Small national parties in Canada in the 2021 election and the connection of district voting to national outcomes

One of the notable trends in polling leading up to the Canadian election of 20 September is the increasing vote share of the Peoples Party of Canada (PPC). At the same time, polls have captured a steady decline of the Green Party as the campaign reaches its end. These two small parties’ trends in national support appear to be happening in all regions of the country, albeit to different degrees (see the graphs at the previous link). That is, while these parties have different levels of support regionally, their trends are not principally regional. Rather, all regions seem to be moving together. This will be a key theme of this post–that politics is fundamentally national, notwithstanding real difference in regional strengths1 and the use of an electoral system in which all seat winning is very local (in each of 338 single-seat districts or “ridings”).

The PPC is a “populist” party of the right. It seems that the Conservatives’ attempt to position themselves closer to the median voter during this campaign has provoked some backlash on the party’s right flank, with increasing numbers of these voters telling pollsters they will vote PPC.

At The Writ, Éric Grenier offers a look into what the polls say about the type of voter turning to the PPC, and whether they might cost the Conservatives seats. The PPC vote share ranges widely across pollsters but in the CBC Poll Tracker (also maintained by Grenier) it currently averages 6.7%. This would be quite a strikingly high figure for a party that is not favored to win even one seat and probably very unlikely to win more than one.2 The Poll Tracker shows a stronger surge in the Prairies region than elsewhere (3.6% on 14 Aug. just before the election was called to 10.9% when I checked on 19 Sept.) and Alberta (4.6% to 9.0% now), but it is being picked up in polling in all regions (for example, from 2.2% to 4.4% in Quebec and 2.9% to 6.1% in Atlantic Canada).

What I wish I knew: Is a voter more likely to vote PPC if he or she perceives that the party is likely to win at least one seat? This question is central to the “all politics is national” model developed in Shugart & Taagepera (2017) Votes from Seats, in chapter 10. We do not mean “all” to be taken literally. Of course, regional and local political factors matter. We mean that one can model the average district’s effective number of parties based on the national electoral system. More to the point, we argue that the way to think of how party systems form under FPTP (or any simple districted system) is not to think in terms of local “coordination” that then somehow gets projected up to a national party system, but rather that the national electoral system shapes the national party system, which then sets the baseline competition in the district contests.

If the PPC or Greens are perceived as likely to have a voice in parliament–and perhaps especially if the parliament is unlikely to have a majority party– voters who like what a small party proposes may be more inclined to support it, even though few voters live in a district where it has any chance of winning locally. Below I will show two graphs, each based on a mathematical model, showing a relationship of local votes to national seats. The first is based on the total available seats–the assembly size–while the second will be based on the seat outcome, specifically the nationwide effective number of seat-winning parties. The formula derived in the book for the connection to assembly size states the following for FPTP systems (every district with magnitude, M=1, and plurality rule):


where NV is the mean district-level effective number of vote-earning parties and S is the assembly size. Please see the book for derivation and justification. It may seem utterly nuts, but yes, the mean district’s votes distribution in FPTP systems can be predicted when we know only how many districts there are (i.e., the total number of seats). In the book (Fig. 10.2 on p. 156) we show that this sparse model accurately tracks the trend in the data across a wide range of FPTP countries, particularly if they are parliamentary. Here is what that figure looks like:

Of course, individual election averages (shown by diamonds) vary around the trend (the line, representing the above equation), and individual districts (the smear of heavily “jittered” gray dots) have a wide variation within any given election. But there is indeed a pattern whereby larger assemblies tend to be associated more fragmented district voting than is the case when assembly size is smaller. At S=338, Canada has a relatively large assembly (which happens to be almost precisely the size it “should be,” per the cube root law of assembly size).

The model for NV under FPTP is premised on the notion that voters are less attuned to the likely outcome in their own district than they are to the national scene. There is thus a systematic relationship between the national electoral system and the average district’s votes distribution.

