Summary of erre_ru_singles-RcRUPR (2015 Data)

Current 338 ridings grouped into a mix of single- and multi-member ridings allowing more single-member ridings. Compensatory seats are gained by reducing the number of seats in the largest multi-member ridings.

Number of Constituency MPs:	293
Number of Top-Up MPs:	45
Total MPs:	338

Number of Single-Member Ridings:	95
Number of Multi-Member Ridings:	55
Total Ridings:	150

Number of Top-up Regions:	10

Single Member Seats:	AV-Ekos
Multi Member Seats:	Riding-CentricSTV
Compensatory Seats:	NA

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%	147	43.5%	135.0	4.0%
Con	5,613,633	31.9%	106	31.4%	107.0	-0.6%
NDP	3,469,368	19.7%	67	19.8%	66.7	0.1%
Bloc	821,144	4.7%	12	3.6%	15.1	-1.1%
Grn	602,933	3.4%	6	1.8%	11.5	-1.7%
Oth	141,453	0.8%	0	0.0%	2.7	-0.8%

MPs: 338Gallagher Index: 3.21Composite Gallagher Index: 5.61

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: 6.1%

Voters shift between NDP and Liberal

Average Gallagher Index: 6.7%

Voters shift between Green and Liberal

Average Gallagher Index: 6.0%

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	6,864,391	40.4%	142	48.5%	118.3	8.1%
Con	5,321,398	31.3%	86	29.4%	91.7	-1.9%
NDP	3,327,838	19.6%	57	19.5%	57.3	-0.1%
Bloc	753,279	4.4%	7	2.4%	13.0	-2.0%
Grn	594,801	3.5%	1	0.3%	10.2	-3.2%

MPs: 293Gallagher Index: 6.46

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	1,709,218	36.1%	32	33.7%	34.3	-2.4%
Lib	1,706,500	36.1%	47	49.5%	34.3	13.4%
NDP	904,705	19.1%	15	15.8%	18.2	-3.3%
Bloc	222,221	4.7%	1	1.1%	4.5	-3.6%
Grn	148,802	3.1%	0	0.0%	3.0	-3.1%

MPs: 95Gallagher Index: 10.49

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	5,157,891	42.0%	95	48.0%	83.2	6.0%
Con	3,612,180	29.4%	54	27.3%	58.3	-2.2%
NDP	2,423,133	19.7%	42	21.2%	39.1	1.5%
Bloc	531,058	4.3%	6	3.0%	8.6	-1.3%
Grn	445,999	3.6%	1	0.5%	7.2	-3.1%

MPs: 198Gallagher Index: 5.19

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	36.3%	14	38.9%	2.6%	14	33.3%	-1.8%
Con	632,704	27.7%	7	19.4%	-8.2%	12	28.6%	-1.4%
NDP	615,156	26.9%	14	38.9%	12.0%	14	33.3%	7.3%
Grn	192,618	8.4%	1	2.8%	-5.6%	2	4.8%	-3.5%
Total Number of MPs:			36			42
Gallagher Index:			11.18			5.95

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	55.3%	37	68.5%	13.2%	37	59.7%	6.4%
Lib	794,831	26.8%	12	22.2%	-4.6%	17	27.4%	-0.9%
NDP	408,493	13.8%	5	9.3%	-4.5%	8	12.9%	-1.5%
Grn	79,213	2.7%	0	0.0%	-2.7%	0	0.0%	-2.6%
Total Number of MPs:			54			62
Gallagher Index:			10.54			5.07

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	44.4%	110	55.8%	11.4%	110	48.5%	5.5%
Con	3,024,049	26.0%	42	21.3%	-4.7%	56	24.7%	-2.3%
NDP	2,277,286	19.6%	38	19.3%	-0.3%	45	19.8%	-0.0%
Bloc	753,279	6.5%	7	3.6%	-2.9%	12	5.3%	-1.6%
Grn	316,437	2.7%	0	0.0%	-2.7%	4	1.8%	-0.9%
Total Number of MPs:			197			227
Gallagher Index:			9.17			4.37

