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Power to the People?
m1 Math Exploration
Eamonn O'Keeffe
"It is obvious that we cannot depart from representation by population."
-George Brown at the Quebec Conference, October 20th 18641
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History of Representation by Population
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The principle of representation by population is the linchpin of Canada's democracy. Efohrined in
the British North America Act of 1867 and endorsed by the Fathers of Confederation, thts concept
prescribes that all citizens have an equal say in electing their representatives. At least in theory, each
Canadian Member of Parliament should represents a roughly equivalent number of citizens.
However, representation by population was not always taken for granted.. A mere thirty-five years
before Confederation, the British Parliament passed The Great Reform Act of 1832, eliminating 57
"rotten boroughs". For centuries, English electoral districts did not change to reflect population shifts,
resulting in ridings that boasted outrageously small populations while the new urban centres of the
Industrial Revolution were woefully underrepresented. Thus, by the time of the 1831 election, out of
406 MPs in the House of Commons, 152 members were elected by fewer than 100 voters, and 88 by
less than 50 voters each. 2 The most notorious rotten borough was Old Sarum, which had elected two
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MPs since its establishment in 1295; it represented seven voters by the time of the Great Reform Act. \Iol C W r
Also known as pocket boroughs, these electoral districts were often used by wealthy landowners to
gain influence and power in the House of Commons. Can we be surprised by the unrest and riots that
stained early 19th century England, such as the 1819 Peterloo Massacre, when the political system was
so inequitable and unresponsive to the needs of the disenfranchised lower classes? rm \.
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The Fathers of Confederation, mindful of repeating these errors, mandated in the British North
America Act that riding boundaries be re-examined after each decennial census.
In Canada, some deviation from the principle of representation by population can be tolerated..
Sometimes the obligation to ensure voter equality must be balanced with the need to ensure that all
regions and populations are adequately represented. For example, each Canadian territory is
represented by a Member of Parliament, despite the fact that the Yukon, the Northwest Territories and
Nunavut combined have a lower population than an average federal electoral district. /
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Purpose
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In this investigation, I want to discover the extent of the voting inequalities that exist in Canada's
federal electoral system between the different provinces and territories. Is each province and territory
fairly represented in the House of Commons?
Canada's adherence to the principle of representation by population is an important topic of study.
The stability of our political system is largely due to the confidence of voters, who perceive Canada's
democracy as fair and equitable. As such, Canada must ensure that the principle of representation by
population, a keystone of our electoral system, is at least loosely followed. As long as electoral
districts are redistributed to account.for shifting demographics, ensuring that provinces with growing
populations are fairly represented, the Speaker of the House of Commons will never
have to call upon
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the Honourable Member for Old Sarum.
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Calculations
In order to ascertain whether each province and territory is fairly represented in the House of
Commons, I will calculate two different statistics:
First, I will compare the population of each province and territory as a percentage of Canada's total
population with their share of seats in the House of Commons. For example, if Ontario's share of the
national population is greater than its share of MPs, it is underrepresented in Parliament. Alternatively,
if Ontario's percentage of Canada's total population is less than its share of MPs, it is overrepresented
in Parliament.
Secondly, I will calculate the "vote weight" of a ballot cast in each province and territory. This
calculation measures the worth or weight of a vote cast in one electoral district or province relative to
. the average weight of a vote cast in Canada. Ideally, each vote would have a value of 1, indicating the
average national vote weight. If this were the case, all Canadians would have an equal say in electing
Members of Parliament.
However, perfectly equal representation is impossible. Voters in electoral districts with high
populations have a low vote weight compared to their counterparts in lower population ridings. For
example, an eligible voter who lives in Calgary Northeast, an electoral district where the local MP
represents 150,000 people, has less say in the outcome of the election than a voter in Nunavut, a riding
with a population of 33,600 people.'
Percentage of Population vs. Percentage of MPs
To calculate each the population of each province and territory as a percentage of the national
population, I used data froy:rStatistics Canada. While I could have used the date from the 2011 Census,
I chose instead to rely ~StatCan population estimates for the 2nd quarter of2012 (April-June 2012),
because it is more recent. 4 As this data is based on projections, it is less precise than the Census results.
While this constitutes a possible source of error, the Q2 2012 estimates give me a more current
reflection of Canada's population. *
So as not to show the same procedure thirteen times with different numbers for each province and
territory, I will explain each step once, using Ontario as the example. The calculations for the
jurisdictions will not be shown but were determined through the same methodology.
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Using the Q2 2012 Statistics Canada data, I calculated the population of each of Canada's provinces
and territories as a percentage of the national population.
= Provincial Population
TP = Canada s Total Population
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TP
=
13,472,438
34,755,634
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Next, I sought to calculate the share of House of Commons seats from each province or territory. I
divided the number of electoral districts in each province by the total number of seats in the House of
Commons.
SP = Seats per Province
TS = Total Seats
SP = 106 "'".3442
TS
308
:. Ontario has 34.42% of the seats in the House of Commons
Vote Weight
The formula for vote weight for a specific electoral district (Electoral District X) is:5
(Average Population of a Federal Electoral District)
(population of Electoral District X)
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This exploration focuses on the disparities in vote weight between different provinces and
territories, rather than specific ridings. Thus, I devised an adapted formula in order to calculate the
average vote weight in in each Canadian province and territory.
