Summary of Single Transferable Vote (Small Regions)-2021
A classic Single Transferable Vote (STV) model with small ridings averaging just over 4 members each. An STV system combines our existing single-member ridings into larger ridings with multiple members. The total number of MPs would remain at 338.
Voters use a ranked ballot. Their vote is initially allocated to their top-ranked candidate. As the count proceeds and it becomes clear that a candidate is assured victory or assured defeat, their excess votes are transferred to the remaining candidates. This proceeds until all positions have been filled.
The grouping of existing ridings into multi-member ridings is based on work by Antony Hodgson, President of Fair Voting BC.
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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 | 5,730,515 | 33.7% | 130 | 38.5% | 113.9 | 4.7% |
| Lib | 5,542,360 | 32.6% | 125 | 37.0% | 110.8 | 4.4% |
| NDP | 3,022,451 | 17.8% | 56 | 16.6% | 60.4 | -1.2% |
| Bloc | 1,301,758 | 7.7% | 27 | 8.0% | 25.1 | 0.3% |
| PPC | 842,969 | 5.0% | 0 | 0.0% | 16.6 | -5.0% |
| Grn | 394,740 | 2.3% | 0 | 0.0% | 8.0 | -2.3% |
| Oth | 156,281 | 0.9% | 0 | 0.0% | 3.2 | -0.9% |
MPs: 338Gallagher Index: 6.06Composite Gallagher Index: 8.96
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: 8.7%
Voters shift between NDP and Conservative
Average Gallagher Index: 8.8%
Voters shift between Green and Conservative
Average Gallagher Index: 9.2%
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 | 5,730,515 | 33.7% | 130 | 38.5% | 114.0 | 4.7% |
| Lib | 5,542,360 | 32.6% | 125 | 37.0% | 110.3 | 4.4% |
| NDP | 3,022,451 | 17.8% | 56 | 16.6% | 60.1 | -1.2% |
| Bloc | 1,301,758 | 7.7% | 27 | 8.0% | 25.9 | 0.3% |
| PPC | 842,969 | 5.0% | 0 | 0.0% | 16.8 | -5.0% |
| Grn | 394,740 | 2.3% | 0 | 0.0% | 7.9 | -2.3% |
MPs: 338Gallagher Index: 6.06
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 |
|---|---|---|---|---|---|---|
| Lib | 18,243 | 36.5% | 3 | 75.0% | 1.5 | 38.5% |
| NDP | 14,588 | 29.2% | 1 | 25.0% | 1.2 | -4.2% |
| Con | 11,086 | 22.2% | 0 | 0.0% | 0.9 | -22.2% |
| Ind | 4,430 | 8.9% | 0 | 0.0% | 0.4 | -8.9% |
| Grn | 1,274 | 2.6% | 0 | 0.0% | 0.1 | -2.6% |
MPs: 4Gallagher Index: 32.21
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 | 5,719,429 | 33.8% | 130 | 38.9% | 112.8 | 5.2% |
| Lib | 5,524,117 | 32.6% | 122 | 36.5% | 108.9 | 3.9% |
| NDP | 3,007,863 | 17.8% | 55 | 16.5% | 59.3 | -1.3% |
| Bloc | 1,301,758 | 7.7% | 27 | 8.1% | 25.7 | 0.4% |
| PPC | 842,676 | 5.0% | 0 | 0.0% | 16.6 | -5.0% |
| Grn | 393,466 | 2.3% | 0 | 0.0% | 7.8 | -2.3% |
MPs: 334Gallagher Index: 6.10
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 | 741,043 | 33.2% | 16 | 38.1% | 4.9% | 16 | 38.1% | 4.9% |
| NDP | 650,606 | 29.2% | 15 | 35.7% | 6.5% | 15 | 35.7% | 6.5% |
| Lib | 602,248 | 27.0% | 11 | 26.2% | -0.8% | 11 | 26.2% | -0.8% |
| Grn | 117,951 | 5.3% | 0 | 0.0% | -5.3% | 0 | 0.0% | -5.3% |
| PPC | 109,676 | 4.9% | 0 | 0.0% | -4.9% | 0 | 0.0% | -4.9% |
| Total Number of MPs: | 42 | 42 | ||||||
| Gallagher Index: | 7.73 | 7.73 | ||||||
