, E, is the percentage of the time between presidential elections at which the assembly election takes place.

For all non-concurrent elections, a best fit shows a steep slope starting at about 1.2 if the honeymoon election is immediately after the presidential election, and dropping steadily as assembly elections occur later in the period between presidential elections. It crosses the 1.00 line (indicating identical assembly and presidential vote shares) at around E=0.28, or just past the quarter mark, then drops to around 0.84 when E=0.5, encompassing the well known midterm-decline phenomenon. Given that for France in 2022 (as in 2017 and some previous cycles), E=0.017, we expect RP=1.19. Taking Macron’s first-round vote of 27.9%, his party should win around 33.1% of the votes. Presumably that would be a plurality and would again be sufficient to win a majority (or close to it) in the assembly when the two-round process is all said and done. Or should we be sure that would be a plurality this time? Let’s see.

Please remember that the equation of this line for presidential vote ratio is not a logical model (like the Seat Product Model or the Cube Root Law), and in any case, even logical model predictions get tripped up by real politics at times! Maybe this honeymoon election will be different. Macron won many voters in the runoff who would have preferred Mélenchon but felt they had to vote to stop Le Pen. There may be much more energy on the side of NUPES than is normal for an alliance that backed a loser.

So how surprising would a good performance be? I decided the best way to put a potential answer to this question in context was to go back to my dataset and augment it with votes data from runners-up and third-place presidential candidates. I have never looked into this before! So here we go…

First, let’s see what it looks like for the party of the candidate who finished second in the second or sole round of presidential voting.

We see that honeymoon elections are really bad for your party if you just lost the presidential election as the runner-up! All data points are below the 1.00 line until nearly E=0.3. The dashed curve is just a lowess (local regression) curve. I did not continue it much past the midterm, because the data get rather sparse late in the term. Not because there are no such elections (again, see the graph for presidential parties), but because the farther you go into the term, the more likely the runner-up’s party does not exist in a recognizable form. Presidential and semi-presidential systems can be that way.

In France 2022, it was Le Pen who finished second, and I do not think anyone would be surprised if her party got less than two thirds of what she won (in other words, around 15%). In fact, it will probably be much worse than that for her.

The topic of interest here, though, is the third presidential candidate’s party. Here is what that graph looks like:

Interestingly, the party backing the candidate who came in third quite often increases its support in a honeymoon election. In most cases, that probably comes predominantly at the expense of the second candidate’s party. But there is probably no reason why it could not come from the winner’s, in a case where there was a good deal of strategic voting in the presidential election (or specifically, in a runoff).

The curve is pretty level until E=0.2, with a mean of almost 1.5. Given how sparse the data are–there are lots of presidential elections with no third candidate or where the third had no party–I would not draw too much of a conclusion from this. However, note that 1.5 times Mélenchon’s vote would reach 33%, or almost exactly what we “predict” for Macron’s La République En Marche! (The exclamation point is in the party name, although you should be as excited about this convergence of their potential shares as I am!) If one were to add in the votes of the other presidential candidates whose parties since have joined NUPES, perhaps we would “predict” a voting plurality for Mélenchon.

So, while I still do not think Mélenchon is going to become premier, this data exploration has led me to believe it would not be as shocking a development as I initially assumed. It could be that this is the honeymoon election that has the ideal convergence of factors to generate an upset. And make no mistake, if a just-reelected president were to be forced to appoint as premier someone opposed to him, it would be an upset. On the other hand, polls do show it will indeed be close, at least in the first round.

France’s toxic combo of institutions finally bites

I still think Emmanuel Macron will win reelection, but it is going to be a closer fight than most prognosticators expected before this past Sunday’s first round. In the results of that vote, Macron has the expected plurality, and it was a few percentage points higher than he got in 2017 (27.8% vs. 24.0%). His runoff opponent in both 2017 and later this month, Marine Le Pen, also improved a bit over last time (23.3% vs. 21.3%). What is new–or really accelerating a trend that was already there–is the total collapse of older established parties. The Republican (mainstream right) got 20% in 2017 but only 4.8% this time, fifth place. The Socialists were already in dire shape in 2017 with 6.4%, but did even worse this time, 1.75%, despite (or because of?) running the mayor of Paris, a seemingly high-quality candidate. Jean-Luc Mélenchon of La France Insoumise, a far left group, made the race for a runoff slot pretty close this time, coming third with just under 22% (19.6% last time, fourth place). Given just over 7% for the far-far-right Eric Zenmour, one could say there was a majority for extremes of one sort or another.

While the Economist’s forecast model still has Macron’s win probability at around 80%, it was just short of 100% as recently as 21 March. An extreme right candidate actually has a roughly 20% chance of being the next president of France.

It is never a good thing for democracy when the fate of the republic hinges on one person. But it is hard to exaggerate how absolutely essential it is that Macron win. France has been running a decades-long experiment in whether a highly presidentialized system would eventually destroy the party system. The French party system held up pretty well, despite the adoption of a relatively strong presidency with the 1958 constitution and direct election to that office in 1965. The party system did indeed become presidentialized in ways that David Samuels and I document in our 2010 book, Presidents, Parties, and Prime Ministers. Parties reorganized themselves internally around the goal of advancing their presidential candidate, rather than emphasizing their parliamentary party organization. This presidentialization was only further enhanced by the decision in 2002 to make assembly elections follow immediately after presidential, with both elected for five-year terms. The party system’s left and right blocs, starting from the 1960s, came to be dominated by whichever party could present the successful presidential candidate–the identity of these parties changed over time on the right, but presidentialization allowed the Socialists to surpass the Communists on the left. However, with the demise of the old right and left, there is not much remaining to the party system other than presidential aspirations. Macron himself is the perfect demonstration of presidentialization–having no party at all till he was on the cusp of the presidency, and then creating one that swept into power on the heels of his own win.

