Canada with the Norwegian electoral system

[Хahar 🤔]

When there was an election in Norway last year, I was struck by the Norwegian electoral system, which features significant rural malapportionment built in and an interesting county-based apportionment system. In general I am interested in ways that proportional representation systems try to provide geographic representation, and it struck me that the Norwegian system would not be workable in most places but might be interesting in Canada. I also wanted to see if I could actually figure out the math based on the online English-language descriptions of the Norwegian electoral system, so I decided to apply that system to the most recent Canadian election.

For simplicity's sake, this exercise presumes that there were six available lists (Liberal, Conservative, New Democratic, Bloc, Green, People's) and ignores all votes for other parties and independents. This should not make a difference in the results. Canada's ten provinces are treated as equivalent to Norway's nineteen counties. There are 150 regular seats (like in Norway) and one leveling seat for each province, resulting in a final count of 160 seats compared to Norway's 169. Because of the Norwegian principle of apportioning seats based on land as well as population, treating the territories equivalently to provinces would make this exercise farcical, so their votes are not counted as part of every province but are counted in the nationwide total. The results are identical to the results if territorial votes were excluded entirely.

We begin with apportionment. In Norway, seats (aside from the leveling seat for each county) are apportioned by county based on a formula of population plus 1.8 times square kilometers. Prince Edward Island would qualify for no seats under this formula, so the island is assigned one seat and the rest are apportioned.

Province	Population	Land area in km²	Formula	Seats	Population per seat
Ontario	13,448,495	1,076,395	15,386,006	50	268,970
Quebec	8,575,779	1,542,056	11,351,479	37	231,778
British Columbia	4,648,055	944,735	6,348,578	20	232,403
Alberta	4,067,175	661,848	5,258,501	17	239,246
Manitoba	1,278,365	647,797	2,444,399	8	159,796
Saskatchewan	1,098,355	651,900	2,271,775	7	156,908
Newfoundland and Labrador	519,720	405,212	1,249,101	4	129,930
Nova Scotia	923,595	55,283	1,023,104	3	307,865
New Brunswick	747,105	72,908	878,339	3	249,035
Prince Edward Island	142,910	5,660	153,098	1	142,910

Next, the 150 ordinary seats are apportioned in each province by the modified Sainte-Laguë method. I will leave out the details here, since they are not interesting.

Province	Lib	Con	NDP	BQ	Grn	PPC	Total
Alberta	3	10	3	0	0	1	17
British Columbia	5	7	6	0	1	1	20
Manitoba	2	4	2	0	0	0	8
New Brunswick	2	1	0	0	0	0	3
Newfoundland and Labrador	2	1	1	0	0	0	4
Nova Scotia	1	1	1	0	0	0	3
Ontario	20	17	9	0	1	3	50
Prince Edward Island	1	0	0	0	0	0	1
Quebec	13	7	4	12	0	1	37
Saskatchewan	1	4	2	0	0	0	7
Total	50	52	28	12	2	6	150

Now we get to the fun part, the leveling seats to ensure nationwide proportionality (and thereby counteract malapportionment, at least in terms of national results). To qualify for leveling seats, a party needs to receive at least 4% nationally.

Party	Votes	Percentage
Conservative	5,739,099	34.08%
Liberal	5,542,193	32.91%
New Democratic	3,024,009	17.96%
Bloc Québécois	1,301,615	7.73%
People's	837,578	4.97%
Green	395,814	2.35%

The Green Party falls below the threshold. The two Green seats won at the constituency level are thus excluded, and instead of apportioning the full 160-seat legislature by party we instead apportion 158 seats.

Party	Total seats	Constituency	Leveling
Conservative	55	52	3
Liberal	50	53	3
New Democratic	28	29	1
Bloc Québécois	12	13	1
People's	6	8	2

Unfortunately, the Bloc being entitled to just one leveling seat means we miss out on the amusing scenario whereby a the leveling seat from a province other than Quebec is assigned to the Bloc. Again I will omit the calculations here, but I will note that the large number of seats relative to population in Newfoundland and Labrador and Prince Edward Island result in those provinces having few wasted votes, which means in turn that their leveling seats are not assigned to the end. In this case that means that the People's Party wins a leveling seat in both provinces on about 3%. If there had been an extra Bloc seat, it would have been here.

Province	Lib	Con	NDP	BQ	Grn	PPC	Total	Leveling
Alberta	3	10	3	0	0	1	17	NDP
British Columbia	5	7	6	0	1	1	20	Lib
Manitoba	2	4	2	0	0	0	8	Lib
New Brunswick	2	1	0	0	0	0	3	Con
Newfoundland and Labrador	2	1	1	0	0	0	4	PPC
Nova Scotia	1	1	1	0	0	0	3	Lib
Ontario	20	17	9	0	1	3	50	Con
Prince Edward Island	1	0	0	0	0	0	1	PPC
Quebec	13	7	4	12	0	1	37	BQ
Saskatchewan	1	4	2	0	0	0	7	Con
Constituency	50	52	28	12	2	6	150
Leveling	3	3	1	1	0	2	10
Total	53	55	29	13	2	8	160

Presented differently:

Party	Votes	Percentage	Seats	Percentage
Conservative	5,739,099	34.1%	55	34.4%
Liberal	5,542,193	32.9%	53	33.1%
New Democratic	3,024,009	18.0%	29	18.1%
Bloc Québécois	1,301,615	7.7%	13	8.1%
People's	837,578	5.0%	8	5.0%
Green	395,814	2.4%	2	1.3%

The results here are basically proportional after accounting for the Green vote is underrepresented due to failure to break the threshold. The Bloc overrepresentation is significant compared to the size of the Bloc vote. Any two of the three largest parties can achieve a majority together, while the other three parties are irrelevant to that process.

What is the takeaway from this? Nothing, really, but I did the work so I thought I'd share it. As a bonus to those of you who made it this far, here's 1993:

Province	Lib	Ref	PC	BQ	NDP	Nat	Total	Leveling
Alberta	4	9	2	0	0	0	15	PC
British Columbia	6	7	3	0	3	1	20	NDP
Manitoba	4	2	1	0	2	0	9	Lib
New Brunswick	2	0	1	0	0	0	3	Lib
Newfoundland	4	0	1	0	0	0	5	PC
Nova Scotia	3	0	1	0	0	0	4	Ref
Ontario	26	10	8	0	3	0	47	PC
Prince Edward Island	1	0	0	0	0	0	1	BQ
Quebec	13	0	5	20	0	0	38	PC
Saskatchewan	3	2	1	0	2	0	8	BQ
Constituency	66	30	23	20	10	1	150
Leveling	2	1	4	2	1	0	10
Total	68	31	27	22	11	1	160

Notably, neither of the Bloc leveling seats are in Quebec.

Party	Votes	Percentage	Seats	Percentage
Liberal	5,647,952	41.3%	68	42.5%
Reform	2,559,245	18.7%	31	19.4%
Progressive Conservative	2,186,422	16.0%	27	16.9%
Bloc Québécois	1,846,024	13.5%	22	13.8%
New Democratic	939,575	6.9%	11	6.9%
National	187,251	1.4%	1	0.6%