Canada and UK 2019: District level fragmentation

With two of the big Westminster parliamentary democracies having had general elections in 2019, we have a good opportunity to assess the state of district-level competition in FPTP electoral systems.

(Caution: Deep nerd’s dive here!)

Before we turn to the district level, a short overview of what is expected at the national level is in order.

As noted previously, Canada’s election produced a nationwide seat balance that was extremely close to what we expect from the Seat Product Model (SPM), yet the nationwide votes were exceedingly fragmented (and, anomalously, the largest seat-winning party was second in votes). The UK election, on the other hand, was significantly less fragmented in the parliamentary outcome than we expect from the SPM, even if it was in key respects a “typical” FPTP outcome in terms of manufacturing a majority for a party with less than a majority of the vote.

In general, over decades, Canada tends to conform well to the SPM expectation for the shape of its parliamentary party system, whereas the UK is a more challenging case from the SPM’s perspective.

The SPM states that the effective number of seat-winning parties (NS) should be the seat product, raise to the power, 1/6. The seat product is the assembly size, times the mean district magnitude. The SPM predictions for NS explain around 60% of the variance in actual outcomes for elections around the world under a wide variety of electoral systems. SPM predictions for other output quantities also explain in the neighborhood of 60%. So the SPM is both successful at explaining the real world of seat and vote fragmentation, and leaves plenty of room for country-specific or election-specific “other factors” (i.e., the other 40%). The SPM is based on deductive logic, starting from the minimum and maximum possible outcomes for a given number of seats at stake (in a district or an assembly). The logic is spelled out in Votes from Seats.

In the case of a FPTP system, the SPM makes the bold claim that we can understand the shape of a party system by knowing only the assembly size. That is because with district magnitude, M=1, the seat product is fully described by the country’s total number of seats, S, which is also the number of districts in which the voting is carried out. Thus we expect NS=S1/6. Let’s call this “Equation 1.”

For Canada’s current assembly size (338), this means NS=2.64, as an average expectation. Actual elections have tended to come pretty close–again, on average. Of course, individual elections might vary in one direction or the other. (The assembly size was also formerly smaller, but in recent times, not by enough to concern ourselves too much for purposes of this analysis.) For the UK, the corresponding expectation would be 2.94 based on a seat product of 650.

The actual Canadian election of 2019 resulted in NS=2.79; for the UK it was 2.39. Thus for Canada, we have a result very close to the expectation (ratio of actual to expected is 1.0578). For the UK, the actual result was quite short (ratio of 0.8913). As I said, the UK is a challenging, even aberrant, case– at least at the national level.

What about the district level? A national outcome is obviously somehow an aggregation of all those separate district-level outcomes. The SPM, however, sees it differently. It says that the districts are just arenas in which the nationwide election plays out. That is, we have a logical grounding that says, given a national electoral system with some seat product, we know what the nationwide party system should look like. From that we can further deduce what the average district should look like, given that each district is “embedded” in the very same national electoral system. (The logic behind this is spelled out in Votes from Seats, Chapter 10).

The crazy claim of the SPM, district-level extension, is that under FPTP, assembly size alone shapes the effective number of votes-earning parties in the average district (N’V, where the prime mark reminds us that we are talking about the district-level quantity rather than the nationwide one). (Note that for FPTP, it must be the case that N’S=1, always and in every district).

The formula for expected N’V under FPTP is: N’V=1.59S1/12 (Equation 2). It has a strictly logical basis, but I am not going to take the space to spell it out here; I will come back to that “1.59” below, however. It is verified empirically on a wide set of elections, including those from large-assembly FPTP cases like Canada, India, and the UK. So what I want to do now is see how the elections of 2019 in Canada and UK compare to this expectation. (Some day I will do this for India’s 2019 election, too.)

If the effective number of seat-winning parties at the national level (NS) is off, relative to the SPM, then it should be expected that the average district-level effective number of vote-earning parties (N’V) would be off as well. They are, after all, derived from the same underlying factor–the number of single-seat districts, i.e., the assembly size (S). We already know that NS was close to expectation in Canada, but well off in the UK in 2019. So how about the districts? In addition to checking this against the expectation from S alone, we can also check one other way: from actual national NS. We can derive an expected connection of N’V to NS via basic algebra. We just substitute the value from one equation into the other (using Equations 1 and 2). If we have NS=S1/6 then it must be that S= NS6. So we can substitute:

N’V=1.59(NS6)1/12= 1.59√NS (Equation 3).

In a forthcoming book chapter, Cory L. Struthers and I show that this works not only algebraically, but also empirically. We also suggest a logical foundation to it, which would require further analysis before we would know if it is really on target. The short version suggested by the equation is that the voting in any given district tends to be some function of (1) the basic tendency of M=1 to yield two-candidate competition (yes, Duverger!) in isolation and (2) the extra-district viability of competing parties due to the district’s not being isolated, but rather embedded in the national system. The 1.59, which we already saw in Equation 2, is just 22/3; it is the expected N’V if there were exactly two vote-earning parties, because it is already established–by Taagepera (2007)–that the effective number tends to be the actual number, raised to the power, two thirds. And the square root of NS suggests that parties that win some share of seats (i.e., can contribute more or less to the value of NS) tend to attract votes even though they may have no chance of winning in any given district. By having some tendency to attract votes based on their overall parliamentary representation, they contribute to N’V because voters tend to vote based on the national (expected, given it is the same election) outcome rather than what is going on in their district (about which they may have poor information or simply not actually care about). If the parliamentary party system were fully replicated in each district, the exponent on NS would be 1. If it were not replicated at all, the exponent would be zero. On average, and in absence of any other information, it can be expected to be 0.5, i.e., the square root.

