Summary of ru_singles-STVplus (2008 Data)

A Rural-Urban design with an emphasis on preserving sparsely populated areas as single-member ridings. It combines existing ridings and parts of existing ridings to free up compensatory seats. The total number of seats in the House is maintained at 308 ridings, as used from 2006-2011.

Number of Constituency MPs:	257
Number of Top-Up MPs:	51
Total MPs:	308

Number of Single-Member Ridings:	76
Number of Multi-Member Ridings:	54
Total Ridings:	130

Number of Top-up Regions:	18

Single Member Seats:	AV-Ekos
Multi Member Seats:	STV-Ekos
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
Con	5,209,068	37.7%	118	38.3%	116.8	0.7%
Lib	3,633,184	26.3%	86	27.9%	81.2	1.7%
NDP	2,515,288	18.2%	56	18.2%	57.2	0.0%
Bloc	1,379,991	10.0%	30	9.7%	28.6	-0.2%
Grn	937,613	6.8%	17	5.5%	20.7	-1.3%
Oth	159,148	1.2%	1	0.3%	3.6	-0.8%

MPs: 308Gallagher Index: 1.58Composite Gallagher Index: 4.56

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 Liberal's votes tracks the line for the Liberal'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.

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 Liberal and Conservative

Average Gallagher Index: 4.9%

Voters shift between NDP and Conservative

Average Gallagher Index: 4.6%

Voters shift between Green and Conservative

Average Gallagher Index: 5.1%

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
Con	5,209,069	37.7%	104	40.5%	96.8	2.8%
Lib	3,633,184	26.3%	81	31.5%	67.5	5.3%
NDP	2,515,288	18.2%	41	16.0%	46.7	-2.2%
Bloc	1,379,991	10.0%	30	11.7%	25.6	1.7%
Grn	937,613	6.8%	0	0.0%	17.4	-6.8%

MPs: 257Gallagher Index: 6.69

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	1,365,239	38.5%	32	42.1%	29.3	3.6%
Lib	888,664	25.1%	22	28.9%	19.1	3.9%
NDP	631,834	17.8%	10	13.2%	13.6	-4.7%
Bloc	370,809	10.5%	11	14.5%	8.0	4.0%
Grn	224,095	6.3%	0	0.0%	4.8	-6.3%
Ind	40,368	1.1%	1	1.3%	0.9	0.2%

MPs: 76Gallagher Index: 7.27

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
Con	3,843,829	37.3%	72	39.8%	67.6	2.4%
Lib	2,744,520	26.7%	59	32.6%	48.3	5.9%
NDP	1,883,453	18.3%	31	17.1%	33.1	-1.2%
Bloc	1,009,181	9.8%	19	10.5%	17.7	0.7%
Grn	713,517	6.9%	0	0.0%	12.5	-6.9%

MPs: 181Gallagher Index: 6.76

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
Con	797,177	44.5%	18	60.0%	15.5%	18	50.0%	5.5%
NDP	467,882	26.1%	8	26.7%	0.6%	10	27.8%	1.7%
Lib	346,344	19.3%	4	13.3%	-6.0%	5	13.9%	-5.4%
Grn	168,282	9.4%	0	0.0%	-9.4%	3	8.3%	-1.1%
Total Number of MPs:			30			36
Gallagher Index:			13.53			5.67

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	1,275,485	59.2%	35	76.1%	16.9%	36	64.3%	5.1%
NDP	379,685	17.6%	6	13.0%	-4.6%	10	17.9%	0.2%
Lib	296,187	13.7%	5	10.9%	-2.9%	7	12.5%	-1.2%
Grn	166,009	7.7%	0	0.0%	-7.7%	3	5.4%	-2.3%
Ind	25,620	1.2%	0	0.0%	-1.2%	0	0.0%	-1.2%
Total Number of MPs:			46			56
Gallagher Index:			13.72			4.18

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
Con	3,096,795	31.7%	50	28.6%	-3.1%	62	29.7%	-2.0%
Lib	2,944,367	30.1%	68	38.9%	8.7%	70	33.5%	3.4%
NDP	1,651,315	16.9%	26	14.9%	-2.0%	35	16.7%	-0.1%
Bloc	1,379,991	14.1%	30	17.1%	3.0%	30	14.4%	0.2%
Grn	596,535	6.1%	0	0.0%	-6.1%	11	5.3%	-0.8%
Total Number of MPs:			175			209
Gallagher Index:			8.26			2.85

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	376,041	35.0%	15	55.6%	20.5%	15	46.9%	11.8%
Con	318,021	29.6%	6	22.2%	-7.4%	8	25.0%	-4.6%
NDP	279,528	26.0%	5	18.5%	-7.5%	7	21.9%	-4.2%
Grn	64,279	6.0%	0	0.0%	-6.0%	1	3.1%	-2.9%
Ind	29,977	2.8%	1	3.7%	0.9%	1	3.1%	0.3%
Total Number of MPs:			27			32
Gallagher Index:			16.87			9.68

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
Con	2,020,641	39.2%	34	39.1%	-0.1%	40	37.7%	-1.5%
Lib	1,743,241	33.8%	36	41.4%	7.6%	38	35.8%	2.0%
NDP	937,921	18.2%	17	19.5%	1.3%	20	18.9%	0.7%
Grn	409,936	8.0%	0	0.0%	-8.0%	8	7.5%	-0.4%
Total Number of MPs:			87			106
Gallagher Index:			7.82			1.88

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
Bloc	1,379,991	38.1%	30	46.9%	8.8%	30	40.0%	1.9%
Lib	860,449	23.8%	19	29.7%	5.9%	19	25.3%	1.6%
Con	784,996	21.7%	11	17.2%	-4.5%	16	21.3%	-0.3%
NDP	441,098	12.2%	4	6.3%	-5.9%	8	10.7%	-1.5%
Grn	125,805	3.5%	0	0.0%	-3.5%	2	2.7%	-0.8%
Total Number of MPs:			64			75
Gallagher Index:			9.48			2.18

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	822,147	64.7%	18	81.8%	17.1%	19	67.9%	3.2%
NDP	160,874	12.7%	1	4.5%	-8.1%	4	14.3%	1.6%
Lib	144,646	11.4%	3	13.6%	2.3%	3	10.7%	-0.7%
Grn	111,334	8.8%	0	0.0%	-8.8%	2	7.1%	-1.6%
Ind	24,907	2.0%	0	0.0%	-2.0%	0	0.0%	-2.0%
Total Number of MPs:			22			28
Gallagher Index:			14.92			3.14

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 0 km² and 90% of our population live in ridings smaller than 0 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	76
2	13
3	22
4	11
5	4
6	3
7	1
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	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
4	1
7	1
8	1
10	1
11	1
12	1
14	3
16	1
17	2
19	2
22	1
26	1
30	1
45	1
Average:	14.7

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: STV-Ekos

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

Top-up Seats

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