Summary of Local Proportional Representation (no top-up) (2015 Data)

Local Proportional Representation: cluster ridings into regions of (ideally) 4-8 ridings. Run an STV-like algorithm to elect as many MPs as ridings in the region. The difference is that a candidate who is the last one left in his or her riding can't be eliminated. This guarantees that each existing riding will have an MP to represent it.

For comparison, the same mapping of ridings to regions was also simulated using STV to see the effects of the special rule described above.

Number of Constituency MPs:338
Number of Top-Up MPs:0
Total MPs:338
Number of Single-Member Ridings:4
Number of Multi-Member Ridings:76
Total Ridings:80
Number of Top-up Regions:0
Single Member Seats:AV-Ekos
Multi Member Seats:Local-PR
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.

PartyPopular Votes1Pct Votes2Elected MPs3Pct Elected MPs4Proportional MPs5Over Representation6
Lib6,942,93739.5%14944.1%135.04.6%
Con5,613,63331.9%10731.7%107.0-0.3%
NDP3,469,36819.7%6820.1%66.70.4%
Bloc821,1444.7%133.8%15.1-0.8%
Grn602,9333.4%10.3%11.5-3.1%
Oth141,4530.8%00.0%2.7-0.8%

MPs: 338Gallagher Index: 4.01Composite Gallagher Index: 5.99

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 from Conservative to Liberal

Average Gallagher Index: 7.0%

Voters shift from NDP to Liberal

Average Gallagher Index: 6.5%

Voters shift from Green to Liberal

Average Gallagher Index: 7.0%

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.

PartyPopular Votes1Pct Votes2Elected MPs3Pct Elected MPs4Proportional MPs5Over Representation6
Lib6,942,93739.5%14944.1%133.44.6%
Con5,613,63331.9%10731.7%107.9-0.3%
NDP3,469,36819.7%6820.1%66.70.4%
Bloc821,1444.7%133.8%15.8-0.8%
Grn602,9333.4%10.3%11.6-3.1%

MPs: 338Gallagher Index: 4.01

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?

PartyPopular VotesPct VotesElected MPsPct Elected MPsProportional MPsOver Representation
Lib34,55654.4%4100.0%2.245.6%
NDP14,67623.1%00.0%0.9-23.1%
Con13,08120.6%00.0%0.8-20.6%
Grn1,2522.0%00.0%0.1-2.0%

MPs: 4Gallagher Index: 39.01

Multi-Member Riding Stats

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

PartyPopular VotesPct VotesElected MPsPct Elected MPsProportional MPsOver Representation
Lib6,908,38139.4%14543.4%131.64.0%
Con5,600,55232.0%10732.0%106.70.1%
NDP3,454,69219.7%6820.4%65.80.6%
Bloc821,1444.7%133.9%15.6-0.8%
Grn601,6813.4%10.3%11.5-3.1%

MPs: 334Gallagher Index: 3.68

BC

Statistics on British Columbia.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib829,81635.1%1638.1%3.0%1638.1%3.0%
Con708,01029.9%1331.0%1.0%1331.0%1.0%
NDP615,15626.0%1228.6%2.6%1228.6%2.6%
Grn194,8478.2%12.4%-5.9%12.4%-5.9%
Total Number of MPs:4242
Gallagher Index: 5.05 5.05

Prairie Provinces

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

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Con1,642,56553.3%3556.5%3.2%3556.5%3.2%
Lib873,37728.3%1727.4%-0.9%1727.4%-0.9%
NDP445,33414.4%1016.1%1.7%1016.1%1.7%
Grn79,2132.6%00.0%-2.6%00.0%-2.6%
Total Number of MPs:6262
Gallagher Index: 3.24 3.24

Eastern Provinces

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

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib5,163,06443.0%11048.5%5.5%11048.5%5.5%
Con3,234,79326.9%5825.6%-1.4%5825.6%-1.4%
NDP2,381,97519.8%4620.3%0.4%4620.3%0.4%
Bloc821,1446.8%135.7%-1.1%135.7%-1.1%
Grn322,3402.7%00.0%-2.7%00.0%-2.7%
Total Number of MPs:227227
Gallagher Index: 4.49 4.49

Maritime Provinces

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

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib769,00058.7%2268.8%10.0%2268.8%10.0%
Con249,13619.0%618.8%-0.3%618.8%-0.3%
NDP234,69917.9%412.5%-5.4%412.5%-5.4%
Grn46,2343.5%00.0%-3.5%00.0%-3.5%
Total Number of MPs:3232
Gallagher Index: 8.45 8.45

Ontario

Statistics on Ontario.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib2,929,39344.8%5847.9%3.2%5847.9%3.2%
Con2,293,39335.1%4335.5%0.5%4335.5%0.5%
NDP1,085,91616.6%2016.5%-0.1%2016.5%-0.1%
Grn185,9922.8%00.0%-2.8%00.0%-2.8%
Total Number of MPs:121121
Gallagher Index: 3.03 3.03

Quebec

Statistics on Quebec.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib1,515,67335.7%3342.3%6.6%3342.3%6.6%
NDP1,075,36625.4%2228.2%2.9%2228.2%2.9%
Bloc821,14419.4%1316.7%-2.7%1316.7%-2.7%
Con709,16416.7%1012.8%-3.9%1012.8%-3.9%
Grn95,3952.2%00.0%-2.2%00.0%-2.2%
Total Number of MPs:7878
Gallagher Index: 6.28 6.28

Alberta

Statistics on Alberta.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Con1,150,10159.6%2367.6%8.1%2367.6%8.1%
Lib473,41624.5%926.5%1.9%926.5%1.9%
NDP224,80011.6%25.9%-5.8%25.9%-5.8%
Grn48,7422.5%00.0%-2.5%00.0%-2.5%
Total Number of MPs:3434
Gallagher Index: 7.40 7.40

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 5,714 km2 and 90% of our population live in ridings smaller than 104,163 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
14
24
316
425
515
611
73
82
Average: 4.2

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
016
Average: 0.0

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
13
41
71
101
111
142
341
361
381
411
423
Average:21.1

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→BlocCHPComConGrnIndLbtLibM-LNDPOth
Bloc1961628
CHP
Com
Con81710
Grn1581622
Ind
Lbt
Lib3121045
M-L
NDP661353
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: Local-PR

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. Surplus votes are transferred.

Top-up Seats

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