How does this hold up in the two elections we are looking at in 2019? Spoiler alert: quite well in the UK, and quite badly in Canada. Here are graphs, which are kernel density plots (basically, smoothed histograms). These plots show how actual districts in each election were distributed across the range of observed values of N’V, which in both elections ranged from around 1.35 to just short of 4.5. The curve peaks near the median, and I have marked the arithmetic mean with a thin gray line. The line of most interest, given the question of how the actual parliamentary outcome played out in each district is the long-dash line–the expected value of N’V based on actual NS. This corresponds to Equation 3. I also show the expectation based solely on assembly size (light dashed line); we already have no reason to expect this to be close in the UK, but maybe it would be in Canada, given that the actual nationwide NS was close to the SPM expectation, based on S (Equation 2).

Here is the UK, then Canada, 2019.

What we see here is interesting (OK, to me) and also a little unexpected. It is the UK in which the actual mean N’V is almost the same as the expectation from nationwide NS (i.e., Equation 3). We have actual mean N’V=2.485 compared to expected N’V from actual NS of 2.45; the ratio of actual to expected is 1.014. We can hardly ask for better than that! So, the nationwide party system (as measured by NS) itself may be well off the SPM expectation, but the vote fragmentation of the average district (N’V) closely tracks the logic that seems to stand behind Equation 3. Voters in the UK 2019 election tended to vote in the average district as if parties’ national viability mattered in their choice.

In Canada, on the other hand, even though national NS was very close to SPM expectation, the actual average district’s N’V (2.97) was really nowhere near either the expectation solely from S (the light dashed line, at 2.58) or the expectation from the actual NS (2.66). The average district was just so much more fragmented than it “should be” by either definition of how things ought to be! (The ratio of actual to that expected from Equation 3 is 1.116; the Equation 3 expectation is almost exactly the 25th percentile of the distribution.)

The Canadian outcome looks as if the exponent on actual NS in Equation 3 were around 0.64 instead of 0.5. Why? Who knows, but one implication is that the NDP (the third national party) performed far better in votes than the party’s contribution to NS implies that it should have. Such an overvaluing of a party’s “viability” would result if voters expected the party to do much better in terms of seats than it did. This is probably a good description of what happened, given that pre-election seat extrapolations implied the NDP would win many more seats than it did (and the Liberals fewer). The NDP also underperformed its polling aggregate in votes (while Liberals over-performed), but it held on to many more voters than it “should have” given its final seat-winning ability would imply. That is, the actual result in votes suggests a failure to update fully as the parties’ seat prospects shifted downward at the very end of the campaign. In fact, if we compare the final CBC poll tracker and seat projections to the ultimate result, we find that their actual votes dropped by 13.6% but their seats dropped by 31.7% (percent change, not percentage points!). In other words, this was just an unusually difficult context for voters to calibrate the expectations that Equation 3 implies they tend to make. (I am assuming the polls were “correct” at the time they were produced; however, if we assume they were wrong and the voters believed them anyway, I think the implications would be the same.)

It should be understood that the divergence from expectation is not caused by certain provinces, like Quebec, having a different party system due to a regional party, as some conventional expectations might point towards. While Quebec’s size is sufficient to exert a significant impact on the overall mean, it is not capable of shifting it from an expected 2.6 or 2.7 towards an observed 3.0! In fact, if we drop the Quebec observations, we still have a mean N’V=2.876 for the rest of Canada. The high fragmentation of the average district in the 2019 Canadian election is thus due to a Canada-wide phenomenon of voters voting for smaller parties at a greater rate than their actual viability would suggest they “should”. In other words, voters seem to have acted as if Trudeau’s promise that 2015 would be the last election under FPTP had actually come true! It did not, and the electoral system did its SPM-indued duty as it should, even if the voters were not playing along.

On the other hand, in the UK, voters played along just as they should. Their behavior produced a district-level mean vote fragmentation that logically fits the actual nationwide seat balance resulting from how their votes translated into seats under FPTP. There’s some solace in that, I suppose.

The Brexit Party

Just a quick add-on to my previous remarks on the UK 2019 election. Via @kiwiting on Twitter comes this example of a Brexit Party local leaflet.

Look closely and you might actually see the local candidate’s name! As I stress in the preceding post, I expect parties under FPTP (at least in parliamentary systems) to require a national presence in the party system in order normally to do well at the constituency level. That is a key insight of the Seat Product Model, and how it stands apart from “bottom-up” approaches that stress local district-level “coordination” as what drives a party system. But this is pretty extreme: the Brexit Party is not only a single-issue party, it is also a one-man band!

Even though this party at one point was polling above 20% (and won a plurality of the UK vote in the European Parliament elections), it was always hard for me to take the Brexit Party seriously. On the one hand, it certainly is a nationally focused party. On the other hand, the leader Nigel Farage made a decision not to contest any constituency, or to target even one seat somewhere that some candidate of the party might win. The process behind the SPM implies that voters respond to the “viability” of a smaller party, and tend to vote for it without too much regard for the viability of its candidate in their own district. But for that to work, it has to be viable–and preferably winning–somewhere. Not only did the Brexit Party not even try this, it pulled its candidates out of seats the Conservatives hold, while retaining candidates only in districts held by other parties. It is a bizarre strategy if the party was serious, and it is no wonder the party is on life support. Of course, they are going to get their one policy issue enacted (even if not as “hard” as they would like), precisely by not posing too big a risk to the incumbent government’s pursuit of a (manufactured) majority.

UK election 2019

The UK general election is almost here. At this point, it seems quite unlikely that the result will be anything other than a good old fashioned FPTP manufactured majority. Boris Johnson and his Conservatives will win a majority of seats, barring a surprise, despite under 45% of the votes, and will be able to pass their Brexit deal.