The combination of direct election of a politically powerful presidency, honeymoon election of the assembly, and majoritarian electoral rules is toxic. It means that someone from outside the party system potentially can win the presidency and then, in short order, a majority in the assembly. If you get lucky with this combination, you get a Macron. If you get unlucky, you get a Le Pen (or potentially a Mélenchon).

Make no mistake. Honeymoon elections, with majoritarian rules, are the real deal. If Le Pen manages to win the runoff, there will be no “second chance” at which voters can check her with a majority opposed to her in a cohabitation via the assembly. Presidential and semi-presidential democracies just do not work that way. If she wins the runoff, we can expect her National Rally to win around 28% of the vote in the first round of the assembly (see the just-linked post or the one from 2017), and that to be a plurality. Could a broad alliance form to block her candidates, given the two-round majority-plurality system? Sure. Just don’t count on it. Do count on her getting support from various other anti-system forces and being in a much stronger position going into the second round of the assembly election than that 28% estimate implies.

Do I think this is the most likely outcome? No, I do not. I think Macron will win, and go on to win a large majority of the assembly. However, it is a bad situation for French democracy–and the world–to be dependent on this one man not slipping up in some way in the final days before the presidential runoff–especially with a major war going on in the extended neighborhood and related economic difficulties at home. France is in dangerous territory in these moments with its toxic institutional combo, and the overly high stakes that combo generates.

Will Macron lose his assembly majority?

French election season is upon us. In four rounds of elections over the next three months France will choose their President and National Assembly. The presidency is elected by two-round majority (10 and 24 April), followed closely by the assembly using two-round majority-plurality (12 and 19 June). Predictably, the news media are already starting to suggest that President Emmanuel Macron, while likely to be reelected, might be at risk of losing his assembly majority (e.g., The Economist). Will he?

What is almost as predictable as the media expressing this outcome as a real possibility is that presidents–just elected or reelected–see their parties do really well in honeymoon assembly elections. You can’t get much more honeymoon-ish than the French cycle. The assembly election occurs with approximately 1/60 of the time between presidential elections having elapsed. It just so happens that we have a formula for this.

Rp=1.20–0.725E,

where Rp is the “presidential vote ratio”– vote share of the president’s party in the assembly election, divided by the president’s own vote share (in the first round, if two-round system)–and E is the elapsed time (the number of months into the presidential inter-electoral period in which the assembly election takes place, divided by the total months comprising that period).

In 2017, there were actually news reports suggesting that because Macron at the time he was elected did not yet have a true political party, he would face cohabitation. That would mean an opposition majority, which under French institutions would also mean a premier (head of cabinet) from parties opposed to the president. This was, even at the time, obviously hogwash.

The formula suggested that, once we knew Macron’s first-round vote percentage, we could estimate his (proto-) party’s first-round assembly vote percentage–assuming he would go on to win his own runoff (which was never seriously in doubt). Given that Macron had won 24% of the vote in his own first round, that implied 29% of the vote for the party in the first round for assembly.

What did his party, branded by then La République En Marche!, get? The answer would be… 28.2%. Not too bad for a political science formula. Not too surprising, either. It does not sound impressive as a vote percentage, but when you have the plurality of the vote in a multiparty field with a two-round majority-plurality electoral system, it can be pretty helpful in terms of seats won. Even more when you are a center party, and your opponents are split between left, right, and farther right (and we should not leave out farther left, too). After the second round, LREM ended up with about 54% of the seats. When combined with a pre-election ally, Democratic Movement, the seat total was over 60% (the two parties had combined for about a third of the first-round votes and got 49% of second-round votes).

The Economist article I linked to in the first paragraph was published in the March 5 edition. I want to check how plausible its claim was, using the Economist’s own election forecast model. As of a few days before March 5, that model was basing its forecast on aggregated polls that averaged about 27% of expected first-round vote for Macron himself. In other words, a few percentage points higher than he ended up winning in the first round in 2017. The model also gave Macron at the time an 88% chance of winning the presidency. Thus on the basis of information available at the time–including the Shugart-Taagepera formula for expected presidential-party vote share–we should conclude that LREM would win about 32% of the vote in the first-round assembly election. Assuming this would be the plurality share–a very safe assumption–that would again imply a strong chance of a single-party majority of seats. Not a loss of the majority, or even the need to forge a post-electoral coalition.

Now, since that article was published, Macron has been enjoying quite a surge in the polls. As of today, the forecast model at The Economist has his odds of winning the presidency above 95%. His polling aggregate as of March 12 is up to 31% (Marine Le Pen, his runoff opponent in 2017, is a distant second with 18%). From this we could estimate the first-round assembly vote share is up to 38%.

I will caution that the formula is not a logical model. It is empirical. There is good logical basis behind the general idea of honeymoon surge (and midterm decline, for countries with such cycles). But the specific parameters of the formula do not have a logical basis. At least yet. The graph of the relationship that is shown in Chapter 12 of Votes from Seats (and also included in the 2017 “predictive” post on France) shows a couple honeymoon elections in various countries that have defied the expected surge. However, only one has an elapsed time of less than 0.1 (the specific example of a relatively early honeymoon decline was Chile 1965, in an election held at 0.083 of the presidential inter-election period.1)

So I can’t predict what LREM will get in June. But it would be a surprise if it was worse than around a third of the vote, even if Macron’s own polling surge does not hold. Given the fragmentation of the party system–which looks even higher now than it was in 2017–and the majoritarian nature of the electoral system, anything short of a majority of seats for Macron would be a surprise at this point.

