Summary of Rural-Urban PR (More Singles, 389 Seats) (2015 Data)

The Rural-Urban Proportional (RUP) model uses multi-member ridings in metropolitan areas and single member ridings in non-metropolitan and rural areas. It adds a small layer of top-up MPs. Together, these two techniques yield excellent proportionality across a wide range of electoral results.

This version of RUP enlarges the House of Commons by about 15% (about 50 additional MPs) so that ridings remain at their current size. Another simulation of this model enlarges the ridings to keep the number of MPs constant at 338.

Number of Constituency MPs:	338
Number of Top-Up MPs:	51
Total MPs:	389

Number of Single-Member Ridings:	92
Number of Multi-Member Ridings:	56
Total Ridings:	148

Number of Top-up Regions:	18

Single Member Seats:	FPTP
Multi Member Seats:	List
Compensatory Seats:	Top-up

Summary Statistics

Statistics concerning all of the MPs elected -- both in local ridings and as top-ups. The "Proportional MPs" column takes into account provincial and territorial boundaries, as required by Canada's constitution.

Party	Popular Votes¹	Pct Votes²	Elected MPs³	Pct Elected MPs⁴	Proportional MPs⁵	Over Representation⁶
Lib	6,942,937	39.5%	159	40.9%	155.4	1.4%
Con	5,613,633	31.9%	130	33.4%	123.5	1.5%
NDP	3,469,368	19.7%	76	19.5%	76.5	-0.2%
Bloc	821,144	4.7%	17	4.4%	17.2	-0.3%
Grn	602,933	3.4%	7	1.8%	13.2	-1.6%
Oth	141,453	0.8%	0	0.0%	3.1	-0.8%

MPs: 389Gallagher Index: 1.89Composite Gallagher Index: 3.43

¹The number of votes each party received in the 2015 election.

²The percentage of the votes each party received.

³The number of candidates elected for each party.

⁴The percentage of MPs that this party was awarded. Ideally, this will match the percentage of the vote.

⁵The number of MPs this party would have if the results were perfectly proportional.

⁶The over (or under) representation of this party in Parliment. That is, the difference between the percentage of MPs and the percentage of the vote.

Vote Swing Analysis

What happens if public sentiment swings towards one party and away from another? This graph tries to answer that question. Using the riding-by-riding results from 2015, it systematically moves an increasing number of votes from one party to another.

If the lines representing the Conservative's votes tracks the line for the Conservative's MPs (and similar for the other parties), then the electoral system is proportional across a wide range of electoral scenarios.

On the other hand, if the lines for the votes earned and the MPs elected are farther apart -- as is the case for FPTP and AV -- then the electoral system is not proportional.

Examples:

At -20% on the bottom axis, 20% of the Liberal's vote in 2015 is given to the Conservatives to simulate an election where the Liberals earned 31% of the vote and the Conservatives earned almost 40%. The lighter red and blue lines show how many MPs would have been elected for each party by this voting system.
At +6% on the bottom axis, 6% of the Conservative's vote in 2015 is given to the Liberals to simulate an even more lop-sided win (41.4% to 30%). Again, the light red and blue lines show how many MPs would have been elected for each party by this voting system.

The black line, hopefully along the bottom of the graph, shows the Gallagher Index, an index of voting proportionality. Smaller numbers are better.

Voters shift between Conservative and Liberal

Average Gallagher Index: 3.6%

Voters shift between NDP and Liberal

Average Gallagher Index: 3.8%

Voters shift between Green and Liberal

Average Gallagher Index: 3.6%

Statistics for various subsets of ridings

Local-Ridings Only

Statistics concerning only the MPs elected in ridings, without the top-up MPs. This is useful for understanding how much the top-up MPs help create proportionality.

Party	Popular Votes¹	Pct Votes²	Elected MPs³	Pct Elected MPs⁴	Proportional MPs⁵	Over Representation⁶
Lib	6,942,937	39.5%	138	40.8%	133.4	1.4%
Con	5,613,633	31.9%	122	36.1%	107.9	4.2%
NDP	3,469,368	19.7%	65	19.2%	66.7	-0.5%
Bloc	821,144	4.7%	12	3.6%	15.8	-1.1%
Grn	602,933	3.4%	1	0.3%	11.6	-3.1%

MPs: 338Gallagher Index: 3.92

¹The number of votes each party received in the 2015 election.