If one looks at the polling aggregate graph by the Economist, one might be tempted to conclude it was also a good old fashioned “Duvergerian” pattern at work. As recently as early October, before the election was legislated, the Conservatives were leading on about 33% of the votes, and three other parties ranged from 12% to 25%. Go back further, to June, and all for were in the 18–25% range (with Labour then on top, and the Brexit Party ahead of the Conservatives). Since the latter part of October, and especially since the campaign formally got underway, Conservatives and Labour have both taken off, at the expense of the LibDem and Brexit parties. Notably, the gap between the top two has been quite steady, at 8-10 percentage points. Unlike 2017, there is no evidence at all that Labour is closing the gap. Labour simply are hoovering up the non-Tory (and Remain or second-referendum) votes at the same time as Leave voters have realized there’s no point in voting for a single-issue Brexit Party when the Tories have a pretty “hard” Brexit deal already to go, if only they win a majority of seats.

So, on the one hand, a far more “normal” election for a FPTP-parliamentary system than seemed possible during the long parliamentary deadlock of the past year or more. Just like Duverger’s “law” predicts, right? Desertion of the third and fourth parties for the top two.

Only sort of. Let’s take the current polling estimates for the parties (and not forgetting to include the current 5% “other”, which I will treat as one party, given most of it is one party–the Scottish National Party). It results in an effective number of vote-earning parties of 3.05. That’s a little high for a supposedly classic two-party system! It is, however, lower than seen at any election from 1997 through 2015. In 2017, however, it was 2.89, which was the lowest since 1979. The top two would be combining for 78% of the votes, which is a little higher than most elections from 1974 (February, in a two-election year) through 2001. Even in 2017, hailed by many at the time as the return to two-party politics–albeit dubiously–had a combined top-two of just 82.4%. (It looks like a high figure only compared to 2005-2015, when it ranged from 65.1% to 67.6%.)

Of course, it is the seats that really matter. Seat projections based on election polls under FPTP are never easy. There are various ones out there, but I will go with YouGov‘s.* It has the Conservatives with a projected 359 seats, which is 55.2%, with Labour on 211 (32.5%). Taking all the parties (and here breaking the “Northern Ireland” bloc down a bit, as we know it will consist of more than one such party), we get an effective number of seat-winning parties around 2.4. That is even lower than 2015, driven mainly by the presence of an expected single-party majority.

[*Note: just after I posted this, YouGov posted an update of their projections. I am not going to revise the numbers here. The differences are small, though potentially politically significant. See my first comment below this post.]

The problem with the standard Duvergerian claims about FPTP is that they ignore assembly size: In a larger assembly, we should expect more parties, other things (like district magnitude and formula) equal. While we could argue over how much the expected results of the 2019 election correspond to the so-called law, I’d rather not. What is of interest to me is that the UK case continues its long-term defiance of the Seat Product Model (SPM), and that’s something that I can’t take lying down.

While the conventional wisdom would see 2017 and 2019 as some sort of return to normalcy, it’s actually a challenging case for me. From the SPM (which explains over 60% of the variation in party-system outcomes worldwide, including FPTP systems), we should expect:

Effective number of seat-winning parties: 2.95.

Seat share of the largest party: 0.445.

Effective number of vote-earning parties: 3.33.

The seat outcomes actually never have come very close to the expectations. As for votes, the 1987 election got it right, but was a terrible performer in terms of seats (effective N=2.17!). Taking all the indicators together, the 2010 election is about the closest to what should be “normal” for a FPTP system with such a large assembly: effective N on votes 3.72, seats 2.57, and largest seat share of 0.47. So why was that not finally the start of the kind of party system the country “should” have? I guess we need to blame Nick Clegg. Or David Cameron. (I’d rather blame the latter; he was the one, after all, who thought a Brexit referendum was a good enough idea to go ahead with it.) More to the point, voters’ reaction to Clegg and the LibDems entering a coalition and–gasp–making policy compromises. After which, voters reverted to supporting the big two in greater shares than they are supposed to. In other words, contingency and path dependency overcome the SPM in this case. I hate to admit it, but it’s the best I’ve got!

Speaking of the LibDems, they should have had an opportunity here. Labour has the most unpopular opposition leader in decades. (Deservedly so, but I digress.) And the best hope for stopping Brexit would be tactical voting to increase their chances to win seats where Labour is not best positioned to defeat a Tory. Yet, despite lots of constituency-level tactical voting advice being offered in this campaign, there’s little evidence the message is getting though.

There is tactical voting happening, but as Rob Johns points out in a short video, it is happening based on the national outcome and not on district level. Under the Duvergerian conventional wisdom, voters are alleged to think of their constituency, and vote tactically (strategically) to effect the local outcome. Yet in real life, only a relatively small minority of voters behave that way. That voters use a strategy based on who is best placed to defeat a party they do not like on the national level, instead of at the constituency level, is a point made forcefully by Richard Johnston in his book, The Canadian Party System. It is also the underlying logic of the SPM itself.

So from the standpoint of the SPM, what is surprising is not that there isn’t more tactical voting at the constituency level. It is that there does not remain (so to speak) a strong enough third party, such as the Liberal Democrats, to appear viable nationally so that voters would be willing to vote for its district candidates. Quite apart from the legacy of the coalition that I referred to above, the case for the LibDems as a viable counterweight probably was not helped by a tactical decision it made in this campaign. Its leader, Jo Swinson, declared that a LibDem government would revoke the Article 50 notification and cancel Brexit. Put aside the ridiculous idea that there would have been a LibDem government. If one had resulted from this election, it would have been on far less than 50% of the votes. So you have a government resting on a minority promising to go back on the majority voice of the 2016 referendum without even bothering with a second referendum. That seemed at the time like a dumb position for the party to take. Only recently has Swinson offered the message of what the LibDems could accomplish in a no-majority parliament. But it’s too late. There almost certainly won’t be such a parliament.

