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.

17 thoughts on “Canada 2019: Results and a good night for the Seat Product Model

  1. The plurality reversal is even more dramatic when Quebec is taken out of the equation: in the rest of Canada, LPC won only 32.7% of the vote to 40.1% for CPC, but the former won 122 of 260 seats to 111 for the latter. Meanwhile, NDP won 17.5% in the ROC, just slightly below the 17.9% it received in that part of the country back in 2015, but even so it went from 28 to 23 seats, for a net loss of five.

    By comparison, in 1972 the old Progressive Conservative Party won 105 of 190 seats in the ROC with 41.5% to 53 for LPC, which received 34.5% of the vote; NDP won 31 seats with 21.9% back then. The main difference is that in 1972 the Liberals lost in every province and territory except Quebec, whereas this time around they carried not only Quebec, but also the four Atlantic provinces and – crucially – Ontario, along with two of the three territories. Moreover, excluding both Alberta and Quebec, the Progressive Conservatives had a narrow one-seat majority and a popular vote plurality in 1972; this time around the Liberals had a narrow popular vote plurality and an overall seat majority (122 of 226) outside those two provinces. In fact, the nationwide CPC popular vote plurality in 2019 came entirely from Alberta: outside Alberta the Liberals won both a popular vote plurality (with 35.6% of the vote to 29.9% for CPC) and a majority of seats (157 of 304).

    At any rate, I had been wondering for a long time if history would repeat itself in Monday’s election, and Justin Trudeau would end up winning but losing his parliamentary majority, as was the case with his father back in 1972. Broadly speaking, that turned out to be the case, although Justin Trudeau will be in a more comfortable position than Pierre Trudeau was back then.

    Finally, the election showed that a vote cast for a no-hope candidate is not the only kind of “wasted” vote under FPTP. CPC ended up with over a million “wasted” votes in uselessly large majorities on ridings in Alberta and other western provinces – votes which under a PR electoral system might have allowed the party to win the largest number of seats in this year’s election. In fact, in Monday’s election 73.3% of all votes cast – and 84.7% in Alberta – didn’t contribute to the election of a member of the House of Commons, either because they went for losing candidates, or because they were cast for winning candidates in excess of the number of votes needed for victory, that is the votes cast for second-place candidates plus one.


  2. Canada’s system is consistent with a parliamentary version of Duverger’s law if there also is subsidization of parties across provinces that are heterogeneous in preferences!

    Perhaps, one might consider my idea of having mega-ridings of 4 with 3 of the seats determined using 3-seat Largest Remainder Hare and 1 seat determined using the Alternative Vote and with 1 seat being determined by an at large Alternative vote to break the tie?

    3-seat LR Hare is the simplest 3rd party friendly of PR elections. It’s just like FPTP, except there are 3 winners and the biggest parties has a vice-candidate who could get a seat if they beat the 3rd place candidate by more than 1/3rd of the total vote.

    I think a rough guestimate of what that would look like is the final distribution wd be the current dist’n of seat divided by 4 + 3/4ths times the dist’n of votes. So the Liberal party would still have a plurality and would have to pit the NDP and the BQ parties off of each other to rule. This is not bad, becuz at least the incentives given to the parties wd be different even if nominally the parties in power do not change. They will become different parties due to the different slash better incentives they face to do well in a 3-seat LR Hare + AV system, along with an at large AV seat…


  3. It seems to me that a lot of Candidates are winning seats in the low 30s. What is the lowest winning percentage that a candidate wins a riding in this election? What would the election result had the Australian preferential vote had been used? Would the Liberals had been more or less likely to win a majority with vote transfers.


    • The lowest percentage of the vote a candidate won a riding with was Trois-Riveres, the results of which MSS mentions in the post. Outside Quebec, the lowest percentage of the vote a candidate won was Liberal Jamie Battiste in Sydney-Victoria in Nova Scotia, with 30.9% (Battiste was opposed by a relatively strong Independent who took 15% of the vote as well as 20% apiece for the NDP and Conservatives).