²The percentage of the votes each party received.

³The number of candidates elected for each party.

⁴The percentage of MPs that this party was awarded. Ideally, this will match the percentage of the vote.

⁵The number of MPs this party would have if the results were perfectly proportional.

⁶The over (or under) representation of this party in Parliment. That is, the difference between the percentage of MPs and the percentage of the vote.

Single-Member Riding Stats

Statistics on all of the single-member ridings as a group. In a FPTP simulation, this will be the same as the above. In an MMP simulation it will be similar to a FPTP because the top-up MPs are not included. A Hybrid model is where it's the most interesting. How out of whack are the single-member ridings?

Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Proportional MPs	Over Representation
Con	1,628,085	36.3%	42	45.7%	33.4	9.4%
Lib	1,592,240	35.5%	35	38.0%	32.6	2.6%
NDP	864,746	19.3%	13	14.1%	17.7	-5.1%
Bloc	222,221	4.9%	2	2.2%	4.6	-2.8%
Grn	137,805	3.1%	0	0.0%	2.8	-3.1%

MPs: 92Gallagher Index: 8.33

Multi-Member Riding Stats

Statistics on all of the multi-member ridings as a group.

Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Proportional MPs	Over Representation
Lib	5,350,697	40.8%	103	41.9%	100.5	1.0%
Con	3,985,548	30.4%	80	32.5%	74.8	2.1%
NDP	2,604,622	19.9%	52	21.1%	48.9	1.3%
Bloc	598,923	4.6%	10	4.1%	11.2	-0.5%
Grn	465,128	3.6%	1	0.4%	8.7	-3.1%

MPs: 246Gallagher Index: 2.94

BC

Statistics on British Columbia.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Lib	829,816	35.1%	12	28.6%	-6.5%	16	33.3%	-1.8%
Con	708,010	29.9%	15	35.7%	5.8%	15	31.3%	1.3%
NDP	615,156	26.0%	14	33.3%	7.3%	14	29.2%	3.2%
Grn	194,847	8.2%	1	2.4%	-5.9%	3	6.3%	-2.0%
Total Number of MPs:			42			48
Gallagher Index:			9.05			3.07

Prairie Provinces

Statistics on all of the "prairie" provinces: AB, MB, SK.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Con	1,642,565	53.3%	42	67.7%	14.5%	42	58.3%	5.1%
Lib	873,377	28.3%	13	21.0%	-7.4%	19	26.4%	-1.9%
NDP	445,334	14.4%	7	11.3%	-3.2%	11	15.3%	0.8%
Grn	79,213	2.6%	0	0.0%	-2.6%	0	0.0%	-2.6%
Total Number of MPs:			62			72
Gallagher Index:			11.84			4.32

Eastern Provinces

Statistics on all of the "eastern" provinces: ON, QC, NB, NL, NS.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Lib	5,163,064	43.0%	108	47.6%	4.6%	118	45.2%	2.2%
Con	3,234,793	26.9%	64	28.2%	1.2%	72	27.6%	0.6%
NDP	2,381,975	19.8%	43	18.9%	-0.9%	50	19.2%	-0.7%
Bloc	821,144	6.8%	12	5.3%	-1.6%	17	6.5%	-0.3%
Grn	322,340	2.7%	0	0.0%	-2.7%	4	1.5%	-1.2%
Total Number of MPs:			227			261
Gallagher Index:			4.06			1.91

Maritime Provinces

Statistics on all of the "Maritime" provinces: NB, NL, NS, PE.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Lib	769,000	58.7%	24	75.0%	16.3%	25	67.6%	8.8%
Con	249,136	19.0%	4	12.5%	-6.5%	6	16.2%	-2.8%
NDP	234,699	17.9%	4	12.5%	-5.4%	6	16.2%	-1.7%
Grn	46,234	3.5%	0	0.0%	-3.5%	0	0.0%	-3.5%
Total Number of MPs:			32			37
Gallagher Index:			13.22			7.14