The UK really needs a national third party (and fourth…). Contrary to the Duvergerian conventional wisdom, the electoral system actually could sustain it; we would expect the party system to look more like Canada’s (which conforms to the SPM very well, both over time and, in terms of seats, in 2019). Given the larger assembly, the British party system should be even less two-party dominated than Canada’s actually is. It is by now rather apparent that the LibDems are not the third party the system needs to realize its full potential. Will one emerge? Alas, not soon enough to stop a hard Brexit from being implemented by a manufactured majority (for a leader who is pretty unpopular himself) while Labour gobbles up most of the opposition, but falls well short.

Canada 2019: Results and a good night for the Seat Product Model

Add Canada 2019 to the set of plurality reversals. As anticipated before the election, the two largest parties each ended up with around one third of the vote. This is the lowest vote percentage for a governing party in Canada ever, I believe. The seats are somewhat less close than the CBC’s Poll Tracker estimated they would be. Instead of 133 seats to 123, the seats split 157 to 121. The Liberals are indeed that largest seat-winner, despite trailing the Conservatives in votes percentage, 34.4 – 33.1.

The NDP was either overestimated by polls or, more likely, suffered some late strategic defection. Instead of the near 19% of the vote in the final Poll Tracker, the party ended up with only 15.9%. More importantly, its seats stand at only 24, well below where estimates late in the campaign had them (per the CBC Poll Tracker).

As excepted the BQ had a good night, with 32 seats. The Greens picked up one new seat to augment the two they already held. The new seat is Fredricton, New Brunswick, whereas the other two are both on Vancouver Island.

In what I will call the two best pieces of news form the night (other than there being no single-party majority), the People’s Party crashed and burned, winning only 1.6% and seeing its leader lose his seat. That and the fact that Jody Wilson-Raybould, the former Attorney General who was kicked out of the Liberal caucus, retained her seat, Vancouver-Granville, as an independent.


Anomalous FPTP

I will certainly use this result often as a demonstration of how the first-past-the-post (FPTP) system can produce strange results.

Not only the plurality reversal for the top two, but the differential treatment of the next three parties, show anomalies of the sort that are inherent to FPTP. The BQ is only somewhat larger in votes than the Green Party, but will have more than ten times the number of seats. Under FPTP, it is good to have efficient regional distribution of support, and getting all your votes in one province, where you perform exceptionally well, is really efficient. The Greens, on the other hand, gained in almost all provinces, but it was good enough to add only one seat.

The NDP’s situation is one of a quite strong third party, but also inefficient regional distribution: 7.1% of the seats on 16% of the votes is a punishing result, but nothing at all unexpected, given the electoral system.

For that matter, the plurality reversal is itself a signal of the problem of inefficient vote distribution. The Conservative Party mostly gained votes where they could not help the party win seats, whereas the Liberals were much more successful winning close contests.

In his victory speech, PM Justin Trudeau was bold enough to use the M-word (mandate), but this most certainly is not one. For the moment, he can be pretty happy he broke that promise on 2015 being the last FPTP election. His party remains in position to form the government, and has a substantial seat bonus. The advantage ratio (%seats/%seats) is 1.40. (How does that compare with past elections? Click to see.)

Canada would be well served by at least some degree of proportionality. In fact, so would the Conservatives, given their tendency to run up margins where they are already strong. (Note that they are only barely over-represented in seats, with 35.8%.) However, this result is unlikely to advance the cause of reform, as the Liberals’ position–46% of the seats and a 36-seat (more than ten percentage point) edge over the runner-up–looks quite solid.

The other reason the country could really use electoral reform is the map. There is no Liberal red to be seen from central Ontario westward, except around Vancouver (and two northern territories). The party lost some of its ministers’ reelection bids in Alberta and Saskatchewan. With even a minimally proportional system, the situation of a governing party without members of its caucus in nearly every province would not happen.

While a PR system would be beneficial, the country is stuck with FPTP at least for now. So how did this result compare to what we should expect from the electoral system actually in use?


The Seat Product Model and the outcome

The Seat Product Model (SPM) performed better than the CBC Poll Tracker’s seat estimator. For an assembly of 338 and districts with magnitude of 1, we should expect the largest party to have, on average, 48.3% of the seats, which would be 163 seats. So the actual result (46.4%) misses the expectation by 6 seats, or 1.78 percentage points (compared to the a 20-plus, or 6 percentage point, miss by the Poll Tracker).

Of course, the SPM has one advantage in its favor: it does not “know” that the seat-winning party would have under 33.3% of the vote, whereas the Poll Tracker must work with this expectation (and, as it turned out, reality). In fact, when a party wins 48.3% of the seats, the formulas of SPM (collected in Table 9.2 of Votes from Seats) expect it to have won 43.3% of the votes. (Theoretically, we do not expect the SPM to perform as well with votes as with the seats that are at its core; but in Votes from Seats, we show that, on average, it performs about equally as well with both.) The Liberals underperformed this expectation by more than ten percentage points! The voters genuinely voted for something their electoral system could not deliver, even if the system indeed delivered what should be expected solely on institutional grounds.

In terms of the effective number of seat-winning parties (NS), the actual result was 2.79. This is slightly higher than the SPM expectation, which is 2.64. The miss is minor, with a result only 1.057 times expectation.

On the other hand, the effective number of vote-earning parties (NV) was 3.79. The SPM expects 3.04. Let me pause and emphasize that point. Because Canada uses FPTP in a 338-seat assembly, we should expect the votes to resemble a “three-party system” and not the two-party system that all the conventional “Duvergerian” wisdom claims. If we calculated expected Nbased on the known NS=2.79, we would expect NV=3.17. However, neither the SPM nor Duverger’s “law” expects that the largest party nationwide should have only around a third of the votes. That is the really remarkable thing about this outcome.