The notion that voters will come out and vote to “check” a just-elected president that they maybe were not all that enthusiastic about is a hard notion for the news media (not only The Economist) to shake. But there just is not much evidence that politics in presidential and semi-presidential systems works like that.2

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1. This election saw the Christian Democratic Party of newly elected President Eduardo Frei win a very strong plurality, 43.6%, but Frei himself had won 56%. The problem–for the formula–is that there were only two serious candidates and three total in the presidential election, whereas the PR-elected legislature featured many parties, including allies of the president running separately. The formula implicitly assumes that all parties contest both elections. This is one of the reasons I can’t call it a logical model, because such conditions have not been incorporated, and perhaps can’t be without making it too complicated to be useful. It is pretty useful as it is, even with its oversimplification and lack of true logical basis!

(By the way, in the next Chilean assembly election, held with 75% of the term elapsed, the party’s vote percentage fell to 31%. The formula suggests 37%, but given that we already know the party did worse than “expected” at the honeymoon, we should just use the expected drop from what it actually had. That would “predict” about 25% of the vote at the late-term election. So they did better than expected, actually.)

2. On this point, let me shout out a just-published article by some recent UC Davis Ph.D.s Carlos Algara, Isaac Hale, and Cory L. Struthers on the Georgia (US) Senate runoffs. Even I was skeptical that honeymoon logic could apply to those elections. And in fact it did not turn out as a Dem surge, but there was clearly no evidence of “checking the president” behavior by voters.

The invasion of Ukraine

My field is not international relations/security nor is it Russian or East European affairs. So I won’t say a lot, or pretend to be speaking from expertise. I will speak more personally. It has been quite some time since an international event has upset and shocked me as much as the Russian invasion of Ukraine.

While I did not believe Putin was bluffing, I was not prepared for such a massive assault on positions all around the country. I guess I was in denial, as the leaked intelligence reports of the week before suggested it could be a really extensive attack.

It is an unprovoked aggression. I would say more unprovoked and more dangerous than any of the other invasions of sovereign states that we’ve seen in many decades. But, again, this is not my speciality. And Putin will get away with it because…. well, because no one with the means to stop him will try. And trying could be… risky. It is just a deeply depressing situation, and feels like a real shift in the international order, whatever that means.

Photos with this post were taken by me in 2005, on one of the most meaningful and interesting foreign travel experiences I have ever had.

Portugal 2022–unexpected majority, but not that rare (for Portugal)

The majority of seats obtained by the Socialist Party (PS) in the recent general election in Portugal was seen as a surprise. Polling generally had not shown a majority as within reach and indeed showed a likely close result. However, Portugal has had relatively frequent parliamentary majorities over the years, despite its proportional representation (PR) system. How unusual was the 2022 outcome?

From 1976 to 2019, the mean seat share for the largest party in Portugal has been 0.478–not a majority, but pretty close. In this election the PS obtained 117 of 230 seats, which is 0.509. (The total includes the four seats for Portuguese abroad.) This is the fifth absolute majority won in 16 Portuguese assembly elections since 1976. Thus in terms of Portugal’s electoral history, the result was not so unusual. How unusual is it relative to what is expected from Portugal’s PR system?

Portugal’s electoral system has a seat product of around 2400. This is a modest seat product by standards of proportional representation, stemming from a moderate assembly size, S (currently 230; 250 before 1991), and a middle-range district magnitude, M (currently 10.5 on average), yielding a seat product, MS=2415. For such a seat product, the expected largest party seat share is 0.378, derived from the formula expecting this share to be (MS)–1/8. Thus Portugal’s actual largest party seat share has averaged 1.26 times the seat product model prediction.1 This indicates that while Portugal’s electoral system is not expected to produce a high degree of fragmentation (38% of the seats is a decent sized largest party2), actual Portuguese politics supports a more de-fragmented party system–at least so far–than what its electoral system could sustain.

As for votes, the associated formula of the seat product model implies we should expect the largest to have 35.4% of the votes, but the average has been 41.8% instead. In this election the PS won 41.7%. So, whatever people expected, it was a pretty ordinary voting result by the standard of Portuguese electoral history. There was a somewhat higher boost for the largest party, however, than the norm. The average advantage ratio (%seats/%votes) has been 1.14; in this election it was 1.22. I would guess that this larger seat bonus for the largest party comes in significant part from the main rival for national power, the Social Democrats (PSD, actually a center-right party) losing votes to a farther right-wing/nationalist party, CHEGA. The latter party was the big gainer in votes and seats in the election, as it had only one seat from 2019 but won 12 in this election. However, it had a very low advantage ratio, with its 5.31% of seats coming on 7.15% of votes, for a ratio of 0.74. Its votes thus did not translate efficiently into seats, which may have helped the PS harvest more seats than normally would be the case for a party with just over 41% of the votes given Portuguese electoral laws.3

