In his latest piece, John Ibbitson from the

*Globe and Mail*argues and shows that the federal Liberals can't expect to form the next government without a big drop of the NDP in Quebec. While his math seemed to add up, I decided to take a look myself.
For this article, let's forget some of the recent polls where the Liberals can be sometimes as low as 23%. Obviously a party finishing third in the popular vote, almost 10 points behind the top party, can't expect to win the most seats. You don't need math or a complicated model to show that. Instead, let's see how high the Liberals need to be outside of Quebec in order to win the next election.

The nice thing for this exercise is that I don't need to make up all the numbers. I can simply take a look at the polls of a couple of months ago when Trudeau and his party were actually polling first (and I'm not even talking of the polls last year that had the Grits on a path to a majority). Take this poll from Forum of last week actually that had the Liberals first with 32%, 1 point ahead of the Tories and 4 of the NDP. This is a poll that could be within the margins of error of the most recent poll average. The problem obviously with this poll is that Trudeau and his party were quite high in Quebec and that goes against what we are trying to do. So let's keep the results outside of Quebec and replace the percentages in la Belle Province by the ones of the most recent Crop (mentioned by John Ibbitson; Notice however that this poll was done before the return of Gilles Duceppe. I cover this below).

Take the numbers, put them into the simulator and what do you get? The Tories with around 110 seats, the LPC at 100 and NDP at 120 (if we round everything). So sure, Trudeau doesn't become the next PM. But we are using a scenario where the Liberals do very average everywhere outside of the Atlantic. In Ontario for instance, the numbers from Forum have this party at 33%, barely ahead of the CPC and NDP (31% each). If anything, these numbers are incredibly good for the NDP, especially in Ontario. And they aren't close to the "best case scenario" used by Ibbitson. Let's compare quickly.

In Atlantic, these numbers would give 29 LPC, 3 NDP. The CPC is wiped out. This is very similar to Ibbitson' scenario.

In Quebec, he gives the LPC 10 gains, my simulation only 4 So I'm actually harder on the Liberals there.

Ontario, 14 seats for the Grits last time (with the new map), 47 this time around based on my numbers. Ibbitson gives them 26 gains (on the old map), my model 33. Even taking the new seats into account, I'm slightly more generous with the Liberals there.

6 gains in the Prairies and Alberta for Ibbitson, I actually only give them 4.

Finally, in BC, my simulations increase the number of seats for the LPC from 2 to 10, compared to 6 in the old map in the Globe and Mail article.

Overall, my relatively "average scenario" is quite often less good for the Liberals than the one of Ibbitson, including in Quebec (it is however better in Ontario and BC). But my 104 seats aren't far from the 109 he had.

But again, my scenario isn't a best case one. It isn't even an objectively good one for Trudeau. In many provinces, the Liberals would be in line (in terms of votes) with 2008 for instance. We could debate whether the Grits can hope to do much better than 2008, but I don't think that this election should represent the best scenario for this party at this point.

So, what is needed for the Liberals to win from there? Do they really need Quebec? It'd obviously help a lot to get more than 12 seats in the French province. The problem is that we need the NDP to fall a lot and the Liberals to increase significantly before the seat gains are important. Remember the Liberal vote in Quebec is concentrated in Montreal. So unless Trudeau can become first or close to first in terms of votes, Quebec will at best provide another 8-10 seats. In a close election, that could well make the difference. Could make the difference in a close election but far from optimal. If anything, if the NDP falls in Quebec, the Bloc will benefit from it. With Duceppe back, some soft NDP voters could go back to the Bloc. So a NDP collapse there would most likely benefit the Bloc, not the Liberals. The recent Leger poll shows NDP voters' second choices are evenly split between LPC and Bloc.

So what's left? The answer: Ontario. Remember that the poll I based my simulations on had the NDP at 31% in Ontario. That's much higher than their 2011 results. So let's put the NDP back at 25% there. Let's also give this province to Trudeau, winning it 37% vs 34% for Harper. So pretty much going back to the 2006 results. With this modification, the Liberals now win the election with 114 seats, 3 more than the Conservatives and 2 more than the NDP.

Let's illustrate the potential of Ontario versus Quebec in two graphs. They both display the possible outcomes (number of seats) for the Liberals as a function of the percentage of votes received in each province. In other words, the horizontal variation is when the Liberals increase or decrease their shares of votes, while the vertical variation (for a given % level) represents the uncertainty of the electoral system (two scenarios with the Liberals at 25% in Quebec won't give the exact same number of seats as it depends on the other parties, the efficiency of the vote, etc).