The district level

At the district level, there were numerous non-Duvergerian outcomes, as would be expected with the known distribution of nationwide votes among parties. According to an extension of the SPM (in a forthcoming book chapter), we should expect the effective number of vote-earning parties at the average district (N’V) to be 1.59 times the square root of the nationwide NS. That would be 2.66. It will be a while before I am able to calculate what it actually was, but it would not surprise me if it was a fair bit higher than that. But, again, let me pause and say that a Duvergerian two-party competition at the district level is NOT to be expected, given both the nationwide electoral system and the actual aggregate seat outcome. (If we went off expected nationwide NS, instead of the known outcome, the district-level mean still would be predicted to be 2.58; see Chapter 10 of Votes from Seats.) Canadian elections of the past several decades have tended to conform closely to this expectation for district-level N’V.

The country does not tend to have two-party contests at district level, nor should it (when we have the Seat Product Model to guide our expectations). In other words, voters do not tend to vote in order to “coordinate” their district outcome around the two most viable candidates. They tend to vote more towards their expectation (or desire) about what the nationwide parliamentary outcome will be. This is so even in Quebec where, in this election, many Francophone voters returned to the regional party, the Bloc Québécois. Quebec has numerous district contests that feature three or four viable parties.

So if your image of Canada’s party system is that in Quebec districts it is BQ vs. Liberal, with other parties barely registering, while elsewhere it is Liberal vs. Conservative, except where it is one of those vs. NDP, it is well past time to update. Canada does not have nationwide multiparty politics because it has separate regional two-party systems (as many folks, even political scientists, seem to believe). Canada has district-level multipartism because it has nationwide multipartism. (See Richard Johnston’s outstanding book for a rich “analytic history” that supports this point.) And this may be even more true in the one province in which there is (again) a strong regional party. Consider the aggregate provincial outcome in terms of vote percentages in Quebec: Liberal 34.2% (slightly higher than nationwide), BQ 32.5%, Conservative 16.0%, NDP 10.7%, Green 4.5%. This gives a provincial-level NV of 3.82, a bit higher than nationwide.

I will offer a few striking examples of multiparty contests at district level, just to illustrate the point. The new Green Party MP from Fredericton, Jenica Atwin, won 32.8% of the vote. The Conservative had 31.1%, the Liberal 27.3%, and the NDP 6.0%. There may indeed have been strategic voting happening here, with some NDP voters–the party had 9.9% in 2015–switching to Atwin to stop the Conservative (and perhaps some who don’t like the Greens boosting the Liberal). But the outcome here is N’V=3.53!

The change from 2015 in Fredericton is really striking, as the Liberal candidate was an incumbent who had won 49.3% in 2015 (against 28.4% for the Conservative, meaning this party gained a little here in 2019). Clearly many Liberals defected from their party to the Green following that party’s success, including a local win, in the recent provincial election. In doing so they only narrowly avoided the serious “coordination failure” that would have been a Conservative win.

Another Green MP, the reelected Paul Manly in Nanaimo-Ladysmith, won 34.5%. This was actually a pretty clear victory despite being barely over a third of the vote; Manly had been elected in a by-election this past May with 37.3%. The runner-up Conservative had only 25.9% in the general election contest, the NDP 23.7%, Liberal 13.6%. N’V=3.83!

Wilson-Raybould’s win in Vancouver-Granville as an independent was also with under a third of the vote. She had 32.3%, beating the Liberal’s candidate (26.6%) and the Conservatives’ (22.1%). The NDP candidate had 13.1%. The Greens, who tried to recruit Wilson-Raybould to be their candidate, put up their own against her, who got 5.0%. It should be noted that the NDP candidate in this riding last time won 26.9%, so it would appear there was ample strategic voting here in Wilson-Raybould’s favor. (She won 43.9% as the Liberal candidate in 2015.) The Green voters, on the other hand, did not seem to warm to their near-candidate; the party’s actual candidate did better in this district in 2019 than in 2015 (when the party got 3.1%).

One of my favorite cases is Sherbrooke, in Quebec. The winner was Liberal Elisabeth Briere with 29.3%, edging out an NDP incumbent who won 28.3% in this election. He had won the seat with 37.3% in 2015. Close behind in this year’s contest was the BQ candidate who had 25.8%. Following behind them was a Conservative (10.7%), and Green (4.5%). N’V=4.06!! The Liberals won this by basically standing still in vote share, having lost this district by a wide margin in 2015 when their candidate had 29.8%.

A few interesting tidbits from candidate backgrounds. Bernier’s defeat in his own riding of Beauce was at the hands of a dairy farmer, Richard Lehoux. The Conservatives recruited him because of Bernier’s opposition to supply management policies in the dairy sector. (Info found in the CBC’s Live Blog.) Lehoux won only 38.6% of the vote, but it was sufficient to beat Bernier rather badly, as the latter (elected as a Conservative in 2015 and previously) had just 28.4%.

There were several mayors recruited to run, including a case in Quebec where the Conservatives hoped the candidate’s local popularity would overcome the party leader’s unpopularity. (The specific case was Trois-Rivières; the Conservative finished a close third in a riding the BQ candidate won with 28.5%.) There was also an Olympic medal-winning kayaker, Adam van Koeverden, whom the Liberals recruited in Milton (in Toronto, Ontario) to run against the Conservative Deputy Leader, Lisa Raitt. He defeated her–easily, winning 51.4% to her 36.5%. Presumably his celebrity (and perhaps his local roots, which he made a point to emphasize in an interview after his victory was confirmed) helped him win despite a nationwide swing against the Liberals and in favor of the Conservatives. (She had won 54.4% in 2015.) In other words, while I may emphasize that district politics under FPTP in a parliamentary system is mostly national politics, there is still plenty of room for local and personal factors to matter.


