PDF
Ian Gray; James Gray
The purpose of this paper
is to calculate what the result of the 2004 federal election in Canada might
have been using a system of proportional representation based on the system in
use for elections to the Scottish Parliament. This is only one possible
model and there are a number of variables within the model. The Scottish
model was recommended by the Law Commission of Canada in its March 2004 report.
The paper does not attempt to deal in any depth with the implications of
a proportional system, such as the possibility that there will always be a
minority government, or with the arguments for and against such a system.
These are canvassed more fully in the Law Commission report.
The Scottish Parliament uses a mixed proportional system.
There are 129 seats (for a population of about 5 million) with 73
constituencies where the person receiving the most votes is declared elected
(termed first past the post or constituency seats). The other 56 seats
are filled from slates of candidates proposed by the parties, or individuals –
7 seats in each of 8 regions of varying population size (termed proportional or
regional seats). Thus 57% of the total seats are first past the post and 43%
are proportional.
The constituency elections and
the regional elections take place at the same time and each elector has two
votes – one for a constituency candidate and one for a party or individual on a
regional list. A person can be a candidate for a constituency seat as
well as being on a party list for a proportional seat. This gives parties
an opportunity to ensure that a particular candidate gets elected, if not as a
constituency member then from the slate. It could also facilitate the
election of more women members. In the 2003 Scottish elections, 50 out of
129 members elected were women – 31 out of 73 constituency seats and 19 out of
56 proportional seats.
The method of calculating the
proportional seats is as follows: For the first proportional seat, divide the
number of votes cast in the region for each party’s regional slate or for each
individual regional candidate by the number of constituency seats that they got
in a region plus 1. So for a party (say Labour)
that got 10 constituency seats in a region, its total number of regional votes
would be divided by 11. For a party (say the Green Party), or individual,
that got no constituency seats, their number of regional votes would be divided
by 1.
Table 1
2003 Scottish Parliament Election Results


