Tuesday, July 17, 2012

Charest holds edge in tight contest in first Quebec projection

Seven weeks from a rumoured election, Jean Charest's Liberals hold a fragile advantage over the Parti Québécois in ThreeHundredEight.com's first official projection for the 2012 Quebec provincial election. While Charest is projected to win a narrow minority government at current levels of support, there is enough uncertainty in the model to give either the Liberals or the Parti Québécois a win if an election were held today.

The last poll to come out of Quebec dates from mid-June, so the numbers are hardly fresh. In all likelihood, a new poll will come out in the next few days and turn these numbers completely on their heads. But until that happens, the Liberals are projected to take 34% of the vote, putting them narrowly ahead of the Parti Québécois, who sit at 33.6%.

At 18.4% support, the Coalition Avenir Québec is well behind. Québec Solidaire is projected to take 8.8% of the vote in an election held today, while 3.4% of Quebecers would vote for the Greens (Parti vert du Québec, or PVQ), 0.8% would vote for Jean-Martin Aussant's Option Nationale, and 1.1% would vote for other parties.

The projected vote of the Liberals and PQ overlaps considerably, with the Liberals projected to be between 33% and 35% and the PQ between 32.6% and 34.6%.

In terms of seats, the Liberals are projected to win 60 and form a minority government. The Parti Québécois is projected to win 55 seats, while the CAQ wins eight and Québec Solidaire two.

Here, the ranges are particularly significant as they give both the Liberals and the PQ the potential to win a majority: the Liberals could win between 40 and 80 seats and the PQ between 39 and 70 seats. That is a wide margin, but this is indicative of how close things are in Quebec. When the two parties are running neck-and-neck, a lot of seats are on the bubble. If one party pulls away from the other the ranges will become narrower.

The CAQ could win between four and 15 seats, keeping them out of the running for the Official Opposition but keeping them ahead of Québec Solidaire, which is projected to have a range of only two seats. Aussant could win his riding, giving his party a high range of one seat.

The regional details and the individual riding projections can be accessed by clicking on the main projection image. As the projection is updated, charts tracking the changing fortunes of the parties involved will be posted.

About the Quebec model

The Quebec model uses the same basic system as the models used to project all elections since the 2011 federal election. With each new vote, lessons are learned and the model is tweaked. The current iteration is very similar to the Alberta model, in that it injects a lot of uncertainty into it. This is a very necessary thing in forecasting, as there is a large degree of uncertainty in this sort of exercise. The polls themselves have their own degree of error, which magnifies errors that a seat projection model can make. But as has been demonstrated to be the case time after time, a seat projection model like ThreeHundredEight.com's can accurately forecast an election result - if the vote projection plugged into it is accurate.

That is why the model adjusted the polls in Alberta and will do so again in Quebec. Polls are very good at assessing the voting intentions of the entire population, but where they fall short is when the entire population differs from the voting population. Based on an analysis of other elections, the polls are adjusted upwards for the governing and opposition parties, in this case the Liberals and the Parti Québécois. The polls are adjusted downwards for "third" parties, in this case the CAQ, Québec Solidaire, and Option Nationale. Parties not sitting in the National Assembly have their poll numbers adjusted downwards by a significant degree - in this case that is what is happening to the PVQ.

But in order to give some basis of comparison and to track what the polls alone are saying, ThreeHundredEight.com will also be recording the unadjusted poll average. It is included in both the main projection and the regional projections.

The Quebec model is the largest provincial model the site has used so far, dividing up the province into six regions. Poll numbers for these sub-regions are sometimes available, but when they are not the sub-regions have their results "projected" using the same sort of swing system that is used for each individual riding. So, for example, if data only for the "Rest of Quebec" is available, the results from that large region is projected downwards into the three parts of the province that make up this larger region: eastern, central, and western Quebec.

The CAQ, Aussant and the floor-crossers

This election poses a few small problems due to the presence of the CAQ and Option Nationale. The decision was made to use the ADQ's results from 2008 as the foundation for the CAQ in 2012, as the party merged with the other and is, in many ways, just an updated version of the old party and should appeal to the same voter profile. For Option Nationale, their projected regional level of support will simply be reflected in each individual riding.

With the exception, of course, of Jean-Martin Aussant. It is somewhat difficult to classify him, as he is not entirely a floor-crosser. The model takes into account floor-crossers, and it is for that reason that the CAQ's François Rebello, Daniel Ratthé, and Benoit Charrette are projected to win their ridings. Floor-crossers historically take a portion of their vote with them, in addition to being able to count upon their new party's base of support. The degree to which their vote transfers from one party to the other has been calculated based on past cases.

But this sort of system would not work for Aussant, as Option Nationale has no base to draw upon from the last election. Instead, Aussant has been treated as an independent that was formerly elected under a party banner. Again looking at past cases, a portion of Aussant's support from 2008 is assigned to him and taken directly from the PQ. Unlike with the floor-crossers, whose support rises and falls based on regional trends like any other candidate, Aussant's support is locked-in (unless a riding poll is released during the campaign). It will fluctuate by a point or two as the model adjusts individual forecasts to ensure they add up to 100%, but will remain independent of ON's position in the polls.

What will not remain locked is his high and low ranges, which will fluctuate according to ON's fortunes. Currently, Aussant has a very wide range of between 1% and 33%. This is unnatural, and is due entirely to where ON is projected to sit in the polls. Their range in his region is projected to be between just above 0% and 1.6%. Because their low range is so close to 0%, Aussant's low forecast is very low. This is one peculiar aspect of the model that will remain peculiar unless ON moves away from the floor.