What it means for the near term

As to the shape of the government to result, it should be a reasonably stable minority government, although it may not last full term. It can form legislative majorities with either the BQ or the NDP, and thus need not be tied to either one in a coalition. And the NDP certainly is not strong enough to demand a coalition (even if it wanted to try). Nor is it likely strong enough to demand action on electoral reform, even if an election in which two thirds of the voters voted against the governing party, and various other aspects of the outcome can be seen as anomalous, suggests that reform is needed more than ever.

Israel 2019b, compared to 2019a

Here, following up on the earlier discussion of post-election bargaining scenarios, I want to compare Israel’s two elections of 2019 on several statistical measures. The 2019b (September) results are not quite official yet, but are very unlikely to change other than in the smallest of voting detail.

The table below compares the votes for Netanyahu’s “Bibi bloc” of right-wing and Haredi parties, by various definitions, as well as the indicators of fragmentation: effective number of parties by seats and votes, total number of lists with seats, and the seats won by the largest list. For each measure, there is a comparison of change from April to September. The final three columns refer to output of the Seat Product Model (SPM) for the indicators of fragmentation–what is expected from the model (given an assembly size of 120 and district magnitude also of 120), and ratios of the actual indicators to the expectation.

Measure April Sept change SPM expected Ratio, April Ratio, Sept.
Bibi bloc (percent votes) 48.7 44.5 -4.2
… plus YB 52.7 51.5 -1.2
… plus Otzma 46.4
… plus YB & Otzma 52.7 53.3 0.6
Effective N, seats 5.24 5.67 0.43 4.93 1.06 1.15
Effective N, votes 6.33 6.11 -0.22 5.23 1.21 1.17
No. of lists with 1 or more seats 11 9 -2 11 1.00 0.82
Seats for largest list 35 33 -2 36 0.97 0.92

The scale of the defeat for the core Bibi bloc is clear. Already in April, these parties had less than 50% of the votes, at 48.7%, which is why they won only 60 seats under Israel’s proportional system. If we include Yisrael Beiteinu in the total Bibi bloc, we get 52.7% (which is why this larger definition of the bloc had 65 seats). As I have explained already–both before and after the most recent election–we should not count YB in the bloc, particularly since it was this party’s actions that precipitated the early elections of 2019–yes, both of them.

In the second election of 2019, this Bibi bloc fell to 44.5% of the vote, a drop of 4.2 percentage points. If we include YB, they do have a narrow majority of votes (51.2%), but we should not include them. However, we probably should include Otzma Yehudit, given that it was part of the Union of Right Wing Parties in April, and probably would have been invited to join a coalition had it cleared the threshold in the September election. But still this is short of a voting majority without YB, at 46.4% (which would mean a loss of 2.3 percentage points off the April showing of 48.7).

For a baseline, consider that the Bibi bloc had 48.4% in 2015, or 53.5% including YB (which was without doubt part of the bloc at that time–their staying out of the coalition initially in 2015 was a surprise). Note that, leaving out YB, they were already below majority voter support in 2015, but had managed 61 seats. The reason they gained ever so slightly in votes in April, yet got only 60 seats, was all the wasted votes for New Right (3.22%), which did not clear the threshold in the April, 2019, election.*

If we include both Otzma and YB in the 2019b election, it looks like a very small gain for the wider bloc. But we should not do this because some of YB’s increased votes probably came from Blue and White or other parties not in the right, due to YB’s promise not to return to a Likud-led government unless it was a “unity” government with Blue and White.

On the fragmentation indicators, the effective number of seat-winning parties went up, from 5.24 to 5.67, despite the drop of the total number of lists winning seats, from 11 to 9. The increase in the effective number is due to the smaller size of the largest party in the more recent election, 33 seats (Blue and White) vs. 35 (tie between Blue & White and Likud).

The effective number of vote-earning parties came down somewhat, from 6.33 to 6.11. None of these measures is much different than what we should expect under the SPM, although the raw number of represented lists this time is actually smaller than expected, while the effective number of seat winning parties was closer to the expectation in April than now.

We should expect the largest party, given this electoral system, to have 30.2% of the seats, which out of 120 works out to 36 (rounded down). The election pretty much nailed that in April, but this election saw a return to a smaller than expected plurality party.

So, strictly from the SPM, this was a slightly less “normal” election than 2019a, although not too far off. From the standpoint of the usual pattern with a “b” election (a second one within a year), it was, as I anticipated, a little unusual. Typically, the effective numbers go down and the size of the largest up. Israel went the opposite way between April and September, and thus government formation still will not be easy.

* We could go back and include Yachad (of which Otzma Yehudit was a part) in the 2015 count, which would bring it to 51.3%, but at the time I do not recall their being taken seriously as part of the bloc. Doing so, of course, increases the scale of the loss of voter support already as of the first election of 2019.

Israel is about to have a very unusual ‘b’ election

Israel is about to hold its second election of 2019, and it will be unusual, relative to other cases of a second election within a year elsewhere. While the number of lists winning seats is likely to go down, other indicators of fragmentation are likely to go up.

Using the National Level Party Systems Dataset (Struthers, Li, and Shugart, 2018), I performed calculations to find out how the standard indicators of party-system fragmentation change from a first election that fails to produce a “stable” government or any government at all, leading to a second election. I looked at all cases in the dataset in which two elections were held in the same Gregorian calendar year, plus all cases where an election is in the second half of a year and followed by another in the first half of the next year. The first table below gives the full list, including the first and second election in each sequence. In one case in the dataset (Greece, 1989-1990) the second election was followed by yet another within a year, indicated by a “3” in the final column. Note that a country’s data sequence begins in the early post-WWII era or when a country democratized and ends in 2016, so any cases outside that timeframe are not included.