(Average Population of a Federal Electoral District)
(Average Population of a Federal Electoral District in Province X)
To calculate the vote weight averages, I must first find the average population of a federal electoral
district in Canada. This can easily be computed by dividing Canada's total population by the number of
seats in the House of Commons:
Canada's Total Population: 34,755,634
The Number of Seats in the House of Commons: 308
34,755,634 = 112 842.96
308
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:. The average population of a federal electoral district in Canada is 112,843 people
Next, I must calculate the average population of federal electoral districts within each province or
territory. This can be achieved by dividing the population of each sub-national jurisdiction by the
number of federal ridings within the respective province or territory. I will use Ontario as an example:
Population of Ontario: 13,472,438
Federal Electoral Districts in Ontario: 106
13,472,438
106
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127 098.47
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:. The average population of a federal electoral district in Ontario is 127,098 people
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Now, in possession of all the requisite date, I can calculate the average vote weight for each
provrnce.
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(Average Population of a Federal Electoral District)
(Average Population of a Federal Electoral District in Province X)
112,843
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127,098
8
878
:. The average vote weight in federal electoral districts in Ontario is 0.89
Results & Data Processing
Table 1. Population and House of Commons Seats and Vote Weight by Province and Territory
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Figure 1. Vote Weight by Province and Territory
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ON
QC
BC
AB
MB
SK
NS
NB
NL
PEI
NT
YT
NU
Province or Territory
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Average (±O.1)
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Above Average
Figure 2. Percentage of National Population vs. Percentage of Seats by Province and Territory
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ON
QC
BC
AB
MB
SK
NS
NB
NL
PEI
NT
YT
NU
Province or Territory
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Percentage of Canadian Population
Percentage of House of Commons Seats
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Reflection & Conclusion
The current distribution of federal electoral districts demonstrates a lax adherence to the principle of
representation by population. As is apparent in Figures 1 and 2, smaller provinces and territories are
over-represented in the House of Commons, at the expense of the three largest English-speaking
provinces: Ontario, British Columbia and Alberta. For example, a vote cast in Prince Edward Island
has a weight three times that of an Ontario ballot.
Some deviations from the principle of representation by population are necessary to ensure that smaller
regions or populations have a voice. For example, the apportionment of one Member of Parliament for
each of Canada's three territories is justifiable, despite their small populations, to ensure that their
needs are not overlooked. Furthermore, the Atlantic Provinces arguably deserve a moderately higher
percentage of seats than their population would merit, to ensure the interests of their region are not
overwhelmed by the concerns of the more populous Central and Western provinces. A small
adjustment, perhaps 1.1 or 1.2 times that of the nationwide average vote weight, might be sufficient to
ensure fair representation without seriously distorting the principle of representation by population.
However, the current average vote weight in the Atlantic Provinces, according to the calculations
above, is 1.53 times the national average. This is unquestionably excessive.
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Moreover, some present deviations from the principle of representation by population appear
unnecessary. For example, votes cast in Saskatchewan carry 1.8 times of the weight of ballots in
neighbouring Alberta. There seems to be little reason for this egregious inequity.
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The results of this exploration clearly demonstrates that the current composition of the House of
Commons does not fairly represent all of Canada's provinces and territories. Sixty-three percent of
Canadians live in Ontario, Alberta or British Columbia," It is intolerable that nearly two-thirds of
Canadian are under-represented in the House of Commons. However, recent legislation will give a
fairer, more proportionate voice to these provinces.
In December 2011, Bill C-20, The Fair Representation Act, received Royal Assent and became law.
The number of electoral districts to be contested in the next federal election (likely in 2015) will
increase from 308 to 338. Ontario will gain fifteen seats, British Columbia and Alberta will both
receive an additional six while Quebec will gain three seats. These extra Members of Parliament will
help address the under-representation of Canada's most populous provinces, although the vote weights
in Ontario, British Columbia and Alberta will still trail the national average",
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Electoral districts that closely follow the principle of representation by population are important to
robust democracies. Citizens must have a roughly equal say in choosing their leaders. The underrepresentation of the populous and fast-growing provinces of Ontario, British Columbia and Alberta is
especially worrying because of the diversity of their populations. These provinces are home to the
largest concentrations of visible minorities and recent immigrants in Canada. 8
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References
1 Sancton, Andrew. The Principle of Representation by Population in Canadian Federal Politics. Mowat Centre
for Policy Innovation, 2010. pg. 2.
Carpenter, William. The People's Book; Comprising their Charted Rights and Practical Wrongs. 1st ed.
London: W. Strange, 1831. 406. Print.
2
Estimates of population, Canada, provinces and territories. Statistics Canada. 2012.
http://www5.statcan.gc.ca/cansim/a26
3
4
Ibid.
5
Mendlsohn, Matthew. Some Are More Equal than Others. Mowat Centre for Policy Innovation, 2010.
Estimates of population, Canada, provinces and territories. Statistics Canada. 2012.
http://www5.statcan.gc.ca/cansim/a26
6
Postmedia News. (2011, December 16). Thirty new seats officially coming to the House of Commons. The
National Post. http://news.nationalpost.com/2011 /12/16/thirty-new-seats-offically-coming-to-the-house-ofcommons/
7
CBC News. (2010, March 9). Minorities to rise significantly by 2031: StatsCan. CBC News. http://www.cbc.ca/
news/canada/story/2010/03/09/statscan-minority.html
8
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