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 | 1,601,663 | 52.9% | 41 | 66.1% | 13.3% | 41 | 66.1% | 13.3% |
| NDP | 610,785 | 20.2% | 14 | 22.6% | 2.4% | 14 | 22.6% | 2.4% |
| Lib | 514,282 | 17.0% | 7 | 11.3% | -5.7% | 7 | 11.3% | -5.7% |
| PPC | 220,440 | 7.3% | 0 | 0.0% | -7.3% | 0 | 0.0% | -7.3% |
| Oth | 38,150 | 1.3% | 0 | 0.0% | -1.3% | 0 | 0.0% | -1.3% |
| Grn | 32,825 | 1.1% | 0 | 0.0% | -1.1% | 0 | 0.0% | -1.1% |
| Total Number of MPs: | 62 | 62 | ||||||
| Gallagher Index: | 11.61 | 11.61 | ||||||
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 | 4,372,428 | 37.7% | 103 | 45.4% | 7.7% | 103 | 45.4% | 7.7% |
| Con | 3,352,804 | 28.9% | 71 | 31.3% | 2.4% | 71 | 31.3% | 2.4% |
| NDP | 1,740,953 | 15.0% | 26 | 11.5% | -3.5% | 26 | 11.5% | -3.5% |
| Bloc | 1,301,758 | 11.2% | 27 | 11.9% | 0.7% | 27 | 11.9% | 0.7% |
| PPC | 510,115 | 4.4% | 0 | 0.0% | -4.4% | 0 | 0.0% | -4.4% |
| Grn | 234,642 | 2.0% | 0 | 0.0% | -2.0% | 0 | 0.0% | -2.0% |
| Total Number of MPs: | 227 | 227 | ||||||
| Gallagher Index: | 7.13 | 7.13 | ||||||
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 | 517,647 | 43.6% | 19 | 59.4% | 15.8% | 19 | 59.4% | 15.8% |
| Con | 374,444 | 31.5% | 12 | 37.5% | 6.0% | 12 | 37.5% | 6.0% |
| NDP | 200,918 | 16.9% | 1 | 3.1% | -13.8% | 1 | 3.1% | -13.8% |
| PPC | 51,731 | 4.4% | 0 | 0.0% | -4.4% | 0 | 0.0% | -4.4% |
| Grn | 37,742 | 3.2% | 0 | 0.0% | -3.2% | 0 | 0.0% | -3.2% |
| Total Number of MPs: | 32 | 32 | ||||||
| Gallagher Index: | 15.87 | 15.87 | ||||||
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 | 2,532,446 | 39.3% | 54 | 44.6% | 5.4% | 54 | 44.6% | 5.4% |
| Con | 2,249,485 | 34.9% | 46 | 38.0% | 3.1% | 46 | 38.0% | 3.1% |
| NDP | 1,151,788 | 17.9% | 21 | 17.4% | -0.5% | 21 | 17.4% | -0.5% |
| PPC | 352,076 | 5.5% | 0 | 0.0% | -5.5% | 0 | 0.0% | -5.5% |
| Grn | 143,218 | 2.2% | 0 | 0.0% | -2.2% | 0 | 0.0% | -2.2% |
| Total Number of MPs: | 121 | 121 | ||||||
| Gallagher Index: | 6.07 | 6.07 | ||||||
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 | 1,361,291 | 33.6% | 32 | 41.0% | 7.4% | 32 | 41.0% | 7.4% |
| Bloc | 1,301,758 | 32.1% | 27 | 34.6% | 2.5% | 27 | 34.6% | 2.5% |
| Con | 755,548 | 18.6% | 15 | 19.2% | 0.6% | 15 | 19.2% | 0.6% |
| NDP | 395,959 | 9.8% | 4 | 5.1% | -4.6% | 4 | 5.1% | -4.6% |
| PPC | 109,046 | 2.7% | 0 | 0.0% | -2.7% | 0 | 0.0% | -2.7% |
| Grn | 61,730 | 1.5% | 0 | 0.0% | -1.5% | 0 | 0.0% | -1.5% |
| Oth | 59,341 | 1.5% | 0 | 0.0% | -1.5% | 0 | 0.0% | -1.5% |
| Total Number of MPs: | 78 | 78 | ||||||
| Gallagher Index: | 6.89 | 6.89 | ||||||
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 | 1,073,103 | 55.3% | 23 | 67.6% | 12.4% | 23 | 67.6% | 12.4% |
| NDP | 370,344 | 19.1% | 7 | 20.6% | 1.5% | 7 | 20.6% | 1.5% |
| Lib | 300,099 | 15.5% | 4 | 11.8% | -3.7% | 4 | 11.8% | -3.7% |
| PPC | 142,673 | 7.3% | 0 | 0.0% | -7.3% | 0 | 0.0% | -7.3% |
| Oth | 30,183 | 1.6% | 0 | 0.0% | -1.6% | 0 | 0.0% | -1.6% |
| Total Number of MPs: | 34 | 34 | ||||||
| Gallagher Index: | 10.64 | 10.64 | ||||||
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 5,602 km2 and 90% of our population live in ridings smaller than 104,163 km2.