country year date mo within_yr_seq
Denmark 1953 4/21/53 4 1
Denmark 1953 9/22/53 9 2
Denmark 1987 9/8/87 9 1
Denmark 1988 5/10/88 5 2
Greece 1989 6/18/89 6 1
Greece 1989 11/5/89 11 2
Greece 1990 4/8/90 4 3
Greece 2012 5/6/12 5 1
Greece 2012 6/17/12 6 2
Greece 2015 1/25/15 1 1
Greece 2015 9/20/15 9 2
Iceland 1959 6/28/59 6 1
Iceland 1959 10/25/59 10 2
Ireland 1982 2/18/82 2 1
Ireland 1982 11/24/82 11 2
Japan 1952 10/1/52 10 1
Japan 1953 4/19/53 4 2
Japan 1979 10/7/79 10 1
Japan 1980 6/22/80 6 2
Moldova 2009 4/5/09 4 1
Moldova 2009 7/29/09 7 2
Spain 2015 12/20/15 12 1
Spain 2016 6/26/16 6 2
Sri Lanka 1960 3/19/60 3 1
Sri Lanka 1960 7/20/60 7 2
St. Lucia 1987 4/6/87 4 1
St. Lucia 1987 4/30/87 4 2
Thailand 1992 3/22/92 3 1
Thailand 1992 9/13/92 9 2
Turkey 2015 6/7/15 6 1
Turkey 2015 11/1/15 11 2
UK 1974 2/28/74 2 1
UK 1974 10/10/74 10 2

The list contains 17 cases of an election within twelve months of the preceding one. Not a large sample; fortunately, this sort of thing does not happen very often. (There are 1,025 elections in the sample.)

If elites and/or voters “learn” from the experience of bargaining failure or lack of stability from the first election in such a sequence, we would expect the second to be less fragmented. We can test this by looking at mean differences between the second election and the first. The indicators I have are the number of parties (or lists, more precisely, counting an independent as a “list” of one) that win at least one seat (NS0), the effective number of seat-winning lists (NS), the effective number of vote-earning lists (NV), the seat share of the largest party (s1), and the vote share of the largest party (v1). The first three should go down if there’s an adaptation occurring, while the second two should go up (i.e., the largest party gets bigger).

Here is what we see from the results, reporting the mean differences:

NS0: –0.215

NS: –0.098

NV: –0.469

s1: +0.010

v1: +0.0035

In terms of raw direction, all are as expected. On the other hand, the number of lists winning seats hardly budges (recall that the first number is the actual number, not “effective”), and the effective number on seats changes much less than the one on votes. The implication is that fewer votes are wasted in the second election, as we would expect. On the other hand, the seat share of the largest party–the single most important quantity because it determines whether there is a single-party majority and if not, how far from majority it is–rises by a very small amount, on average. That is partly due to most of these systems being proportional, so large shifts should be unusual. The complete list of elections and their indicators is provided in an appendix below.

As far as statistical significance is concerned, only in NV and v1 is the difference significant (NV at p<0.03; v1 at p<0.10), when comparing these “second” elections to all others. (This is not meant to be a sophisticated test; I am not comparing to a country baseline as I really should.)

We might expect that the first election in such a sequence is anomalously fragmented, hence the need for a second election to calm things down once again. That is also supported, for NV and v1 again, but also, crucially, for s1.

Now, how might the Israeli second election of 2019 compare? We can use the polling average from Knesset Jeremy (using the poll of polls from three weeks before the actual election), and compare to the actual results of 2019a (the first election in the sequence) and the previous election (2015). Also included in the Seat Product Model expectation.

measure 2019b (poll avg) 2019a actual diff 2015 diff SPM expected
NS0 9 11 –2 10 1 11
NS 6.04 5.24 0.801 6.94 –1.70 4.93
NV ? 6.33 ? 7.71 –1.38 5.24
s1 0.258 0.292 -0.034 0.25 0.042 0.3
v1 ? 0.2646 ? 0.234 0.031 0.289

For the number of lists that look likely to clear the threshold, we have the direction expected: currently there are 9 likely to win seats, compared to 11 in April. In turn, the April figure was one seat-winning list higher than in 2015. However, in terms of both NS and s1, the case is anomalous. All indications are that the largest party will be smaller than it was in April, which also will drive up the effective number. Moreover, these measures in April were less fragmented than they had been in 2015; that is, the first election of the 2019 sequence was not unusually fragmented. Quite the contrary; I called it a “normal” election at the time for a reason.

So the Israeli sequence of two elections in 2019 is unusual indeed.


Below are two tables. One has all the “second” elections, and changes in the various measures. The second has all “first” elections. In each case, the comparison is just to the immediately preceding election (not to all other elections), so we can see how much short-term fluctuations were affecting the process in each sequence.