Notes

  1. The mean actual largest party seat share in a sample of 634 simple electoral systems is only 1.048 times the model prediction; for PR systems the model is even better, with a ratio of 1.033. So a ratio of 1.26 indicates a strong degree of politics being needed in addition to institutions to explain an outcome. Less than a quarter of PR elections have ratios that high or higher.
  2. The mean largest party seat share for the sample of 280 PR elections in parliamentary (or semi-presidential) democracies that I am working with happens to be 38.2%.
  3. Relative punishment of smaller parties is an inherent feature of the system’s moderate seat product. For instance, in this election the significantly smaller Liberal Initiative won 3.5% of seats on just under 5% of votes. The wasted votes by smaller parties have to go somewhere; given that Portugal uses the D’Hondt formula, the result will tend to be generally more favorable to the largest party than it would be with other PR formulas, for a given seat product. (This is not unusual; more than two thirds of all simple PR systems use D’Hondt.) Still, for a party in its range of vote percentage, CHEGA’s advantage ratio is quite low. For instance, in 2019, the Left Bloc and Unitary Democratic Coalition, with 9.5% and 6.3% of votes, respectively, had advantage ratios of 0.86 and 0.82. So CHEGA must have had an unusually inefficient geographic spread for a party of its approximate size. Indeed, skimming the table the Wikipedia page offers for district-level results, it is easy to spot districts where CHEGA received above its nationwide vote share yet won no seats. As a final note on CHEGA, I will add that its single seat in 2019 was won in Lisbon, where the district magnitude is 48, on 2% of the vote.

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.

The Austrian Question: Or how I corrected some data I’ve been using on two-tier systems

In the previous planting, I presented a revised version of the extended Seat Product Model. I noted that in the process of attempting to improve on the logical model, I discovered some inconsistencies in the treatment of remainder pooling systems in the dataset used in Votes from Seats. Here I describe the problem and how I corrected it. The changes here may still require further refinement, but at least they make the treatment of the cases internally consistent.

This first began to bother me even before Votes from Seats had been published. Figure 17.2 in the book shows how well (or not) the extended seat product model accounts for the effective number of seat-winning parties (NS) over time in several two-tier PR systems (plus Japan, included despite not fitting the category for reasons explained in the book). It plots every election in the dataset for this set of countries, with the observed value of NS shown with the solid grey line in each country plot. The expectation from the extended Seat Product Model (Equation 15.2) is marked by the dashed line. This equation is:

NS = 2.5t(MSB)1/6,

where NS is the effective number of seat-winning parties (here, meaning the expected NS), M is the mean district magnitude of the basic tier, SB is the total number of seats in the basic tier, and t is the “tier ratio” defined as the share of the total number of assembly seats allocated in the compensatory tier.

For countries that changed from simple to complex, the plots also show the expectation in the era of the simple system with the solid dark line. The troublesome case here is Austria, but why? That is my “Austrian Question.” It led me down quite a rabbit hole, but I think I have it figured out, more or less.

Figure 17.2 in Votes from Seats. Expected and actual effective number of seat-winning parties (NS) over time in long-term democracies with two-tier electoral systems. (Click for larger version.)

It always seemed unlikely that the design of the Austrian electoral system was such that expected NS could have reached well over 6 in the latter part of the time series! But that is what our data showed, supposedly. When you get an absurd result, generally you should impeach the data, not the model.1

The problem turned out to be that for several remainder-pooling systems, including Austria, some seats were effectively counted twice in the derivation of the extended seat product. We drew most of our data from Bormann and Golder’s Democratic Electoral Systems Around the World. However, the manner in which we did so handled remainder-pooling systems poorly. With one important exception that I will note below, the error was not in the original data, but in our application of it.

In a remainder-pooling system there is no fixed upper tier. Most two-tier compensatory systems have a fixed number of seats which are allocated nationally (or regionally) to “correct” for distortions in votes-to-seats allocation produced by the lower district magnitude of the basic tier. An example would be the system of Denmark, with 139 basic-tier seats and 40 compensatory seats. Others have a fixed minimum, such as the MMP systems of Germany and New Zealand (where the upper tier can expand if needed due to “overhang” seats, but it has a fixed starting size). In a remainder-pooling system, on the other hand, the “upper tier” can be as large or as small as needed to generate compensation. In theory, all seats could be allocated in the basic tier, and it would end up no different from a simple system. Typically these systems work by stipulating that parties earn seats based on full quotas (usually Hare quota, sometimes Hagenbach-Bischoff) in the districts. Any seats not filled are then “pooled” in a supra-district tier where they are allocated based on pooled votes, rather than being filled within districts. The upper tier is thus whatever number of remainder seats there are from all of the districts, which can vary from election to election depending on how votes are distributed among the parties and across the basic-tier districts.

A particular challenge in the analysis of these systems is that all seats may be attached to districts, and national reporting agencies vary in whether they indicate that a given seat is actually based on supra-district allocation. Thus a district might have, say, five seats, and in the determination of quotas, two parties may have obtained a total of three seats through quotas in the district. The other two seats go to the remainder pool. Maybe, once all the national seat allocation is complete, one of those two remainder seats goes to the largest party (bringing it up to three) and one goes to a third party that was short of a quota in the initial allocation. The complication is that while all five seats are assigned to candidates who were on party lists in the district, only three were assigned based solely on votes cast in the district. The other two were assigned according to the compensation mechanism, drawing upon the pooled votes from across multiple districts. Where is the upper tier? It is sort of a phantom, and if we count the two seats in our hypothetical example as part of the upper tier, and we also count them as part of the district (basic tier), we have double counted them!

Here is where the Austrian case comes in. If we look at the 1990 election, we see an assembly size of 183, with 9 basic-tier districts, averaging 20.3 seats apiece. Bormann and Golder report that 25 seats were allocated as “upperseats”. In our Equation 15.2, the input parameters were MSB=20.3*(183–25)=3207 (rounding off) and t=(25/183)=0.137. That is, the basic-tier seat product is mean district magnitude multiplied by the size of the basic tier (which is total assembly size minus upper seats). But hold on! Those 25 upper-tier seats are taken out of the 20.3 seats per (average) district. Yet our original calculation takes them only out of the “S” part, but not out of the “M” part. They should not be counted in both tiers! Those 25 seats came from the 9 districts, so 25/9=2.8 remainder seats per district, on average. This gives us an adjusted basic-tier M=20.3–2.8=17.5. Now we have MSB=17.5*(183–25)=17.5*158=2765, and t=0.137. This changes the “expected” NS (based on Equation 15.2) from 4.35 to 4.25. Not a huge difference, but one that more accurately reflects how the system actually works.