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 | 4 |
| 2 | 5 |
| 3 | 17 |
| 4 | 26 |
| 5 | 16 |
| 6 | 10 |
| 7 | 3 |
| 8 | 1 |
| Average: | 4.1 |
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 | 31 |
| 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 |
|---|---|
| 1 | 3 |
| 4 | 1 |
| 7 | 2 |
| 9 | 2 |
| 10 | 3 |
| 11 | 3 |
| 12 | 5 |
| 13 | 2 |
| 14 | 4 |
| 15 | 4 |
| 16 | 1 |
| 18 | 1 |
| Average: | 10.9 |
Methodology
Single-Member Ridings: AV-2021
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 | CHP | Com | Con | Grn | Ind | Lbt | Lib | M-L | NDP | Oth | PPC |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bloc | 23 | 14 | 20 | 10 | ||||||||
| CHP | ||||||||||||
| Com | ||||||||||||
| Con | 6 | 10 | 12 | 18 | 12 | |||||||
| Grn | 15 | 8 | 16 | 22 | ||||||||
| Ind | ||||||||||||
| Lbt | ||||||||||||
| Lib | 2 | 17 | 8 | 46 | 2 | |||||||
| M-L | ||||||||||||
| NDP | 2 | 12 | 18 | 39 | 3 | |||||||
| Oth | ||||||||||||
| PPC | 30 |
This table is based on 2021 Ipsos polling reported here augmented with guesses about PPC transfers and Green transfers.
Ideally, we would have different tables for each region of the country (at least Quebec and the rest of Canada) as well as for each election year. But we don’t. The same table is currently used everywhere.
Source: https://www.ipsos.com/en-ca/news-polls/canadians-remain-open-to-changing-their-vote-as-debates-loom
Multi-Member Ridings: STV-2021
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 | CHP | Com | Con | Grn | Ind | Lbt | Lib | M-L | NDP | Oth | PPC |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bloc | 23 | 14 | 20 | 10 | ||||||||
| CHP | ||||||||||||
| Com | ||||||||||||
| Con | 6 | 10 | 12 | 18 | 12 | |||||||
| Grn | 15 | 8 | 16 | 22 | ||||||||
| Ind | ||||||||||||
| Lbt | ||||||||||||
| Lib | 2 | 17 | 8 | 46 | 2 | |||||||
| M-L | ||||||||||||
| NDP | 2 | 12 | 18 | 39 | 3 | |||||||
| Oth | ||||||||||||
| PPC | 30 |
This table is based on 2021 Ipsos polling reported here augmented with guesses about PPC transfers and Green transfers.
Ideally, we would have different tables for each region of the country (at least Quebec and the rest of Canada) as well as for each election year. But we don’t. The same table is currently used everywhere.
Source: https://www.ipsos.com/en-ca/news-polls/canadians-remain-open-to-changing-their-vote-as-debates-loom
Top-up Seats
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