A response to Ipsos Reid, Part II

This is Part II in a three part series.
For Part I, click here.  For Part III, click here.

A Response to Ipsos Reid, Part II: How to “prove” that the Canadian House of Commons actually has 429 seats instead of the 308 seats it actually has.

Here’s how you do this: just use the mathematical practice of taking the average of several unequally-weighted averages.  Normally, this would be considered a big “no-no” in the world of statistics, but since a senior official with the prestigious Ipsos Reid polling firm recently came out and endorsed this practice, we’re good to go.

First we need some numbers.

According to Statistics Canada, the most current estimates of the Canadian population are the following:

	January, 2009
Canada	33,504,680
Newfoundland	508,990
PEI	140,402
Nova Scotia	939,531
New Brunswick	748,319
Quebec	7,782,561
Ontario	12,986,857
Manitoba	1,213,815
Saskatchewan	1,023,810
Alberta	3,632,483
British Columbia	4,419,974
Yukon	33,442
Northwest Territories	42,940
Nunavut	31,556

Now, each province has the following number of seats in the House of Commons:

Canada	308
Newfoundland	7
PEI	4
Nova Scotia	11
New Brunswick	10
Quebec	75
Ontario	106
Manitoba	14
Saskatchewan	14
Alberta	28
British Columbia	36
Yukon	1
Northwest Territories	1
Nunavut	1

So, we just do a little long division using our handy computer machines and we get the following estimation of the population per seat in each province:

Newfoundland	72,713
PEI	35,101
Nova Scotia	85,412
New Brunswick	74,832
Quebec	103,767
Ontario	122,518
Manitoba	86,701
Saskatchewan	73,129
Alberta	129,732
British Columbia	122,777
Yukon	33,442
Northwest Territories	42,940
Nunavut	31,556

Now, using this methodology, there should be nothing wrong with just taking the average of these averages to come up with the Canadian average:

Doing so, we get an average population/seat value of:

Canada

78,048

… But, we already know from Stats Canada’s data that Canada has a total population of roughly 33,504,680 people.  Therefore:

33,504,680 ÷ 78,048 = 429 seats

QED.

And presto, voila!  You’ve just proven that the Canadian House of Commons has 429 seats even though it actually contains 308.

Can you spot the problem?  The problem is that this practice — which Mr. Wright publicly came here and said was legitimate — does not take into account that taking an unweighted average of several averages means that Ontario (population 12,986,857) and Nunavut (population 31,556) are considered equally weighted.