How to read the projection

Seat projection models are best used to get a global picture of what the polls are likely to deliver in an election. Individual riding projections are presented for transparency, and also because people find them interesting (if I didn't include them, I would be asked to on a daily basis). They should not, however, be the focus of attention. They should not be used to make strategic voting decisions. That the forecast model puts one candidate behind another is not a sign that this candidate will certainly lose, or is losing support among his or her constituents. To read the projection as 125 individual projections is to miss the forest for the trees. The province-wide result is what is most important, as well as the range of possibilities.

The level of uncertainty presented in the model is based entirely on how much the polls are diverging from one another. When the electorate is volatile, the polls will disagree wildly and the range of projected outcomes will increase. When the electorate is settled, the polls will agree with one another and the range of projected outcomes will shrink. Consider the Alberta election - there was enough volatility in the last week of polling that the uncertainty model forecasted that a P.C. majority was a possibility.

As the campaign unfolds, several polls per week could be released. The poll average and vote projection will be able to cut through this cacophony, providing a clearer picture of what the polls are saying and where they are moving. The seat projection model will take that information and turn it into seats, which will demonstrate whether one party or another is likely to win a majority or minority government. It will then be up to the voters, but polling in Quebec has generally been good. I'm confident that the projection model will be able to tell a real story of what is going on during the campaign.


  1. Highs and lows in % are only ~2% apart, yet highs and lows in seats range from 30 to 40 seats (PQ & PLQ)...

    Isn't that astounding? Result of three way races?

    1. It's the result of a lot of close races, and some diverging poll results at the regional levels, particularly in central Quebec and the Montreal suburbs.

    2. Wow. It shows how every tiny fraction of point will make or break the election... Ah, if only more people could vote!

    3. You should join Fair Vote Canada Eric (if you aren't already a member).

      Proportional representation would make your job a lot easier lol.

  2. "Poll numbers for these sub-regions are sometimes available, but when they are not the sub-regions have their results "projected" using the same sort of swing system that is used for each individual riding. So, for example, if data only for the "Rest of Quebec" is available, the results from that large region is projected downwards into the three parts of the province that make up this larger region: eastern, central, and western Quebec."

    I think I follow most of this but I'm not sure how this works when you average the polls together?

    1. When determining the poll averages for the sub-regions, each individual poll is split up into the sub-regions and then the averages are calculated for those sub-regions using those "split-up" results.

  3. Eric, I don't know if I missed it somewhere, but is it possible to get a breakdown of which ridings are in which region? My Quebec geography isn't good enough to know just from the names. Thanks!

  4. I'll post a list on the Quebec projection page.

  5. S.-É. Parent17 July, 2012 16:39

    The model appears to be faulty. Since increasing a % has to decrease at least another one, at least one covariance is forced to be negative. The range with low and high is difficult to interpret, since they do not sum up to 100% or 125 seats. You might consider using compositional analysis techniques to compute unbiased predictions.


    1. The high and low ranges in seats and vote share are for each individual party, not in relation to each other.

      The Liberals can win between 40 and 80 seats, according to the model. Obviously, if the Liberals win 80 the PQ will not also be able to win 70, which is their high range. Instead, they will be forced towards their lower range of 39.

      Conversely, if the Liberals win 40 seats, the PQ will likely be up to the their high range of 70.

      It is the same with the vote share. As one party pushes towards its higher range, others must automatically be forced downwards. The range of this movement is within each party's high and low projections.

      The model automatically does this when calculating the high and low ranges.

  6. What are your thoughts on L'Assomption? Last I checked, Legault still planned on running there. I know the best result you predict the CAQ can get is coming a close second, but do you think this will be the case? Do you think Francois Legault might win it just because he's Francois Legault?

    1. Legault already has the star bonus in L'Assomption, but I think he could out-perform even those expectations.

      I don't expect this will be a problem come election day, though, as I suspect the CAQ's numbers will improve and L'Assomption will fall within the CAQ's range.

      If their numbers don't improve, Legault would have trouble getting elected anywhere.

    2. Cf. my analysis of L'Assomption (en français), which has changed greatly due to the new electoral map:


  7. Calling Charest "Teflon" hardly describes it, eh?

  8. Who provides the numbers? We have had several problems with poll institute(s) throwing deontology out the window to assist the PLQ...

  9. The polls are those released to the media, such as those from Leger and Crop. You can see the full listing of polls included in the model at the bottom of the page.

  10. Hi Eric:

    Any chance we'll see your take on the Nanos Numbers this week?


  11. Le PQ aurait pris la tête des intentions de vote

    26 juillet 2012

    Le parti de Pauline Marois compterait sur l'appui de 33% des électeurs, tandis que les libéraux obtiendraient 30% du vote et la Coalition avenir Québec 21%.

    Si on considère seulement les électeurs francophones, le PQ décrocherait 38% des intentions, la CAQ 23% et les LIB 25%.

    1. Mais fait attention, parce que c'est un sondage interne du PQ.

  12. Several new polls in Québec... are you sleeping on the switch on the eve of the election?????

    1. What polls are you talking about? I already wrote about the internal PQ/CAQ polls, as well as why I can't include them in the model.

  13. Léger!!!!!

    Le PQ part en tête
    Geneviève Lajoie @
    Journal de Québec, 31 juillet 2012,

  14. Actually, the real lesson for Canadians to be confused now is that most of us aren't prepared to have Pauline Marois and a Parti Quebecois government be elected on Sept. 4th.


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