Trying to math the next redistribution

Figuring out how many ridings each province "deserves" as part of the redistribution formula is super easy. Just take the electoral quotient, and divide it into the various provincial populations.

Figuring out the electoral quotient, however, seems to be not quite so easy.

According to the Fair Representation Act of 2011, C 26, it is calculated as thus:

In these rules, “electoral quotient” means

(a)  

111,166, in relation to the readjustment following the completion of the 2011 decennial census, and

(b)

 in relation to the readjustment following the completion of any subsequent decennial census, the number obtained by multiplying the electoral quotient that was applied in the preceding readjustment by the number that is the average of the numbers obtained by dividing the population of each province by the population of the province as at July 1 of the year of the preceding decennial census according to the estimates prepared for the purpose of the preceding readjustment, and rounding up any fractional remainder of that multiplication to one.

That. uh. is a bit confusing. What it simplifies to, is taking the "now population" of each province - with now being the 2021 census - and dividing the "then population" of each province - being the 2011 census - and averaging all the results.

Since it is not 2021, I will use 2019 numbers. Ontario has 14,465,515 people. The "then" population was 12,852,821. Thus our result is 1.124083116

Averaging all the results gets you 1.095575368

You then take that number and multiply it by 111,166 and round up to the nearest one. The result: 121,790.

Then we get to the easy bit, dividing this into the populations for every province. Before we do, however, lets work out the share of the total population of all 10 provinces that Quebec has, as, this will come in later. 22.67%

Now, when we apply our number to all the provinces, you get the following:

119 ON
70 QC
42 BC
36 AB
11 MB
10 SK
8 NS
7 NB
5 NL
2 PE

the "round up" clause really helps some provinces here.

Apply the Senate and Grandfather clauses and you get the following:

119 ON
75 QC
42 BC
36 AB
14 MB
14 SK
11 NS
10 NB
7 NL
4 PE

Now, lets determine what share of these seats Quebec has. 22.59%.

Because this is below Quebec's share of the population, it gains an additional seat. We also add 1 seat for each territory. Thus our final result is as follows:

119 ON (-2)
76 QC (-2)
42 BC (0)
36 AB (+2)
14 MB (0)
14 SK (0)
11 NS (0)
10 NB (0)
7 NL (0)
4 PE (0)
1 NT (0)
1 YK (0)
1 NU (0)
336 CAN (-2)

It remains to be seen if politics will change the formula, as, losing 2 seats will not go over well in either Ontario or Quebec.