Final projections for the Federal Election 2015: Liberal minority, surprises possible

After the longest campaign in Canadian history, it appears voters have made their choice and will elect a Liberal minority on Monday. There is however enough uncertainty for a surprise to happen, whether it's a Conservative minority or a Liberal majority.

This will be a very long post. The first part is the summary and then you have the detailed analysis. So for those who don't like to read, here are the final projections.

Voting intentions; Seat projections with 95% confidence intervals; Chances of winning the most seats

These projections are really my best guess for tomorrow. Given past election results, the multitude of national and riding polls and how accurate polls can be, I get that Justin Trudeau has about a 82% chance of becoming the next Prime Minister. I should probably phrase it more as "winning the most seats", but it'll ultimately be the same.

So another minority, but most likely a stable one for a while as both the Conservative (for sure) and the NDP (I predict it'll be the case) will be looking for new leaders. I think for Thomas Mulcair, it depends on the extent of the loss tomorrow. 72 seats isn't too bad, especially if they keep Quebec. But it could also get ugly. According to polls, the NDP is actually down in every single province or region!

You have the riding by riding projections (with chances of winning for each candidate) below. You can either click here or use the Scribd thingy (if you are on mobile, avoid Scribd at all cost).

All in all, the big picture take-away from these numbers is that a Liberal minority is by far the most likely outcome that can occur tomorrow. But odds show a Conservative minority is possible as well as a Liberal majority. I know it sounds like I'm trying to cover every possible scenario so that I'll at least have the correct one, but it's more about putting odds on those scenarios. The same way that when you go to the casino, you know you can win, but you also want to know how likely you are to become rich.

Remember that polls and projections have a lot of uncertainty. It's important to reflect this uncertainty the best possible way. Still, don't get me wrong, anything but a Liberal minority tomorrow would be a big surprise and a punch to pollsters and people making projections like me.

If you are interested in more details and analysis, then please keep reading.

Conservatives underestimated?

Still, it's far from a sure thing. How is that? Well first of all, I slightly adjust the polls to account for the likely underestimation of the incumbent, This is a phenomenon we have observed in multiple elections, including the last 3 federal ones. You can also see this as accounting for the so-called "shy tory" effect where people are too embarrassed to admit they'll vote Conservative (what might have happened in the UK earlier this year). Additionally, we need to remember the Tories usually do better among older demographics and they tend to vote more (although Ekos and Forum actually show the Liberals ahead in every age group).

My adjustments are relatively small and boost the Tories by 1.5 points compared to a simple poll average. They are definitely smaller than the adjustments of others or what we've seen from Angus Reid with the Likely Voters adjustments. Is it a good assumption or should I go with the 3 points of last time? Or maybe even more as Conservative voters might feel even less likely to admit who they are voting for. Ekos for instance note that the Conservatives are lower in phone polls with live interviewers (aka a human person) versus automated phone calls. At the end of the day, this is the part where this becomes more of a guess than anything else.

Another illustration of the possible underestimation of the Tories come from the numbers among people who voted in advance. Ekos actually show the Conservatives ahead while Angus see them neck and neck. When I looked at patterns between the turnout and other variables, I didn't find much. Abacus also concludes that people who voted by anticipation do not significantly differ from others. Still, it shows that even though these advanced polls took place right when the Liberals were surging, the Tories were still in the game. As I said before, Liberal supporters need to remain cautious, their party hasn't won yet.

All in all, I'm pretty convinced the Tories are indeed underestimated. But by how much? Well your guess could be as good as mine. I think whatever boost they'll enjoy could ultimately be canceled out by the last minute momentum of the Liberals and the possible switch of some NDP voters (see below).

However, it's really important to realize that if the polls are underestimating the Conservatives as much as they did in 2011 (especially in Ontario), then Stephen Harper could well win more seats tomorrow. This is a possibility we need to acknowledge.


The chances of a Liberal majority are actually smaller than of a Conservative minority. That should put things in perspective. Yes it's possible and last minute, one-day polls of Forum for instance show the trend is in favour of the Liberals, but the average doesn't. Still, if we allow for the possibility that the Conservatives will be underestimated, we need to do it for the Liberals as well. In order to win 169 seats and more, Justin Trudeau would need to finish first in Quebec in terms of votes, clean Ontario and win BC. Possible, but unlikely.

One thing for sure, the last minute trend was incredibly favourable to the Liberals. Nanos shows the Liberals increasing over the weekend, so does Forum and Ekos. So if you believe that one-day polls done during the weekend can accurately measure last minute shifts (I'm skeptical and prefer averaging over a couple of days; I also tend to think pollsters love using the last minute shift as an excuse when they're wrong), then you should actually prepare for a Liberal majority. Not that the Tories are collapsing, but the NDP sure is.