Where things really went haywire was with the electoral reform that took place before the 1994 election. The Bormann and Golder dataset correctly notes that the number of basic-tier districts was increased to 43. With S=183 unchanged, this is a mean district magnitude of M=183/43=4.26, a figure which matches the description in Electoral System Change in Europe, maintained by Jean-Benoit Pilet and Alan Renwick. However, for some reason, the Bormann and Golder gives first-tier mean district magnitude for the post-1992 system as 17.2. The indicated values of “upper seats” range from 78 to 111 in the elections of 1994–2008. When we apply the same procedures of the preceding paragraph to elections in these years, we get a reduction in MSB from the 2669 we used in the book to a more accurate 196.7. That is quite a change! It comes from the reduction in district magnitude to 4.26, which in turn greatly pushes up the number of seats allocated in upper tiers.2 When we stop double counting the remainder seats, we actually have an adjusted basic-tier magnitude of less than 2, and an upper tier ratio, t=0.5. This changes that rather absurd “expected NS” depicted in Figure 17.2 as 6.3 for recent elections to a more reasonable 3.83. And, in fact actually observed NS in recent years has tended to be in the 3.4–4.2 range.

Here is the corrected version of the figure. (I left Japan off this one.) In addition to using the corrected data, as just explained, it also uses the revision of the extended Seat Product Model:

NS = (1–t)–2/3(MSB)1/6.

Version of Figure 17.2 in Votes from Seats using corrected data. (Click for larger version.)

Austria is no longer shown as system that should be “expected” to have an effective number of parties around six! It still has an observed NS in most years that is smaller than expected, but that’s another story. We are not the first to observe that Austria used to have an unusually consolidated party system for its electoral system.3 In fact, in recent years it seems that the revamped design of the system and the increasingly fragmented party system have finally come into closer agreement–provided we use the revised SPM (as explained in the previous planting) and the corrected electoral-system data, and not the inconsistent data we were using before.

And, here for the first time, is a graph of largest party seat share in these systems, compared to expectations. This seemed worth including because, as noted in the previous planting, the s1 model for two-tier works a little better than the one for NS. Moreover, it was on s1 that the revised logic was based.

Expected and actual largest party seat share (s1) over time in long-term democracies with two-tier electoral systems. (Click for larger version.)

Note that the data plots show a light horizontal line at s1=0.5, given the importance of that level of party seat share for so much of parliamentary politics.

Notes

1. Assuming the model is on solid grounds, which was very much not the case of the original version of application to two-tier PR. I hope it is now, with the revision!

2. Plural because the 9 provincial districts still exist but are now an intermediate compensation tier, and there is a single national final compensation tier. This additional complication should not affect our estimation of the system’s impact on party-system outputs. (It principally affects which candidates from which of a given party’s lists earn the various compensation seats.)

3. This is not unique to Austria. Several European party systems used to have effective number of parties smaller than expected for their electoral system. In recent decades, many have become more fragmented, although the fragmenting trend is not significant, when compared to the SPM baseline). The trend implies that, in many cases, their electoral systems are shaping their party systems more as expected now than in the early post-war decades. In the past, the full electoral system effect may have been tamped down by the stronger role of the major party organizations in society. This is a very big question that it far beyond the scope of my current tasks.

Further note

In order to attempt a further validation of the procedure, I calculated the number of quota seats expected in each district based on my district-level dataset, derived originally from CLEA. I can then sum this up across districts in a given election, and subtract the result from the total assembly size to arrive at an indicator of what the upper-tier size should have been in that election. When I do this, I usually come close to the value for “upperseats”in Bormann & Golder, although not always precisely. I do not know what explains the deviations, but in all but one election they are so small that I would not fret. For the two elections used as examples from Austria above, I get 24 remainder-pooled seats in 1990 (vs. B&G 25) and 111 in 2008 (identical to B&G). Ideally, we would be able to estimate what upper-tier seats should be, on average, for a given design of a remainder-pooling system. Then we could estimate the parameters needed for the extended SPM even if data sources do not separate out the seats allocated on district votes from those allocated via supra-district pooling. This would introduce some unknown error, given that the actual number of remainder-pooled seats can vary depending on election results, for constant institutions. For instance, for the current Austrian system, it has ranged from 81 to 111 between 1995 and 2008. Perhaps there is some mathematical relationship that connects this average (92) to fixed parameters of the electoral system, and that works across remainder-pooling electoral systems. If there is, it has not revealed itself to me yet.

MMP as sub-category of two-tier PR–some basis for doubt

In yesterday’s review of the German election outcome, I used the extended Seat Product Model (SPM) formula for two-tier PR systems. I have done this many times, and Rein Taagepera and I (in our 2017 book, Votes from Seats) do explicitly include mixed-member proportional (MMP) in the category of two-tier PR systems.

However, there is one problem with that characterization. All other two-tier PR systems that I can think of entail a single vote, which is then used both for allocating seats in the basic tier and pooled across districts for national (or sometimes regional) compensation.

