Quebec pro-PQ bias and electoral reform

By JD Mussel

The Montreal Gazette has reported about the Mouvement Démocratie Nouvelle (MDN), which recently launched its campaign for proportional representation in Quebec, specifically MMP.

The article mentions a number of factors that may be at involved in creating the apparent pro-Parti Quebecois bias in First-Past-the-Post in Quebec. Firstly, ridings in Montreal traditionally favour the Liberals, where their votes are very concentrated, to the party’s disadvantage. Secondly, the article highlights malapportionment in the Province, which may be one of Canada’s worst. The overrepresented ridings are generally more likely to be rural and francophone, while the underrepresented ones tend to be more urban and are likely to have a larger anglophone population, as illustrated here.

There have been three plurality reversals in Quebec since the rise of the Union Nationale (1936), all of which occurred in elections where the Liberals had received a plurality of the vote.

The article also included projections, produced by Wilfred Day of what the 2012 result would have been under pure PR and MMP. I am very curious as to the exact model used for the latter projection!

Meanwhile, the MDN’s website (in French) is worth a browse, in particular its historic overview of all Quebec elections since Confederation, showing vote shares vs seat shares as well as some historic background.

Quebec election, 2014

Quebec’s general election will be 7 April. From my cursory reading of the news prior to the election call, I had the impression that a majority for the Parti Quebecois (PQ) was all but in the bag. (The PQ currently heads a minority government.) However, sometimes funny things happen during campaigns.

Looking at the projections at, which are based on aggregating and weighting polls, one can see that the Liberals are now ahead of the PQ in the vote projection. As of today, they are even ahead outside the projection tool’s estimated confidence intervals*, which range 41%-47% for Liberals and 32%-36% for the PQ.

Seat projections, however, remain closer: 61-76 for Liberals, 46-59 for PQ. If the race tightens even a little bit, the prospect of a plurality reversal becomes real, given the near overlap in project ranges for seats despite the existing minimum projected gap of five points in votes. If we convert the projections into advantage ratios (%s/%v)**, we get a range for the Liberals of 1.18 to 1.28, but for the PQ of 1.16 to 1.31. We can see that either party would benefit from the over-representation expected from a plurality electoral system, but the PQ benefits slightly more–from the model’s projections–when it is at the higher end of its vote range, even though its current maximum projection would not give it a plurality of the vote. Extrapolating from these figures, the PQ might be able to win a majority of the seats on only around 38% of the vote and with the Liberals still slightly ahead.

A reversal–and not the first in the province–happened as recently as 1998, when the Liberal party had 43.55% of the vote and 48 seats, while the PQ had 42.87% but 76 seats. Yes, 76, for a really large majority despite losing the province-wide vote.

I think I will start paying more attention to the Quebec campaign now.

* Taking the confidence interval to be the range from “low” to “high” rater than minimum-maximum.

** Using low-end or high-end projections for both seats and votes in all cases.

Quebec election campaign 2012

Quebec’s National Assembly (i.e. provincial) election is 4 September. It is a three-way race, which is always interesting–and potentially anomaly-generating–under plurality (first-past-the-post) rules.

The incumbent is a majority government of the Liberal Party, re-elected most recently in 2008, with the Parti Quebecois (PQ) as its main opponent. The newly created party in the mix is the Coalition Avenir Québec (CAQ), and there are other smaller parties as well.

The CAQ is trying to make a splash by bringing Jacques Duchesneau, a “celebrity whistleblower” (as the Ottawa Citizen described him) into the contest as one of its candidates. This personnel strategy by an upstart party is an excellent example of attempting to use a high-profile individual to signal something about the party as a whole.

The PQ is attempting as well to use a newly recruited candidate to help re-brand the party. The “sovereigntist” message of the party is in danger of not resonating with younger voters who have grown up under policies implemented by past PQ governments, and continued by Liberal ones. So to try to counter this lack of appeal, it has nominated Léo Bureau-Blouin, a 20-year-old leader of the recent Quebec student strike. As Konrad Yakabuski comment in the Globe and Mail: “Mr. Bureau-Blouin’s candidacy brings much more to the PQ than a chance at picking up a seat. It sends a message to Quebeckers that the party and its mission will live on.”