Moreover, by combining the known relationship between the national electoral system and the national party system, we can see there should be a direct connection of the district vote distribution to the national distribution of seats. The Seat Product Model (SPM) states that:


where NS is the nationwide effective number of seat-winning parties. For FPTP, this reduces to NS=S1/6, because M=1. In terms of a FPTP system, this basically just means that because there are more districts overall, there is room for more parties, because local variation in strengths is, all else equal, likelier to allow a small party to have a local plurality in one of 400 seats than in one of 100. So, more seats available in the assembly (and thus more districts), more parties winning seats. The model, shown above, connecting district-level votes (NV) to the assembly size (S) then suggests that the more such seat-winning opportunities the assembly affords for small parties, the more local voters are likely to give their vote for such parties, pushing NV up. The process probably works something like this: Voters are aware that some small parties might win one or more seats somewhere, providing these parties a voice in parliament, and hence are likelier to support small parties to some degree regardless of their local viability. It is national viability that counts. “All politics is national.” The posited connection would be more convincing if it could be made with election-specific seat outcomes rather than with the total number of available seats. We can do that! Given the SPM for the national seat distribution (summarized in NS) based on assembly size, and the model for district-level votes distribution (NV), also based on assembly size, we can connect NV to NS algebraically:


(Note that this comes about because if NS=S1/6, then S=NS6, giving us NV=1.59(NS6)1/12, in which we multiply the exponents in the final term of the equation to get the exponent, 1/2, which is also the square root. A full discussion and test of this formula may be found in my forthcoming chapter with Cory Struthers in an volume in honor of Richard Johnston being edited by Amanda Bittner, Scott Matthews, and Stuart Soroka. Johnston’s tour de force, The Canadian Party System likewise emphasizes that voters think more in terms of national politic than their local contest.)

Here is how this graph looks:

This again shows elections with diamonds and individual districts in small gray dots. The diagonal line is the preceding equation. It most definitely fits well. Note that it even fits India if we base the nationwide party system on the alliances (shown by squares), as we should, given that they and not the many parties are the nationwide actors, whereas each alliance is represented by a given component party in each district. (The graph also shows India if we use individual parties in the calculation of NS, which is useful because it makes clear just how well India, in the era of competing alliances, follows the S model–the one in the first graph. It obviously would not fit the NS model if we did not use the alliances, but again, it is the alliances that it should track with if the model is correct in its grounding district-level vote outcomes in the national balance of seats among the national political forces–parties elsewhere, including Canada, but alliances in India.)4

By implication, this connection of district-level NV to national NS may arise because voters have some estimate of how the national parliament is going to look when they decide whether or not to support a party other than one of the two leading national parties. For instance, a voter wavering between the NDP and the Liberals might be more likely to support the NDP if she estimates that there will be no majority, thereby allowing a smaller party like the NDP to be more influential than if one of the big parties has a majority on its own.

A vote for a much smaller party, like the PPC, might be simply expressive–“sending a message” to the Conservatives that they are not sufficiently right wing or populist. For a purely expressive voter, the national seat outcome may be irrelevant. Such a voter simply wants to register a protest. There still might be a connection to expected national votes: If such a voter thinks the PPC can get 7% he might be likelier to vote for it than if it’s only 3%.3 If, however, the connection runs through thinking about the national parliament, and whether one’s party will have voice there, it should help the party win votes around the country if its potential voters perceive that it will win one or more seats–in other words, that it is viable somewhere. I hope there is some polling data that I can find some day that allows us to get at this question, as it would connect the aggregate outcome demonstrated here with individual-level voter behavior. As the Canadian 2021 campaign has developed, it would be an especially good test of the model’s underlying individual-voter premise, given the surge of a small national party that is probably not likely to have a voice in the House of Commons. (But maybe its voters believe it will! They might even turn out to be correct.)

I do not, however, currently know if any polling or voter surveys exist to get at these questions. Such a survey ideally would ask the respondent how many seats they believe the various parties will get in the election. This would allow a rough construction of voter-expected effective number of seat-winning parties even though no voter actually has to know what that concept means or how to calculate it for the premise of the model to work. Minimally, as noted, it would at least be useful to know if voters choosing a small party think that party will indeed get one or more seats.

I have so far focused on the PPC in the Canadian 2021 election, as a possible example of a wider phenomena connecting local voting to the (expected) national seat outcome. A similar logic on the left side of politics should apply for the Green Party. Does its perceived viability for seats in parliament affect the tendency of voters to vote for it outside the specific districts where it is locally viable? The very big wrinkle this time around for the Greens, however, is that the party is struggling mightily, with an ongoing conflict between its leader and much of the rest of the party. It is currently projected to win no more than two seats, and perhaps none. It might be expected to retain the former leader’s seat in British Columbia, but even that may be in jeopardy with the national party in such disarray.