The exact chances of a majority depend on how we model uncertainty (see below for the technical discussion). It's between 3.2% and 17.9%. I thus went with the average, middle of the road scenario for the pdf above.

The reason I believe a majority is out of the question for the Liberals is because even the last minute polls don't show a much larger lead in Ontario. The surge seems to be coming from elsewhere. But Ontario is really the key to a majority for the Liberals.

Here below you have a graph representing the probability of a Liberal majority as a function of the lead (in percentage points) in Ontario. As you can see, the Liberals start having a chance around 15 or 16 points. Polls haven't shown the lead to be that wide in average. Of course, the Liberals could win Ontario by "only" 11 points and do better in Quebec and BC. I'm simply showing one of the key determinants here.

Vote splitting

One of the infamous issues of our electoral system where two parties can split the same vote and allow a third one to go through. It's often blown out of proportion because people assume that all the NDP voters would switch to the Liberals for instance when it's not that simple. I re-run the analysis I did the other day and with the final numbers, I get that vote splitting allows the Tories to win 35 seats. There a total of 64 ridings where the total of the NDP and Liberals votes is greater than the number of votes for the Conservatives, but only in 34 of those would a unique candidate actually defeats the Tory candidate. Still, it means that without vote splitting, the results would be:

CPC LPC NDP Green Bloc
Normal projections 120 137 72 1 8
Without vote splitting 85 165 79 1 8
Difference -35 28 7 0 0

It's a simulation and you can take from it whatever you want. It's possible that this issue will occur for the last time as both the NDP and Liberals want to change the electoral system (although they don,t currently agree on which system is better).

And now some remarks and analysis by topics.

1. The polls.

As usual for a federal election, we got a lot of polls. Every major firm provided numbers in this last week, some even multiple times over the weekend. Only Abacus strangely decided not to release final numbers.

These polls have shown a remarkable convergence. Even Ekos who had a tight race just two days ago ultimately showed the Liberals up by around 4 points. This is very similar to the latest numbers from Angus Reid. The rest, from Nanos, Leger to Forum (and others) all have the Liberals well ahead of the Tories. Not only is this true at the national level, it's true in the crucial Ontario where Justin Trudeau appeared to have taken the lead during the first week of October.

We also got a lot of riding polls. Some matched my projections exactly, some didn't. I had more success with polls from Forum and Mainstreet than the ones from Environics in general. When the differences were too important (and especially when they were confirmed by more than one poll), I adjusted the projections.

2. The story of this campaign

I covered this in details in my article yesterday for the Huffington Post.

3. A look at some province

The Atlantic provinces won't be the source of much uncertainty tomorrow. The Liberals should pretty much sweep the region. The Liberals will therefore take a very early lead in the seat count on your television (or Ipad, you crazy kids). There is really nothing much to say there. The Liberals have been ahead in this region the entire campaign and their lead actually increased.

Quebec is possibly the most unpredictable province. After weeks of dominance by the NDP (where, at some point, we wondered if the NDP would not be able to win over 70 seats there), the niqab happened and started the downward trend. Thomas Mulcair never managed to recover. As of tonight, we can't even be sure the New Democrats will finish first in Quebec, both in terms of votes and seats. The electoral system and the fact that the Bloc appears to be stuck at 20% or less in average means the NDP is likely to win the most seats though. The chances are 58% to be precise. The NDP could finish second in votes and still win more seats. Look at the detailed analysis in French. Note that technically, all four parties have a shot at winning Quebec! If polls have shown a convergences in Ontario, they definitely haven't in Quebec.

The Conservatives seem poised to at least make some gains in Quebec, thanks to the drop of the NDP and a small increase compared to 2011. It won't ultimately be enough to compensate the losses pretty much everywhere else.

As for the Bloc, well, this is kind of the wild card. Its confidence interval is quite wide (relatively) and, by being around 20%, is right at the threshold between winning many seats or losing them all. Even Gilles Duceppe isn't sure to win his riding.

Ontario is ultimately the reason Trudeau will likely become Prime Minister. If you look at the graph, you actually see the Tories increasing in most provinces over the last two weeks, except in Ontario. Not sure what happened there in early October but there was a sharp shift in the voting intentions.We moved from a tight race between the Tories and Grits to a situation where the Liberals were enjoying a comfortable lead. In this last week, the trend has been very constant and this is the main reason we don't think a majority is really likely for the Liberals.

The Prairies and Alberta are still Conservative in majority but the Liberals will definitely make gains there. This is especially possible in Manitoba and in cities in Edmonton. As the NDP was falling in Quebec and its chances were going away, it appears some voters switched to the Liberals in order to defeat Harper.