Total Number
of Seats

Share of Total Seats

Number of Constituency Seats

Share of Constituency Votes

Number of Regional Seats

Share of Regional Votes

Labour

50

38.8%

46

34.6%

4

29.3%

Scottish
Nationalist

27

20.9%

9

23.8%

18

20.9%

Conservative

18

14.0%

3

16.6%

15

15.5%

Liberal
Democrat

17

13.2%

13

15.4%

4

11.8%

Green

7

5.4%

0

0.0%

7

6.9%

Scottish
Socialist

6

4.7%

0

6.2%

6

6.7%

MSP for Falkirk West

1

0.8%

1

0.8%

0

0.0%

Save Stobhill
Hospital

1

0.8%

1

0.6%

0

0.0%

Senior
Citizens Union

1

0.8%

0

0.1%

1

1.5%

Margo
MacDonald

1

0.8%

0

0.0%

1

1.4%


129


73


56


Table 2


Actual 2004 Election Results in Canada

Model Results


% of Popular Vote

No. of Seats

% of Seats

No. of Seats

% of Seats

Liberal

36.7%

135

43.8%

120

38.6%

Conservative

29.6%

99

32.1%

96

30.9%

NDP

15.7%

19

6.2%

47

15.1%

Bloc Québécois

12.4%

54

17.5%

38

12.2%

Green

4.3%

0

0.0%

9

2.9%

Other

1.3%

1

0.3%

1

0.3%



308


311


The party or individual with
the highest number after the division is completed gets the first proportional
seat. For the second proportional seat, the same calculation is made 
divide the number of regional votes for each party or individual by the number
of constituency seats that they got plus 1 – but this time any proportional
seat is added. So, if Labour obtained the first
proportional seat, its number of regional votes would be divided by 12.
For the Green Party, its number of regional votes would again be divided
by 1. And so on for all 7 proportional seats in each region.
Elections for the Scottish
Parliament are held on a fixed date every 4 years, except if there is a
twothirds majority vote by members for an earlier election or if Parliament
cannot agree on the nomination of a First Minister. Table 1 shows the results
of the 2003 election.
The proportional vote for the
major parties is generally less than the constituency vote as electors take the
opportunity to split their voting allegiance – a fact that some would consider
a benefit of a proportional system. In the case of the Green Party, they
ran no constituency candidates but gained all their seats as a result of their
proportional vote.
Applying the Scottish Model
to Canada
Canada has 308 constituency seats. For
purposes of applying the Scottish model to Canada, we have chosen to make the
constituency seats 2/3 of the total number of seats and the proportional seats
1/3. This is consistent with the assumption made in the Law Commission of
Canada report in its simulation of the 2000 Canadian election results based on
the Scottish model. There are, therefore, 206 constituency (first past
the post) seats, and 102 seats to be distributed among parties in proportion to
the votes they receive. We have added 3 proportional seats, one for each
of the territories because otherwise they would have to share a proportional
seat, for a total of 105 proportional seats.
Normally there would be a
separate vote for the proportional seats that would provide the basis for the
proportional calculations. As there was only one vote, the constituency
vote, in the 2004 Canadian election, we have used that vote as the basis for
the calculation of proportional seats.
For simplicity, and because
there were no regional slates with individual candidates or minor parties, we
have only allocated the proportional seats among political parties that
obtained a substantial number of votes (Liberal, Conservative, Bloc, NDP and
Green).
We used provinces and
territories as the regional unit rather than creating larger units that might
have more logic to them. This was partly to avoid possible constitutional
pitfalls and because it is easier to work with the Elections Canada figures by
province and territory. The Elections Canada figures that we have used
are the preliminary results reported as of election night, as being the best
figures available at the time we made our calculations.
The basic steps in applying
the model are: firstly, the total electoral seats for each province are divided
into 2/3 first past the post seats and 1/3 proportional seats; then the 2/3
first past the post seats are allocated among the parties in proportion to the
seats they won in the actual election; finally, the 1/3 proportional seats are
allocated in each province in accordance with the formula described above for
Scotland, using the total number of votes obtained by each party in that province.
Table 2 above shows the results of applying the Scottish model and compares
them with the actual results in the 2004 Canadian election. The method for
allocating the proportional seats and the results of the allocation for each
province are set out in more detail in Table 3 below.
It is evident that the current first past the post
system does not reflect the popular vote as well as the proportional model
does. A key factor that influences how closely the popular vote is reflected is
the split between the first past the post and proportional seats (in the model,
the split is 2/3 first past the post and 1/3 proportional). For example a
50/50 split would give more emphasis to the proportional allocation and would
more closely reflect the popular vote. Of course, if the goal was to have
the number of seats mirror the popular vote exactly, a pure proportional
representation system would be used.
The mixed model used here has
the effect of decreasing a party’s domination in any particular region.
For example:
 In
the West, where the Conservatives are strong under the first past the post
system, they do not gain much in the allocation of proportional seats.
 Similarly,
in the Atlantic provinces
and Ontario
the Liberals do not gain much under the proportional allocation. Indeed,
in Ontario
they do not gain a single proportional seat. This reflects the fact that
despite gaining only 45% of the vote in Ontario,
the Liberals won over 70% of the first past the post seats.
 In
Quebec, the
Bloc only gains 2 of the proportional seats; the other 23 are divided among the
other parties, who all stand to gain.
 While
the NDP gains almost everywhere else, in Manitoba
they do not gain any proportional seats.
As a party that is strong in one province but nonexistent in the other parts
of the country, the Bloc Quebecois would gain less
seats under the proportional representation model. The Liberals would
also lose ground, mostly as a result of their disproportionate winning of seats
in Ontario.
The Conservatives would only lose one or two seats. The NDP would
benefit substantially from the model, as would the Green Party.
In conclusion, a mixed system
of proportional representation, based on the Scottish model, would more fairly
reflect the parties’ share of the popular vote, both nationally and regionally,
to the benefit of parties that are unable to see this popular support
translated into seats under the present first past the post system. At
the same time, it would allow the parties that have traditionally benefited
from the first past the post system to maintain some of this advantage.
Table 3
Simulated Canadian Election Results 2004 by Party and Region


Lib

Cons

NDP

Bloc Québécois

Green

Total Seats by Province


FPTPs
Seats

PR
Seats

FPTPs
Seats

PR
Seats

FPTPs
Seats

PR
Seats

FPTPs
Seats

PR
Seats

FPTPs
Seats

PR
Seats

FPTPs
Seats

PR
Seats

Nfld and Lab.

4

0

1

1

0

1

0

0

0

0

5

2

PEI

2

1

0

1

0

0

0

0

0

0

2

2

NS

4

1

2

1

1

2

0

0

0

0

7

4

NB

5

0

1

2

1

1

0

0

0

0

7

3

Que.

14

12

0

6

0

3

36

2

0

2

50

25

Ont

50

0

16

17

5

14

0

0

0

4

71

35

Man.

2

3

4

2

3

0

0

0

0

0

9

5

Sask.

1

2

8

0

0

3

0

0

0

0

9

5

Alta.

1

5

18

1

0

2

0

0

0

1

19

9

BC

5

4

15

0

3

6

0

0

0

2

24*

12

YT

1

0

0

0

0

1

0

0

0

0

1

1

NWT

1

0

0

0

0

1

0

0

0

0

1

1

Nun.

1

1

0

0

0

0

0

0

0

0

1

1

Seat totals
by type and party

91

29

65

31

13

34

36

2

0

9

206

105

* There are
24 first past the post seats in B.C. under the model. However, there
was one independent MP elected, so the number of first past the post seats
allocated among the parties is 23.
Step 1: 1/3 of the seats become proportional. Calculating 1/3 for
each province, and adding one proportional seat for each territory, the
number of first past the post seats is 206 and the number of proportional
seats is 105. Taking Ontario
for example, 106 seats are split into 71 first past the post seats and 35
proportional seats.
Step 2: For each province and territory, determine the number of first
past the post seats to be allocated to each party by dividing the seats
gained by each party by 2/3. Continuing with Ontario as an example, the Liberals’ 75
seats are reduced to 50, the Conservatives’ 24 seats are reduced to 16 seats
and the NDP’s 7 seats are reduced to 5.
Step 3: Calculate each
party’s proportional seats in a province based on the formula for Scotland
described above. The 35 proportional seats in Ontario are allocated as follows:
Conservatives 17, NDP 14, Green Party 4, while the Liberals did not gain any
proportional seats (due to their high number of first past the post seats in
relation to their share of the popular vote).