As for the three-way race, Eric Grenier notes in the Globe and Mail, even before Duchesneau’ entry, “the CAQ, even at these low levels of support in the polls, could still win as many as 11 seats, Québec Solidaire as many as two, and Option Nationale one, making it possible for either of the two main parties to form some sort of working arrangement or formal coalition in order to govern if they do not win a majority on their own.”

Quebec had a real three-way race in March, 2007, when the largest party was the Liberals, but with only 38% of the seats on just under a third of the vote. The Assembly elected then lasted only about a year and a half, and new elections were held in December, 2008, producing the majority that is attempting to defend its position now.

A leader of a past (Equality Party, 1989) attempt at third-party politics, Robert Libman, has made an appeal for strategic voting:

“Anglophones… should perhaps, in order to send a message to the Liberals, consider voting for the CAQ,” said Mr. Libman, “(but) only in areas where there is no danger of splitting the vote and electing the PQ.”

The ridings Mr. Libman has in mind are largely located in Montreal’s west end, with a few more in western Quebec. There are also a handful of ridings where any wavering by Anglo voters could spark big swings in close local races.

With so many outcomes being plausible–including a majority government by either major party–and dependent on results of key districts (ridings), this will be a contest to watch.

Quebec’s election

[Replanted, originally from 4 Dec.]

With so much attention focused on Canada’s federal government, and the government-in-waiting, I almost forgot that Quebec is about to go to the polls in a provincial assembly election. That’s happening on Monday! {Today!}

(Click “Qc.” above to see discussion of the previous election, in March, 2007.)

PQ as the arbiter?

The arbiter role in a minority government in Quebec was to have fallen to the ADQ. But a funny thing happened on the way to its arbiter status: It emerged as the official opposition.

Paul Wells gets it right, I think:

I won’t game out the parliamentary confrontation that seems almost certain, except to point this much out: the assumption until now was that the ADQ would arbitrate, between Libs and PQ, as to who formed the government. But if the ADQ and the Libs turn out to be rivals, with Charest unable to lead (what will still be, constitutionally, until a confidence vote) his government from within the National Assembly, then it is at least conceivable that the arbitrator’s role falls to the PQ. Does the PQ vote no confidence in a Liberal government? Does it then support Mario Dumont? That dilemma would risk tearing the PQ apart.

Yes, this is going to be fun to watch.

And then things are also going to be pretty interesting in Ottawa:

how does [federal Liberal leader] Stéphane Dion feel, knowing that 46 Quebec seats are now held by Liberals who agree with Stephen Harper on federalism and 42 Adéquistes who agree with him on everything else?

Also recommended on what this three-party dynamic, with the “ethnic nationalists” in third place, might mean: The Pithlord, Scott Lemieux, Jacob T. Levy, and various others that they link to. Quite an interesting discussion.

In particular, reflecting on Premier Charest’s interest in parlaying his new federal money into a tax cut that the ADQ will have to support him on (thereby postponing the PLQ-ADQ rivalry that Wells referred to), Pithlord notes:

Harper’s shown that you can play a minority with strength if your opponents don’t want an election. Charest isn’t as clever, but the way seems clear.

Related plantings:

Quebec stunner: Liberal minority government, ADQ close second

Quebec’s results and the performance of FPTP

Quebec’s results and the performance of FPTP

The results of the Quebec provincial election were stunning enough, as we have been discussing in the previous planting. No one saw the strong showing of the ADQ coming. The fall of the ruling PLQ to minority status was expected, but there was quite a late swing away from the PQ. A few days before the election, it looked as if a PQ minority government was possible, but the party wound up in third place.

In this entry, I want to look not at the shifts in voter sentiment, but rather at how the electoral system took those actual votes and turned them into seats. This is a politically relevant question for Quebec given that the province: (1) has never before had an election result in a minority situation, and (2) has had a recent electoral-system review process. The minority government might be seen as a sign of the “failure” of the FPTP system just at a time when there has been discussion of replacing FPTP with some form of PR.

The seat-vote result is striking in being almost proportional:

    PLQ, 33.1% votes, 38.4% seats
    ADQ, 30.8% votes, 32.8% seats
    PQ, 28.3% votes, 28.8% seats

We certainly do not normally expect such close correspondence of votes and seats percentages in FPTP systems.