The trend line shows the average number of seats for every possible percentage level. As we can see, getting more votes obviously leads to more seats in average. Nevertheless, let's compare the effect of a 10-points increase in Quebec and in Ontario. In the former, moving from 21% to 31% allows the Liberals to gain roughly 10-12 seats (from 12 to 23 approx.). In Ontario, moving from 28% to 38% allows the Liberals to gain 30 seats (from 30 to 60). These graph should make it very clear that if there is one province where Trudeau needs to increase, it's Ontario. The potential for seats in Quebec simply isn't there. It'd be there of course if the Liberals could climb to 35-40% in Quebec, but this is highly unrealistic. Once again, if the NDP was to fall that bad, the Bloc would benefit just as much as the Liberals.

Let's illustrate the potential of Ontario versus Quebec in two graphs. They both display the possible outcomes (number of seats) for the Liberals as a function of the percentage of votes received in each province. In other words, the horizontal variation is when the Liberals increase or decrease their shares of votes, while the vertical variation (for a given % level) represents the uncertainty of the electoral system (two scenarios with the Liberals at 25% in Quebec won't give the exact same number of seats as it depends on the other parties, the efficiency of the vote, etc).

The trend line shows the average number of seats for every possible percentage level. As we can see, getting more votes obviously leads to more seats in average. Nevertheless, let's compare the effect of a 10-points increase in Quebec and in Ontario. In the former, moving from 21% to 31% allows the Liberals to gain roughly 10-12 seats (from 12 to 23 approx.). In Ontario, moving from 28% to 38% allows the Liberals to gain 30 seats (from 30 to 60). These graph should make it very clear that if there is one province where Trudeau needs to increase, it's Ontario. The potential for seats in Quebec simply isn't there. It'd be there of course if the Liberals could climb to 35-40% in Quebec, but this is highly unrealistic. Once again, if the NDP was to fall that bad, the Bloc would benefit just as much as the Liberals.

If we go back to our scenario with Trudeau becoming PM, this would obviously be a super close election and I think Ibbitson forgets that with three parties around 30%, the number of seats required to win could well be very low this October. This scenario however involved the Liberals doing (very) badly in Quebec. We also didn't go into extreme cases outside of this province. The domination in Atlantic Canada is likely to happen, given all the polls for the last two years. There were only minimal gains in the Prairies (the LPC was third there). Really, the one province where I increased the LPC by a lot was Ontario. And this is really my point: The Liberals don't necessarily need the NDP to collapse in Quebec, they need this party not to increase in Ontario. This is the one province they need to win. Taking 20 seats in Quebec would be nice and helpful, but won't likely be the difference between Trudeau PM or Trudeau MP. Moreover, my scenario didn't involve a sweep of Ontario like Jean Chrétien used to do (when the Right in this country was divided). It only required the Liberals to reclaim the title of first party in Ontario. Can they do that? I don't know and I acknowledge it's not a simple task. At the same time, if you want to become PM, you better be able to win at least one big province. It could be Quebec, but it

*doesn't*have to be
As pointed out by Darrel Bricker (from Ipsos) in the article, if you want to win an election, it's nice and almost necessary to have at least one region where you dominate and win pretty much all the seats. The Tories have Alberta, the NDP probably will have Quebec. The Liberals have the Atlantic. The 30 seats in the Atlantic for the Liberals is very comparable to the 30-33 seats guaranteed for the CPC in Alberta. At this game, the NDP might have a head start, but it doesn't mean the Liberals can't win.

What is true however is that as opposed to the Tories, the Liberals can't dream of majority without a good showing in Quebec. Five months before the election though, a majority seems out of reach of any party. So let's forget about it for now.

At the end of the day, I simply disagree with the statement that the Liberals can't win without a drop of the NDP in Quebec. This is simply not true. Not only would such a collapse most likely benefits the Bloc just as much (if not more) than the Grits, the province that Trudeau absolutely needs to win (and needs the NDP to remain low there) is Ontario. Even by winning only 10-15 seats in Quebec, Trudeau could get 115-120 Canada-wide and for this election, that could well be enough to become PM.

What is true however is that as opposed to the Tories, the Liberals can't dream of majority without a good showing in Quebec. Five months before the election though, a majority seems out of reach of any party. So let's forget about it for now.

At the end of the day, I simply disagree with the statement that the Liberals can't win without a drop of the NDP in Quebec. This is simply not true. Not only would such a collapse most likely benefits the Bloc just as much (if not more) than the Grits, the province that Trudeau absolutely needs to win (and needs the NDP to remain low there) is Ontario. Even by winning only 10-15 seats in Quebec, Trudeau could get 115-120 Canada-wide and for this election, that could well be enough to become PM.