MMP, of course, usually entails two votes–a nominal (candidate) vote used only in the basic tier, and a second, party-list, vote used for determining overall proportionality. (In MMP, the basic tier is a “nominal tier” because the vote there is cast for a candidate, and the district winner earns the seat solely on votes cast for him or her by name.) This two-vote feature is a complex feature of MMP that is actually emphasized in my more recent coauthored book, Party Personnel Strategies, but which I may have tended to underplay in my comparative work on modeling the effects of electoral systems on party systems. Of course, by being two-tier, it is already a non-simple system, as Taagepera and I define that term. But we also say that two-tier PR, including MMP, is as simple as an electoral system can be and still be included in the complex category (see p. 263 and 299 of Votes from Seats).

Maybe that is not an accurate statement for two-vote MMP. Our definition of simple (pp. 31-36) concentrates on two features: (1) all seats allocated within districts, and (2) adherence to the rank-size principle, such that the largest party gets the first seat in a district, and remaining seats are allocated in a way that respects their relative sizes (i.e., by any of the common PR formulas). We further say that for simple PR, “the vote for candidate and for party is one act” (p. 35). This latter condition still holds for any two-tier list-PR system, because there is a list vote that applies both for allocating seats within a district, and also for the “complex” feature of the supra-district compensation mechanism. Obviously, however, MMP as used in Germany violates the principle that “the vote for candidate and for party is one act.” So maybe it is not “simple enough” to qualify as an almost-simple complex system. (Yes, that was a complex statement, but that’s kind of the point.)

If MMP were to tend to produce a party system more fragmented than expected from the extended SPM, it might be due to the “second” vote, i.e., the list vote. To test this, one could aggregate all the nominal votes and use them as the notional list votes in a simulated compensation. (This is how MMP in Germany worked in 1949, albeit with compensation only at state level. It is also how MMP now works in Lesotho.) The aggregation of basic-tier votes should work better from the standpoint of modeling the party system impact of the key features of a given MMP system–the size of the basic tier and the share of seats in the compensation tier.

The catch in all this is that, of course, till quite recently German MMP was under-fragmented, according to the SPM, despite using a separate list vote. Thus the issue did not arise. The New Zealand MMP system also has matched expectations well, after the first three post-reform elections were over-fragmented relative to model prediction. The graph below shows the relationship over time between the expectations of the SPM and the observed values of effective number of seat-winning parties (NS) in both Germany and New Zealand. For the latter country, it includes the pre-reform FPTP system. In the case of Germany, it plots NS alternately, with the CDU and CSU considered separately. As I noted in the previous discussion, I believe the “correct” procedure, for this purpose, is to count the “Union” as one party, but both are included here for the sake of transparency. In both panels, the dashed mostly horizontal line is the output of the extended SPM for the countries’ respective MMP systems1; it will change level only when the electoral system changes. (For New Zealand, the solid horizontal line is the expectation under the FPTP system in use before 1996.)

The German party system from 1953 through 2005 was clearly fitting quite poorly, due to how under-fragmented it was for the electoral system in use. The old CDU/CSU and SPD were just too strong and overwhelmed the considerable permissiveness of the electoral rules.2 So clearly the question I am raising here–whether the two-vote feature of MMP means it should not be modeled just like any (other) two-tier PR system–is moot for those years. However, perhaps it has become an issue in recent German elections, including 2021. The underlying feature of voter behavior pushing the actual NS to have risen to well above “expectation” would be the greater tendency of voters towards giving their two votes to different parties. At least that would be the cause in 2021, given that we saw in the previous post that the basic tier produced almost exactly the degree of fragmentation that the SPM says to expect. It is the compensation tier that pushed it above expectation, and the problem here (from a modeling perspective) is that the formula implicitly assumes the votes being used in the compensation mechanism are the same votes being cast and turned into seats in the basic (nominal) tier. But with two votes, they are not, and with more voters splitting tickets, the assumption becomes more and more untenable.

The previous planting on this matter emphasized that the SPM is actually performing well, even in this most recent, and quite fragmented, election. I am not trying to undermine that obviously crucial point! However, the marked rise in NS since 2009–excepting 2013 when the FDP failed to clear the threshold–may suggest that the model’s assumption that the two votes are pretty similar could be problematic.

Maybe two-vote MMP is more complex after all than its characterization as a two-tier PR system–the simplest form of complex electoral system–implies. In fact, maybe I should stop referring to MMP as a sub-category of two-tier PR. Yet for various reasons, it is a convenient way to conceptualize the system, and as yesterday’s discussion of the recent German election showed, it does work quite well nonetheless. It could be based on a flawed premise, however, and the more voters cast their nominal and list votes differently, the more that flaw becomes apparent.

A work in progress… in other words (fair warning), more such nerdy posts on this topic are likely coming.

Notes

1. The “expected NS” line for Germany takes the tier ratio to be 0.5, even though as I argued in the previous entry, we really should use the actual share of compensation seats in the final allocation. This would have only minimal impact in the elections before 2013; in 2021, it makes a difference in “expected” NS of 0.36.

2. Partly this is due to the 5% list-vote threshold, which is not a factor in the version of the SPM I am using. In Votes from Seats, we develop an alternate model based only on a legal threshold. For a 5% threshold, regardless of other features, it predicts NS=3.08. This would be somewhat better for much of the earlier period in Germany. In fact, from 1953 through 2002, mean observed NS=2.57. In the book we show that the SPM based only on mean district magnitude and assembly size–plus for two-tier PR, tier ratio–generally performs better than the threshold model even though the former ignores the impact of any legal threshold. This is not the place to get into why that might be, or why the threshold might have “worked” strongly to limit the party system in Germany for most of the postwar period, but the permissiveness of a large assembly and large compensation tier is having more impact in recent times. It is an interesting question, however! For New Zealand, either model actually works well for the simple reason that they just happen to arrive at almost identical predictions (3.08 vs. 3.00), and that for the entire MMP era so far, mean NS has been 3.14.