To get an idea of whether this aspect of the election is a “surprise” or not, I turned to one of my favorite tools, the seat-vote equation (originally devised by Rein Taagepera). If you are unfamiliar with the seat-vote equation, I suggest clicking on those words at the top of this planting and scrolling back in time–especially to the first planting in that orchard block (an estimation of seats in the then-upcoming Canadian federal election). But the short version is that the seat-vote equation allows us to estimate a “normal” seats distribution based on the following inputs (and only these inputs):

    The votes shares of the leading parties
    The total number of votes cast
    The number of seats in the legislature
    The number of electoral districts

Naturally, in FPTP systems, those last two are the same quantity.

The s-v equation does not incorporate any information about the geographic distribution of the parties’ supporters, notwithstanding the obvious importance of such distribution to the actual outcome. Parties win seats in FPTP systems solely based on where their votes are–no district-level plurality, no seat–rather than as a function of their jurisdiction-wide votes shares.

So, how did the equation perform in this election? Asking this question is really another way of asking a more politically relevant question: How did the electoral system perform? The latter question assumes that there is some “expected” relationship between jurisdiction-wide party support and their legislative support. Deviations from the s-v equation estimates would suggest that the electoral system is not translating votes into seats in a predictable manner. Again, we should not necessarily expect such a predictable translation when the system is FPTP, because of the dependence of parties on local pluralities rather than on jurisdiction-wide support in order to win seats.

Following are the (rounded) predictions of the seat-vote equation, based on the known values of the input variables indicated above:

    PLQ, 51
    ADQ, 42
    PQ, 32

These hardly differ from the actual result (48, 41, 36). The s-v equation expects the largest party to get a bigger bonus than it actually got and the third party to get slightly more punished than it actually was. But it tells us that, in a jurisdiction with FPTP and the number of seats and voters that Quebec has, an election so close among the top three parties in votes should produce a fairly close correspondence of seats and votes. The predicted advantage ratio for the PLQ was 1.23; its actual ratio was 1.16. Even FPTP with three-way competition can produce moderate deviations from proportionality and Quebec’s 2007 result was one where moderate deviations were both expected and actually materialized.

As for the impact of this outcome on the electoral system review, I am not in a position to predict the political consequences of this outcome on that review, but I would conclude that the outcome has not made the objective case for PR stronger. None of the formal review processes in FPTP jurisdictions in the last four decades stemmed from a minority situation, and Quebec’s result was not even disproportional. The existing electoral system gave Quebec voters pretty much what they voted for.


Paul Wells and his readers have been having fun figuring out the smallest shifts of votes that could have produced a very different seats result–a reminder that s-v correspondence in FPTP systems does sometimes rest on knife’s edge results.

Mr Wells also offers a great video link on the PQ, 1976. Ah, those were the days…

Quebec stunner: Liberal minority government, ADQ close second

Update 2: Democratic Space provides an overview of the projections and where they were wrong. Excerpts:

Our under-estimation of the ADQ came from a greater than expected swing towards the ADQ in just 2 regions: Lanaudiere-Laurentides and the Monteregie (largely due to the abandonment of the PQ in these regions). […]

Overall, of the 21 incorrect ridings, 16 were in our “too-close-to-call” or “tight race” categories. So there were 5 genuine surprises.

(Well, the real surprise is that virtually every close riding swung the same way. In other words, it was not a case of “too close to call” but of the pollsters having missing the underlying trend.)

The remainder of this planting is unchanged since last night, but comments have kept coming in.

The Quebec provincial election has produced a Liberal minority government, the first resulting from an election in the history of the province (and the first at any time since 1878).

But here is the stunning part: The close race proved to be not between the Liberals and the Parti Québécois, but between the Liberals the Action Démocratique du Québec!

The ADQ, which had five seats in the previous parliament, will have 41 members in the new one, just seven seats behind the Liberals. Current Premier Jean Charest barely held his own riding. The PQ has 36 seats.

In the votes, it was Liberal 33.1%, ADQ 30.8, PQ 28.3, Green 3.9, Québec Solidaire 3.7.

I agree with those who say this result gives federal Prime Minister Stephen Harper the incentive to force (and lose) a vote of confidence sooner rather than later: The provincial ADQ vote surge is encouraging news for Harper’s federal Conservatives. They just might gain enough in Quebec to win a majority of seats in the House of Commons. The very bad result for the PQ is also bad news for its federal equivalent, the Bloc Québécois. Looks like the BQ was right to fear an election, as I suggested in commenting on their support of the recently tabled federal budget.