Summary of Alternative Vote-2018

Alternative Vote (AV aka Instant-Runoff Voting) is a model which retains single-member ridings but elects the MP using a ranked ballot. Ballots are counted by repeatedly removing the candidate with the fewest votes and transferring their votes to the remaining candidates based on each voter's ranking on their ballot. This process ends when one candidate has at least 50% + 1 of the votes.

Number of Constituency MPs:124
Number of Top-Up MPs:0
Total MPs:124
Number of Single-Member Ridings:124
Number of Multi-Member Ridings:0
Total Ridings:124
Number of Top-up Regions:0
Single Member Seats:AV-2021
Multi Member Seats:NA
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
Con2,326,52340.5%6350.8%50.210.3%
NDP1,929,96633.6%5241.9%41.78.3%
Lib1,124,34619.6%86.5%24.3-13.1%
Grn264,5194.6%10.8%5.7-3.8%
Oth99,5061.7%00.0%2.1-1.7%

MPs: 124Gallagher Index: 13.48Composite Gallagher Index: 13.48

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.

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
Con2,326,52340.5%6350.8%50.210.3%
NDP1,929,96633.6%5241.9%41.78.3%
Lib1,124,34619.6%86.5%24.3-13.1%
Grn264,5194.6%10.8%5.7-3.8%

MPs: 124Gallagher Index: 13.48

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
Con2,326,52340.5%6350.8%50.210.3%
NDP1,929,96633.6%5241.9%41.78.3%
Lib1,124,34619.6%86.5%24.3-13.1%
Grn264,5194.6%10.8%5.7-3.8%

MPs: 124Gallagher Index: 13.48

BC

Statistics on British Columbia.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Total Number of MPs:00
Gallagher Index: 0.00 0.00

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
Total Number of MPs:00
Gallagher Index: 0.00 0.00

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
Con2,326,52340.5%6350.8%10.3%6350.8%10.3%
NDP1,929,96633.6%5241.9%8.3%5241.9%8.3%
Lib1,124,34619.6%86.5%-13.1%86.5%-13.1%
Grn264,5194.6%10.8%-3.8%10.8%-3.8%
Total Number of MPs:124124
Gallagher Index:13.4813.48

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
Total Number of MPs:00
Gallagher Index: 0.00 0.00

Ontario

Statistics on Ontario.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Con2,326,52340.5%6350.8%10.3%6350.8%10.3%
NDP1,929,96633.6%5241.9%8.3%5241.9%8.3%
Lib1,124,34619.6%86.5%-13.1%86.5%-13.1%
Grn264,5194.6%10.8%-3.8%10.8%-3.8%
Total Number of MPs:124124
Gallagher Index:13.4813.48

Quebec

Statistics on Quebec.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Total Number of MPs:00
Gallagher Index: 0.00 0.00

Alberta

Statistics on Alberta.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Total Number of MPs:00
Gallagher Index: 0.00 0.00

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
1124
Average: 1.0

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
01
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
1241
Average:124.0

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→BlocCCFCHPCORComConFCPFreeGrnIndLabProgLbtLibLibLabLibProgM-LNAPNDPNLPOthPPC
Bloc23142010
CCF
CHP
COR
Com
Con610121812
FCP
Free
Grn1581622
Ind
LabProg
Lbt
Lib2178462
LibLab
LibProg
M-L
NAP
NDP21218393
NLP
Oth
PPC30

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: NA

An election strategy for where none are applicable. For example, for multi-member ridings in a FPTP simulation.

Top-up Seats

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