The Germany 2021 result and the electoral system

The German general election of 2021 has resulted in a situation in which neither major party can form a government without either the other, or more likely, a coalition that takes in both the liberal FDP and the Greens. With the largest party, the social-democratic SPD, under 30% of seats, it is an unusually fragmented result compared to most German elections. Naturally, this being Fruits & Votes, attention turns to how much more fragmented this outcome is than expected, given the electoral system. The answer may be a bit of a surprise: not all that much. I expected this outcome to be a significant miss for the Seat Product Model (SPM). But it is really not that far off.

For a two-tier PR system, of which Germany’s MMP can be thought of as a subtype, we need to use the extended version of the SPM developed in Votes from Seats.

NS = 2.5t(MSB)1/6,

where NS is the effective number of seat-winning parties (here, meaning the expected NS), M is the mean district magnitude of the basic tier, SB is the total number of seats in the basic tier, and t is the “tier ratio” defined as the share of the total number of assembly seats allocated in the compensatory tier. For Germany, basic-tier M=1 and SB=299. The tier ratio could be coded as 0.5, because the initial design of the system is that there are 299 list tier seats, allocated to bring the result in line with the overall party-list vote percentages of each party that clears the threshold. However, in Germany the electoral law provides that the list tier can be expanded further to the extent needed to reach overall proportionality. Thus t is not fixed; we should probably use the ratio that the final results are based on, as NS would necessarily be lower if only 299 list seats had been available. In the final result, the Bundestag will have 735 seats, meaning 436 list seats, which gives us a tier ratio of t=436/735=0.593. Plug all this into the formula, and you get:

NS = 2.50.5932991/6=1.72*2.59=4.45.

Now, what was the actual NS in the final result? We have to ask ourselves whether to count to two Christian “Union” parties, the CDU and the CSU, as one party or two. The answer really depends on the question being asked. They are separate parties, with distinct organization, and they bargain separately over portfolios and policy when they are negotiating a coalition with another party. However, for purposes of the SPM, I firmly believe that when two or more parties in a bloc do not compete against each other (or, alternatively, do so only within lists over which votes are pooled for seat-allocation1), they should be treated as one. The SPM does not “care” whether candidates of the bloc in question are branded as CSU (as they are in Bavaria) or as CDU (the rest of Germany). It simple estimates the effective number of “agents of the electorate” given the electoral rules. In terms of national politics, these are the same “agent”–they always enter government together or go into opposition together, and they jointly nominate a leader to be their Chancellor candidate.

Taking the CDU/CSU as a “party” for this purpose, we get actual NS =4.84 in the 2021 election. So, given an expectation of 4.45, the actual outcome is just over 8.75% higher than expected. That is nothing too extraordinary. For comparison purposes, we can just take the ratio of actual NS to expected NS. Here are some elections in the dataset used for Votes from Seats that are in the same range of over-fragmentation as Germany 2021:

      country   year   simple   Ns   exp_Ns   ratio 
     Barbados   1981        1    1.87   1.735597   1.077439  
       Norway   1965        1    3.51   3.255616   1.078137  
    Sri Lanka   1970        1    2.49   2.307612   1.079037  
Dominican Rep   1990        1    3.05   2.810847   1.085082  
     Trinidad   2002        1    1.98   1.824064   1.085488  
      Iceland   1963        0    3.33   3.060313   1.088124  
       Israel   1961        1    5.37   4.932424   1.088714  
     Trinidad   2001        1       2   1.824064   1.096452  
     Trinidad   2000        1       2   1.824064   1.096452  
      Iceland   1999        0    3.45   3.146183   1.096567  
      Denmark   1950        0    3.98   3.624933   1.097951  
     

(The table indicates as ‘simple’ those with a single tier; others are two-tier.)

The ratio variable has a mean of 1.021 in the full dataset and a standard deviation of 0.359. Its 75th percentile is 1.224 (and 25th is 0.745). So the German election of 2021 is actually very well explained by this method. The degree of fragmentation we saw in this election is not too surprising. It is about what should be expected with MMP consisting of 299 nominal-tier M=1 seats and a very generous and flexible compensation tier.

As an aside, if we used the initial tier size (299, so t=0.5) in the formula, we would get an “expected” NS=4.09. This would mean a ratio of 1.183, still short of the 75th percentile of the 584 elections included in the book’s main statistical test. Here is the company it would be keeping in that neighborhood:

            country   year   simple   Ns   exp_Ns   ratio 
            Germany   2009        0    4.83   4.121066   1.172027  
St. Kitts and Nevis   2000        1    1.75   1.491301   1.173472  
         Luxembourg   2009        1    3.63   3.077289    1.17961  
             Canada   2004        1    3.03   2.560218   1.183493  
            Denmark   1998        0    4.71   3.965222   1.187828  
          Venezuela   1963        0    4.32    3.63006   1.190063  
        Korea South   1988        0    3.55   2.981969   1.190488  
     Czech Republic   2010        1    4.51   3.767128   1.197199  
            Iceland   1991        0    3.77   3.146183   1.198277  

This would put the German 2021 election about as “over-fragmented” as the Canadian election of 2004. In other words, still not a big deal. If we count the two “Union” parties separately, obviously the degree of over-fragmentation goes up considerably. As I have said already, I think for this purpose counting them as one is the correct decision.2

As far as size of the largest seat-winning party is concerned, the SPD has 206 seats, for 28.03%. The SPM would predict, given expected NS=4.45, that the largest should have 32.6% (240 seats out of 735); that’s a ratio of 0.860 (which is a slightly bigger miss than the NS ratio of 1.088, the reciprocal of which would be 0.919). It is worth pausing on this for a bit. Polling before the election said the largest party might be only on a quarter of the votes. This was accurate, as the SPD won 25.7%. The advantage ratio (%seats/%votes) is 1.09, which is rather high for an electoral system that promises as near-perfect proportionality as Germany’s current system does, with its compensation for overhangs (cases in which a party has won more nominal-tier seats in a state than its list votes would have entitled it to). This bonus is a result of a rather high below-threshold vote. Not as high in 2013, of course, when two parties (FDP and AfD) narrowly missed the nationwide 5% threshold. But still considerably high, at 8.6% combined for all parties that failed to win a seat.