      • According to the election night results, 123 candidates were elected with absolute majorities, while 149 arrived first with 40-50% of the vote, and 66 topped the poll with less than 40%, of which two received less than 30%.


  4. “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.”

    My understanding is it was more than just his celebrity, but also his stamina. He personally knocked on more than 10,000 doors in the riding. By my rough math I think he personally spoke to about 1/3 of voters.


  5. I was wondering how high, relative to past Canadian elections, that largest-party advantage ratio of 1.40 was. It has been reached or exceeded four times since 1949: in 1949, 1958, 1984, and 1993. It came close two other recent times: 1.394 in 2000 and 1.377 in 2015. It was pretty high in 2011, too: 1.369.

    For all Canadian general elections in that period, the mean is 1.28. The 2015 value is the 75th percentile.

    The highest is the 1984 value, at 1.496.


  6. FYI, corrected a pretty dumb arithmetic error on how much the SPM missed by. It still did not miss by much, but it is a very slightly bigger miss than the original text said. Still under 1.8%, which I can be happy with!


  7. Hi Matthew,

    I had previously emailed the below thoughts to Mike Thies and he said you might appreciate them as a comment here… (First, totally agreed on the affective big wins of Bernier being tossed and JWR being re-elected!)

    I have been doing some thinking lately about the use of entropy-based measures of competition, like E_v and others. These are obviously great at capturing a certain cross-sectional snapshot of preference heterogeneity in a district, but I think they also obscure structural stability.

    Think of a district with relatively tight competition but no elasticity as to vote share; e.g. much of the American south in the last 20 years strikes me like this, where there’s a large minority of (mostly nonwhite) Democratic voters and a slight majority of (mostly white) Republican voters, but the probability of a Democrat remains extremely low. Or, generalizing: in a two-party election with a lopsided vote, E_v tends to 1 while p(trailing win) is 0; in a two-party election with a minority party that has a high vote floor, but a ceiling no higher, E_v tends to 2 while p(trailing win) is still 0. Setting aside changes in the composition of the electorate, once measure of competitiveness might be some sort of medium-run p(turnover) for the district.

    My own riding tends to attract 25% CPC vote, but has been NDP-Liberal marginal since time immemorial, and so I feel like E_v would “falsely” lead someone to believe the district is multi-party when in fact it is fairly stable two-party. I’ve been trying to do some thinking about how to measure the trouble I have here. On the night of the election I was surprised to see a fair number of CPC-NDP marginal seats pop up out west, so I decided to just pull the “top 2 party” set for each district, and then look at what I’ll call “top 2 transitions” between 2015: cases where at least one of the top two parties was not one of the top two parties last time. In a world where ridings actually exhibit 3+ party competition, we’d expect to see a lot of movement on this measure (and the movements should be maybe a little more colloquial than the macro swings we expect across the country.)

    Of the 338 ridings, 238 exactly had no “top 2 transition”. 30 went from LIB-NDP -> BQ->NDP (NDP collapse in Quebec); 14 went from CPC-LIB -> CPC->NDP (Liberal collapse in AB/SK); 12 went from LIB-NDP -> CON-LIB (general rightward swing); and only 44 had some other transition pair. To me, this suggests that many of the ridings that have E_v >> 2 are actually still only “two party competitive”.

    Side note: Only two ridings had turnover among BOTH top two parties. Both odd duck cases where the 2015 elected member resigned, the by-election produced an unusual result, and the election carried through the by-election.

    To cap off a long comment — I am playing around with this measure and am vaguely interested if you think there’s any juice or know of anyone else in the comparative electoral institution literature that has maybe explored this territory before.


    • Thank you for this comment. It is very interesting. Do you know Gaines and Taagepera’s effort to measure the “top two-ness” of elections? It is based on a similar dissatisfaction with effective N for the sorts of situations you mention.

      I do not doubt that lots of districts have some inter-election continuity in which two parties are locally most viable. Of course, I am using N because it still gives us a nice window on overall fragmentation patterns, but you are absolutely right that it masks where turnover vs. stability might be most pronounced.

      I am very interested in exchanging ideas about this. Perhaps we should be in touch over email or other means in the near future.


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