Ontario

Statistics on Ontario.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Lib	2,929,393	44.8%	54	44.6%	-0.2%	63	45.0%	0.2%
Con	2,293,393	35.1%	47	38.8%	3.8%	51	36.4%	1.4%
NDP	1,085,916	16.6%	20	16.5%	-0.1%	24	17.1%	0.5%
Grn	185,992	2.8%	0	0.0%	-2.8%	2	1.4%	-1.4%
Total Number of MPs:			121			140
Gallagher Index:			3.36			1.47

Quebec

Statistics on Quebec.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Lib	1,515,673	35.7%	32	41.0%	5.3%	33	37.1%	1.3%
NDP	1,075,366	25.4%	20	25.6%	0.3%	21	23.6%	-1.8%
Bloc	821,144	19.4%	12	15.4%	-4.0%	17	19.1%	-0.3%
Con	709,164	16.7%	14	17.9%	1.2%	16	18.0%	1.3%
Grn	95,395	2.2%	0	0.0%	-2.2%	2	2.2%	-0.0%
Total Number of MPs:			78			89
Gallagher Index:			5.03			1.83

Alberta

Statistics on Alberta.

			Ridings Only			Ridings + Top-up
Party	Popular Votes	Pct Votes	Elected MPs	Pct Elected MPs	Over Rep	Elected MPs	Pct Elected MPs	Over Rep
Con	1,150,101	59.6%	25	73.5%	14.0%	25	62.5%	2.9%
Lib	473,416	24.5%	7	20.6%	-3.9%	10	25.0%	0.5%
NDP	224,800	11.6%	2	5.9%	-5.8%	5	12.5%	0.9%
Grn	48,742	2.5%	0	0.0%	-2.5%	0	0.0%	-2.5%
Total Number of MPs:			34			40
Gallagher Index:			11.20			2.91

Population vs. Riding Area

One concern in developing an electoral system for Canada is the diversity in riding geographical sizes. They currently range from as small as 6km²to almost 2.1 million km². This graph gives the means to compare how different electoral systems deal with riding sizes. It answers the question "What percentage of Canada's population lives in ridings smaller than xkm²?".

This graph shows that with this model 50% of our population would live in ridings smaller than 2,574 km² and 90% of our population live in ridings smaller than 36,188 km².

X Scale: LogarithmicLinear

District Magnitudes

The district magnitude is the number of MPs that represent as specific area. With FPTP, all ridings are represented by a single MP, so the district magnitude is 1 for every riding. In other systems, the number of MPs may vary. These tables show the number of districts (riding or region) that have a given number of MPs representing it for this electoral model.

Riding-Level District Magnitudes

When we considers the local riding, how many MPs are there? How many ridings have that same number?

# of MPs	# of Districts
1	92
2	8
3	8
4	13
5	14
6	8
7	4
8	1
Average:	2.3

Region-Level District Magnitudes

When we considers only the top-up MPs in a region, how many MPs are there? How many regions have that same number?

# of MPs	# of Districts
0	3
1	4
2	4
3	6
4	3
9	1
Average:	2.4

Combined District Magnitude

When we consider the total number of MPs in a region (all of the local riding plus the top-up MPs), how many MPs are there? How many ridings have that same number?

In electoral models that don't have the concept of a region with top-up MPs (like STV, FPTP, and AV), the "region" is the province. Territories are always excluded from this table.

# of MPs	# of Districts
1	3
5	1
8	1
10	1
11	1
13	1
16	2
18	1
20	2
22	4
30	1
31	1
36	1
64	1
Average:	18.5

Methodology

Single-Member Ridings: FPTP

After collapsing all candidates running for the same party into one virtual candiate, choose the virtual candidate with the most votes.

Multi-Member Ridings: List

Calculate the number of votes for each party and from that the determine the number of seats won by each party using a highest averages method -- specifically as described in "Quota system". After calculating the number of seats for each party, make a list of all the candidates for the party, ordered by number of votes in the 2015 election, and choose the first n candidates as the winners.

Top-up Seats

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