It is also worth asking whether the logic behind the extended SPM for two-tier systems holds for this German election. The formula says that the basic tier produces an initial allocation of seats consistent with the SPM for simple systems, and then inflates it based on the size of the compensation tier. So we can ask what the effective number of seat-winning parties is in the basic tier alone. It should be NS =(MSB)1/6= 2991/6= 2.59. In fact, the basic-tier NS in this election was 2.51 (as before, taking CSU/CSU as one party). The ratio of 0.969 is a pretty trivial miss. We should expect the largest party to have won 0.490 of these seats (about 146). Actually the Union parties, which together won the most single-seat districts, won 143 (0.478). Thus Germany’s MMP system, in the 2021 election, actually did produce a basic-tier (nominal-tier) party system pretty much just like it should, given 299 seats and M=1 plurality, and then augmented this through a large compensatory national tier. The actual inflator is a factor of 1.93=4.84/2.51, rather than the expected 1.72=2.50.593. Had it been 1.72 instead, the final effective number of seat-winning parties would have been 4.32, about “half a party” less than in reality, implying almost exactly one third of seats to the SPD instead of just 28%.

This surprised me (pleasantly, of course). When I saw that the Greens and AfD each had won 16 seats in the nominal tier, I thought that was too many! But in fact, it works out. Maybe sometimes even I think Duverger had a law, or something. But given 299 single-seat districts, this is pretty much in line with expectations.

The outcome is interesting in the many ways that it serves as a primer on details of the electoral system. Here I mean not only the substantial expansion of the Bundestag from 598 to 735 seats, due to the way the compensation mechanism works, but also the thresholds. One of the best known features of the German electoral system is the 5% nationwide threshold. But of course, the threshold is more complex than that. It is 5% of the national party-list vote or three single-seat wins, except if a party is an ethnic-minority party. All these provisions were on display. For instance, the Linke (Left) party fell below the 5.0% threshold, yet is represented at full proportionality. That is because it won three individual mandates, thus fulfilling the “or” clause of the threshold. There was a point on election night when it looked as if the Linke might hold only two single-seat districts. In that case, with less than 5% of the list votes nationwide, it would have held only those seats as its total. By winning three, it is entitled under the law to full proportional compensation, and as a result it was awarded 36 list seats. Then, for the first time in a very long time, an ethnic party has won a seat. The South Schleswig Voters’ Association (SSW), which had not contested federal elections in decades, ran in this one and was able to win a single (list) seat, because as a representative of the Danish and Frisian minorities, it is exempt from the usual threshold provisions, as long as its votes are sufficient to qualify it for a seat when the threshold is ignored. Its 0.1% of the national vote was good enough. The SSW has had some renewed success in state elections in Schleswig-Holstein recently, and now it has scored a seat in the federal parliament for the first time since 1949. In 1949, the MMP system was a bit different, in that the 5% threshold was determined state-by-state, rather than nationwide. If the threshold had been state-by-state in this election, one other party would have earned seats. The Free Voters won around 7.5% of party-list votes in Bavaria. However, they managed only 2.9% nationwide (and no district seat), so they are shut out.

Now attention turns to what the coalition will be. Two options are on the table: SPD+Greens+FDP (“traffic light”) or CDU/CSU+Greens+FDP (“Jamaica”). The possibility of a broad left coalition has been ruled out by the election results: SPD+Green+Linke is not a majority. It was never likely anyway; the SPD and Greens did not spend recent years convincing voters they were safe options near the center of German politics to team up with the far left. Nonetheless, had it been mathematically possible the SPD might have used it as leverage against the FDP. My guess is that the traffic light coalition will form. Despite some serious policy differences between the FDP and the other two, it would be a government made up of the winners of the election, as these three parties all gained votes compared to 2017. On the other hand, one led by the CDU/CSU would be led by a pretty big loser, even though it is mathematically possible and the Greens seem to have been positioning for it over the last several years.3 Following the election, the DW live blog has been reporting on comments by various prominent CDU and CSU politicians that could be interpreted as saying the bloc needs some time in opposition, after the disappointing result. I suspect this is the view that will prevail, and after a lot of intense and difficult bargaining, Germany will be led by a traffic light coalition for the first time.

____

Notes

1. Here I am thinking of cases like Chile, where alliance lists contain candidates of different parties, but for purposes of how the electoral system assigns seats between competing teams of candidates, we should count the alliances, not the component parties. The same condition applies in Brazil and Finland, only there it is essentially impossible to aggregate to a meaningful national alliance category because the combinations of parties are not always the same across districts. In Chile, and also in the FPTP case of India–as well as in the current case of Germany–there is no such problem, as the alliances are nationwide in scope and consistent across districts.

2. For the record, counting them separately yields NS=5.51 in this election, which would put the ratio just barely above the 75th percentile.

3.To be clear, they are much happier working with the SPD, but what I mean is that their positioning for the possibility of a coalition with the CDU/CSU should make finding common ground with the FDP easier than it otherwise would have been.