Finally, British Columbia is the other wild card of this election. The NDP was dominating it for the first couple of weeks but could end up third there. The Liberal vote might be too concentrated in Vancouver, so that the Tories should win this province. If the polls, somehow, end up being wrong in Ontario and the race is tight as we start getting the BC numbers, it'll mean we'll most likely have to wait until late before calling this election

4. Could the Conservatives win when almost 70% of the population don't support this government?

The Conservatives won a relatively surprising majority last time. I say surprising because polls and projections were mostly predicting a minority. But a 2-3 points underestimation nationally and a 3-4 one in Ontario allowed Stephen Harper to win his majority. He even won seats in Toronto, something that was definitely the biggest surprise of the night.

This time around, his support was always gonna be stable but limited. Stable because at barely over 30%, he only has the core Conservative voters left. This matches perfectly with the around 30% of people who like Stephen Harper, think he's doing a good job and don't want to change government. Limited because many voters really despise him by now and would go as far as voting strategically in order to defeat him and his party. The ceiling for the Tories has been low for a long time now.

Ultimately, the only way he was gonna win was by having the other two parties splitting each other. Such vote splitting still occurs in some ridings (see above), but the Liberals have managed to gather enough support around them (and/or the NDP collapsed enough) to win anyway.

Stephen Harper also wanted the voters to mostly think of the economy and not take a chance with the other guys. But it appears that values could play a bigger role this time around, as shown by the latest Ekos and Abacus polls. Plus, of course, the fact that 60-65% of people have consistently shown they wanted a change of government. If you think about it, it's still pretty surprising the Tories are even in this race and they can thank the electoral system for that.

5. Uncertainty

The chances for the Tories depend on how you model uncertainty. I get the probabilities by doing simulations where I randomize the vote intentions (to account for the possible errors of the polls) as well as the distribution of the vote (to account for the fact the electoral system doesn't translate votes into seats perfectly). The idea is really to see all the possible outcomes and how likely they are. 

So a good case scenario for a party is when it beats the polls and has an efficient vote. The question is whether we should add correlation across provinces. For instance, if the Liberals out-perform the polls in Atlantic, are they more likely to outperform them in Alberta? The answer isn't very clear, so I did both. Adding correlation means that a party could be fortunate and do better pretty much everywhere.

So I ran the simulations twice, once with correlation and once without. Without, I find the odds of a Conservative victory to at 10.6%. With, they increase to 25%.

Similarly, having more uncertainty means more extreme scenarios. For the Liberals, adding correlation (which could be interpreted as a last minute boost, most likely coming from the fact some NDP voters would switch) increases the chances of a majority from 3.2% to 17.9%

Ultimately, I believe the truth is somewhere in the middle and this is what the graphic above displays.

Also, my simulations have proven to work remarkably well at the riding level (and this part doesn't depend on cross-province correlation). After 4 elections using the model (BC 2013, Quebec 2014 - and 2012 retroactively, Ontario 2014 and Alberta 2015), here where it stands.

Projected chances of winning Actual win percentage
0% 0%
1-30% 11%
30-50% 45%
50-80% 57%
80-99% 89%
100% 100%

As you can see, it works. So if your favourite candidate is projected at 0% in my final projections, I'm sorry but the odds are that he or she will lose (note: because I round the numbers, some candidates appear at 0% but are not. If they are at like 0.5%, the pdf will at least show some color on top of the percentage). Similarly, anybody projected with 100% confidence level should win tomorrow.

Therefore, maybe a better way to look at the race tomorrow is to see how many ridings each party is guaranteed to win and how many close races there are.

First, let's see how many ridings are at exactly 100% certainty for each party:

Conservatives: 23
Liberals: 38 (17 in the Atlantic)

None for the NDP or the Bloc. For the NDP, this is pretty insane. Just a couple of weeks ago, this party had half the ridings in Quebec completely locked up. If people will likely remember this election as Trudeau's triumph, we should also remember it was Mulcair's spectacular failure.

How many ridings are at 0.0% and therefore completely out of reach?

CPC: 99
LPC: 25
NDP: 181
Green: 332 (so 3 ridings where they can win because these simulations don't include the territories)
Bloc: 25 (in Qc)

Let's this information sink for a moment: there are only 25 ridings where the Liberals have no chance at all. This is incredibly impressive and shows how widespread this party's support is.

Finally, for each party, the number of seats currently projected as a loss by less than 5 points.

CPC: 19
LPC: 31
NDP: 13
Bloc: 9

See for the Liberals, this means they could actually get quite a lot higher than my projections. It really depends if the last minute shift observed by some pollsters will translate into actual votes on Monday. More generally, here are the distributions of the chances of winning by parties.