It is even questionable whether the Green Party still meets the criteria of a “national” party this time around; I do not (yet) have a really precise working definition of how many districts the party must be present in to qualify as “national.” The Green Party has not fielded a candidate in about a quarter of the ridings nationwide. Grenier has reviewed the 86 Green-less constituencies and whether their absence could affect outcomes among the contesting parties. Obviously the connection between expected seat winning nationally and obtaining votes in contests around the country is broken in any district in which there is no candidate running for the party. No candidate, no possibility of the local voters augmenting the party’s aggregate vote total. In any case, the party has dropped in national polls from 5.4% on 14 August to 3.2% now.

Further emphasizing now the Greens may not be a “national” party in this election is the campaign behavior of the leader. The CBC recently noted that the leader, Annamie Paul, is not exactly campaigning like the leader of a national party:

Asked why she hasn’t campaigned in more ridings, Paul acknowledged Friday that some candidates may want her to steer clear. She has campaigned outside of her home riding of Toronto Centre twice so far — once in a neighbouring riding and then Monday, in P.E.I.

Candidates distancing themselves from the leader is not normally a good sign for a party, particularly in a parliamentary system. “All politics is national,” after all. As explained in Votes from Seats (ch. 10), the impact of national politics on local voting is likely enhanced by parties bringing resources into districts to “show the flag” even where they are not likely to win a seat. (The PPC leader is certainly doing this.) If your leader remains mostly ensconced in her own district, the party is not deploying what is normally one of its best resources–the leader making the case for her party.

Nonetheless, it still might matter for the party’s ability to get votes, even in ridings it surely will not win, whether its potential voters believe it is viable for seat-winning somewhere. The good news for the party–and there is little of that–is that the province where it currently holds two seats, BC, is one of those where its polling has declined least: 7.0% on 14 August to 6.3% now. So, politics is still at least a bit more regional for the Greens than for other “national” parties, perhaps.

In conclusion, the district-level extension of the Seat Product Model states that in FPTP systems, district-level effective number of vote-earning parties can be predicted from the national electoral system–specifically, the assembly size. By further extension (in the aforementioned chapter I am working on with Struthers for the volume honoring Johnston), it should also be tied to the nationwide effective number of seat-winning parties, and to voter perceptions in the campaign as to how parties are doing at the national level. The result would be that voters are more likely to vote for even a small party under FPTP to the extent that they expect it to have a voice in parliament, and to the extent that the parliament may not have a majority party. The Canadian 2021 election, with a surging small party (the PPC) and another one declining (the Greens) offers an excellent case study of the phenomenon that is behind these models.



1. Obviously, things are different for an explicitly regional party (one that does not present candidates outside its region) like the Bloc Quebecois, which I will leave aside for this current discussion.

2. Perhaps it has some chance of winning the leader’s riding of Beauce (in Quebec), but as Grenier notes in a post the day before the election:

There’s nothing about Bernier’s Beauce riding that makes it particularly open to a party that has been courting the anti-vaxxer, anti-vaccine mandates and anti-lockdowns crowd. It’s hard to know where in the country that crowd would be big enough to elect a PPC MP.

He does also note that one poll, by EKOS, has put the party second in Alberta, albeit with only 20% of the vote. Maybe they could get a local surge somewhere and pick up a seat there.

3. Indeed, it might seem that we could make a similar algebraic connection. The Seat Product Model expects national effective number of vote-earning parties to be NV=[(MS)1/4 +1]2/3. This is confirmed in Votes from Seats. However, this can’t easily be expressed in terms of just S (even for FPTP, where the term for M drops out) and therefore is complicated to connect to the NV formula. In any case, the theoretical argument works better from seats–that voters key on the expected outcome of the election, which is a distribution of seats in parliament and whether one or another party has a majority or not. These outcomes are summarized in the effective number of seat-winning parties.

4. This graph is a version of the one that will be shown in the previouysly mentioned Shugart & Struthers chapter.