What is the key factor for Trudeau winning a majority?

My latest projections (done before the latest Abacus and Angus-Reid polls but adding them doesn't change much) showed Trudeau and the Liberals in majority territory, I also mentioned that this majority was far from guaranteed. Many things would need to go right (or stay right) for the LPC to get over 169 seats. The chances were about 66%, not bad but an early summer eleciton 9during a potential 4th wave) does have some risks for Trudeau.

I then wondered which variable was the most important. Is it the lead the Liberals have over the Bloc in Quebec? Or maybe it's the lead they have over the CPC in Ontario. Or maybe the key is actually in Alberta and BC. The beauty of running simulations is that I can then use the data to answer such questions. So I used the results of the simulations (specifically the number of seats won by the Liberals) and looked at the correlations with multiple variables. I used a Logit regression to do so. Here below is the result.

If you don't know what a regression is (even less a logit regression), just know that it measures correlations while holding the other variables constant. So we get marginal effects. A logit is just a specific form of regression used when the dependent variable (the one we are trying to explain) is binary (1 for a majority, 0 otherwise). Using the results, we can estimate marginal probabilities (what happens to the chances of a majority if the Bloc gains 2 points over the Liberals in Quebec?) as well as doing some nice little graphs.

For the logit regression, I included the following variables: the gap (in voting intentions in %) between the LPC and Bloc in Quebec, the gaps between the LPC and CPC (as well as LPC and NDP) in Ontario, Alberta and BC. I didn't include the country-wide numbers as they were irrelevant (I tried at first), which makes sense.

So, what is the single most important factor? In magnitude, it's the LPC-CPC gap in Ontario, followed closely by the lead of the Liberals over the Bloc. The two are very similar and the LPC-Bloc gap is actually more significantly statistically. I'm not saying that the lead of the Liberals over the NDP in BC isn't important, just not as much.

It makes sense really and you can simply use the model to run some simple simulations (you can try with the simulator yourself although the current numbers in it aren't the most up to date, but you can change them). Using my model with the most updated numbers, I get that a swing of 10 points (-5 and +5) from the LPC to the Bloc would cause the Liberals to lose 11 seats. A same swing between Liberals and Conservatives in Ontario would cost Trudeau 17 seats.

Both simulations show that the Liberals need to keep those two leads if they want to win a majority. If they were to lose either of them (note: at this point, their lead in Ontario is a lot more solid than their lead over the Bloc as Quebec is always unpredictable), their chances of a majority would essentially become 50-50 at best.

Graphically, let's represent the probabilities of a Liberal majority as a function of the lead of the Liberals over the Bloc in Quebec and over the CPC in Ontario:

The current leads are, respectively, about 10-11 points over the Bloc and about 9-10 points over the Tories in Ontario. Both would indicate about a 60-70% chances of a majority, which matches (obviously) my latest projections. But what this graph shows is that the chances are more sensitive to a drop of this lead in Ontario (steeper slope). All those seats in the 905 would come back into play if O'Toole could gain a little bit over the Liberals compared to 2019. Side note, but this is why I don't think the Tories really have no chance of winning a plurality or that they were soooo far from it in 2019. The fact is that you can easily have 10-20 seats flipping in Ontario and doing so would bring the Liberals not only below 170, but much closer to the Conservatives.