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	60.5%	24	88.9%	28.4%	24	75.0%	16.3%
NDP	227,288	17.9%	2	7.4%	-10.5%	3	9.4%	-8.5%
Con	218,619	17.2%	1	3.7%	-13.5%	5	15.6%	-3.4%
Grn	46,234	3.6%	0	0.0%	-3.6%	0	0.0%	-3.5%
Total Number of MPs:			27			32
Gallagher Index:			23.58			13.46

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	46.4%	55	52.4%	6.0%	55	45.5%	0.7%
Con	2,166,006	34.3%	36	34.3%	-0.0%	42	34.7%	-0.3%
NDP	988,638	15.7%	14	13.3%	-2.3%	20	16.5%	-0.1%
Grn	180,089	2.9%	0	0.0%	-2.9%	4	3.3%	0.5%
Total Number of MPs:			105			121
Gallagher Index:			4.96			0.68

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	36.8%	34	50.0%	13.2%	34	43.6%	7.9%
NDP	1,075,366	26.1%	22	32.4%	6.2%	22	28.2%	2.9%
Bloc	753,279	18.3%	7	10.3%	-8.0%	12	15.4%	-4.0%
Con	650,139	15.8%	5	7.4%	-8.4%	10	12.8%	-3.9%
Grn	95,395	2.3%	0	0.0%	-2.3%	0	0.0%	-2.2%
Total Number of MPs:			68			78
Gallagher Index:			13.29			7.28

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	61.4%	23	76.7%	15.2%	23	67.6%	8.1%
Lib	426,054	22.8%	5	16.7%	-6.1%	8	23.5%	-1.0%
NDP	213,218	11.4%	2	6.7%	-4.7%	3	8.8%	-2.8%
Grn	48,742	2.6%	0	0.0%	-2.6%	0	0.0%	-2.5%
Total Number of MPs:			30			34
Gallagher Index:			12.23			6.39

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	95
2	9
3	22
4	9
5	12
6	3
Average:	2.0

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	3
2	3
4	1
6	1
10	1
16	1
Average:	3.5

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
4	1
7	1
10	1
11	1
14	2
34	1
42	1
78	1
121	1
Average:	26.0

Methodology

Single-Member Ridings: AV-Ekos

During the election in each riding, votes were transferred in two steps. First, if a member of party X is eliminated and there are other members of party X still in the race, ALL of the votes are split equally between the remaining members of party X.

When the last member of a party is eliminated, the votes are transferred according to the following table.

Xfer from↓ to→	Bloc	Con	Grn	Lib	NDP
Bloc		19	6	16	28
CHP
Com
Con			8	17	10
Grn	15	8		16	22
Ind
Lbt
Lib	3	12	10		45
M-L
NDP	6	6	13	53
Oth

This table is based on Ekos polling performed just before the 2015 election which asked for voters' second choice party. As Wilf Day has pointed out,

On Oct. 14 it had Liberals at 33.5%, Conservatives 32.6%, NDP 22.9%, Greens 5.6%, Bloc 3.4%. However, the E-day figures were Liberal 39.5%, Conservatives 31.9%, NDP 19.7%, Green 3.4%, and Bloc 4.7%. Obviously a lot of NDP and Green second-choices for Liberals had switched by E-day

However, it appears to be the best data we have.

Source: http://www.ekospolitics.com/wp-content/uploads/full_report_october_15_2015.pdf

Multi-Member Ridings: Riding-CentricSTV

An STV-like strategy that guarantees electing a candidate in each old riding that makes up a multi-member riding. It does so by prohibiting the elimination of the last candidate in the old riding.

The multi-member riding typically has at least one of its seats designated as an adjustment seat. The topup algorithm selects a candidate from an empty old riding (ie the adjustment seat).

Top-up Seats

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