Elections ocurring within one year of previous, compared to previous results
country year mo diff_Ns0 diff_Ns diff_Nv diff_s1 diff_v1
Denmark 1953 9 1 -0.2199998 -0.1000001 0.014 0.009
Denmark 1988 5 -1 0.0100002 0 0.005 0.005
Greece 1989 11 1 -0.0800002 -0.1700001 0 0
Greece 1990 4 5 0.05 0.0700002 0.005 0.017
Greece 2012 6 0 -1.07 -3.75 0.07 0.108
Greece 2015 9 1 0.1490002 -1.19 -0.014 -0.008
Iceland 1959 10 0 0.24 . 0 .
Ireland 1982 11 -1 -0.01 0.03 0 0
Japan 1953 4 . 0.8099999 0.8999999 -0.088 -0.091
Japan 1980 6 -8 -0.3999999 -0.24 0.074 0.033
Moldova 2009 7 1 0.8699999 0.27 0 -0.048
Spain 2016 6 -1 -0.3700004 -0.7999997 0.04 0.043
Sri Lanka 1960 7 . -1.22 -2.52 0.166 0.032
St. Lucia 1987 4 0 0 -0.1099999 0 0.007
Thailand 1992 9 0 -0.0999999 0.0999999 0 0.017
Turkey 2015 11 . -0.322 0.03 -0.126 -0.089
UK 1974 10 -1 -0.01 -0.02 0.028 0.021
Election that is the first in a series of two within a year, compared to preceding election
country year mo diff_Ns0 diff_Ns diff_Nv diff_s1 diff_v1
Denmark 1953 4 0 -0.1300001 -0.0900002 0.013 0.008
Denmark 1987 9 0 0.27 0.5799999 -0.009 -0.023
Greece 1989 6 1 0.26 0.1400001 -0.044 -0.006
Greece 2012 5 2 2.24 5.79 -0.173 -0.25
Greece 2015 1 0 -0.6700001 -0.77 0.067 0.066
Iceland 1959 6 0 -0.28 . 0.035 .
Ireland 1982 2 -2 -0.05 -0.1699998 -0.039 0.009
Japan 1952 10 . . . . .
Japan 1979 10 -1 0.1199999 -0.2199998 -0.002 0.027
Moldova 2009 4 1 0.1400001 0.1600001 -0.079 0.035
Spain 2015 12 -3 1.93 3.23 -0.18 -0.159
Sri Lanka 1960 3 . 1.456 2.26 -0.206 -0.043
St. Lucia 1987 4 -1 0.55 -0.0800002 -0.295 -0.049
Thailand 1992 3 . . . . .
Turkey 2015 6 . 0.4320002 0 0.002 0.005
UK 1974 2 2 0.1900001 0.6900001 -0.05 -0.077


Ukraine honeymoon election today

Ukrainians are voting today in an assembly election. It is a relatively extreme “honeymoon” election, as the new president, Volodomyr Zelensky, was just elected in March-April of this year (two rounds). There was already an assembly election scheduled for October of this year, which certainly would have qualified as a honeymoon election. But in his inauguration, Zelensky announced he would dissolve the Verkhovna Rada and call an election even earlier.

And why not? Based on much experience in presidential and semi-presidential systems, we know that there is a strong tendency for the party of a newly elected president to gain a large boost in votes the earlier it is held following the presidential election. This topic of the impact of election timing has been a theme of my research ever since my dissertation (1988), an early APSR article of mine (1995), and most recently in a whole chapter of Votes from Seats (2017).

At the time Zelensky was elected, various news commentary had the all-too-typical concern that the new president would be weak, because he is an “outsider” with no established political party. We got similar useless punditry when Emannuel Macron was elected in France in 2017. And we know how that turned out–his formed-on-the-fly party did slightly better than the 29% of votes I projected, based on an equation in Votes from Seats, prior to Macron’s own runoff win. (The electoral system helped turn that into a strong majority in the assembly.)

In May of this year, I projected that Zelensky’s Servant of the People party could get around 34.5% of the votes in an election held on 28 July. (One week earlier obviously does not change anything of substance.)

Early polling had him short of this (not even 25% just before the presidential first round), but predictably, SoP has been rising in the polls ever since Zelensky took office. The party almost certainly will beat this projection, and may even have an electoral majority. If short of 50% of votes, the party still looks likely to win a parliamentary majority, given the electoral system (discussed below).

A bigger boost than average (where the average across systems with nonconcurrent elections is what my projections are based on) is to be expected in a context like Ukraine, in which the party system is so weak. That is, poorly institutionalized party systems would tend to exaggerate the normal electoral cycle effect. The effect will be only further enhanced by low turnout, as opponents of the new president have little left in the way of viable political parties to rally behind. Thus a performance in the range of the mid-40s to over 50% of the vote would not be a surprise.

As for the electoral system and election itself, Ukraine is using again (for now, at least) its mixed-member majoritarian (MMM) system. It consists of 225 single-seat districts, decided by plurality, and 225 closed-list proportional representation seats, in a single nationwide district. The two components are in “parallel”, meaning seats won by any given party in districts and seats won from party lists are simply summed; there is no compensatory process (as with MMP). There is a 5% threshold on the list component; quite a few small opposition parties may waste votes below this bar. Due to parts of the country being under Russian occupation, only 199 single-seat contests will take place.

In some past MMM elections in Ukraine, a large share of the single-seat districts have been won by independents or minor parties, whereas the national parties (such as they are) have, obviously, dominated the nationwide list seats. It is probably quite likely that this rather extreme honeymoon election will result in most of the seats in both components being won by “Servants.”

On that theme, a tweet by Bermet Talant makes the following points (and also has some nice polling-place photos) based on conversations with voters in Kyiv:

• Ppl vote for leaders. Few know other candidates on party lists, even top5

• Servant of the People = Zelensky. Bscly, ppl vote for him again

• In single-member districts, ppl vote for a party too, not candidate

This is, of course, as expected. It is a completely new party. Many voters will be wanting to support the new president who created the party. The identity of candidates will not matter, either on party lists (where at least the top ones might be known in a more conventional party) or in the districts (where the vote is cast for a candidate). The single-seat districts themselves are referred to as the “twilight zone” of Ukrainian elections in a fascinating overview of the candidates and contests in the district component published in the Kyiv Post. These contests attract “shady candidates” many of whom are “largely unknown”. If a given election lacks a strong national focal point, it would tend to favor independents and local notables. In an election with an exceptionally strong focal point–as in a honeymoon election, more or less by definition–that will benefit whoever has the “Servant of the People” endorsement.

The timing of the election, and the likely dominance of an entirely new pro-Zelenskyy party, really is presidentialization at its very “finest”.

I am just going to quote myself, in the final paragraph of an earlier post about Macron’s honeymoon election, as it totally applies here, too: “All of the above should serve as a reminder of two things: (1) the purpose of the upcoming election is to ratify the new executive’s direction, not to be a second chance for an alternative vision; (2) the honeymoon electoral cycle matters.”

Expect the new Verkhovna Rada to be Servants of Zelenskyy.