Summary of Alternative Vote-2021

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:338
Number of Top-Up MPs:0
Total MPs:338
Number of Single-Member Ridings:338
Number of Multi-Member Ridings:0
Total Ridings:338
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
Con5,730,51533.7%11534.0%113.90.3%
Lib5,542,36032.6%16348.2%110.815.6%
NDP3,022,45117.8%308.9%60.4-8.9%
Bloc1,301,7587.7%288.3%25.10.6%
PPC842,9695.0%00.0%16.6-5.0%
Grn394,7402.3%20.6%8.0-1.7%
Oth156,2810.9%00.0%3.2-0.9%

MPs: 338Gallagher Index: 13.26Composite Gallagher Index: 18.37

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: 19.6%

Voters shift between NDP and Conservative

Average Gallagher Index: 19.1%

Voters shift between Green and Conservative

Average Gallagher Index: 19.4%

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
Con5,730,51533.7%11534.0%114.00.3%
Lib5,542,36032.6%16348.2%110.315.6%
NDP3,022,45117.8%308.9%60.1-8.9%
Bloc1,301,7587.7%288.3%25.90.6%
PPC842,9695.0%00.0%16.8-5.0%
Grn394,7402.3%20.6%7.9-1.7%

MPs: 338Gallagher Index: 13.26

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
Con5,730,51533.7%11534.0%114.00.3%
Lib5,542,36032.6%16348.2%110.315.6%
NDP3,022,45117.8%308.9%60.1-8.9%
Bloc1,301,7587.7%288.3%25.90.6%
PPC842,9695.0%00.0%16.8-5.0%
Grn394,7402.3%20.6%7.9-1.7%

MPs: 338Gallagher Index: 13.26

BC

Statistics on British Columbia.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Con741,04333.2%1228.6%-4.7%1228.6%-4.7%
NDP650,60629.2%1535.7%6.5%1535.7%6.5%
Lib602,24827.0%1433.3%6.3%1433.3%6.3%
Grn117,9515.3%12.4%-2.9%12.4%-2.9%
PPC109,6764.9%00.0%-4.9%00.0%-4.9%
Total Number of MPs:4242
Gallagher Index: 8.28 8.28

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
Con1,601,66352.9%4979.0%26.2%4979.0%26.2%
NDP610,78520.2%58.1%-12.1%58.1%-12.1%
Lib514,28217.0%812.9%-4.1%812.9%-4.1%
PPC220,4407.3%00.0%-7.3%00.0%-7.3%
Oth38,1501.3%00.0%-1.3%00.0%-1.3%
Grn32,8251.1%00.0%-1.1%00.0%-1.1%
Total Number of MPs:6262
Gallagher Index:21.2521.25

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
Lib4,372,42837.7%13559.5%21.8%13559.5%21.8%
Con3,352,80428.9%5423.8%-5.1%5423.8%-5.1%
NDP1,740,95315.0%94.0%-11.0%94.0%-11.0%
Bloc1,301,75811.2%2812.3%1.1%2812.3%1.1%
PPC510,1154.4%00.0%-4.4%00.0%-4.4%
Grn234,6422.0%10.4%-1.6%10.4%-1.6%
Total Number of MPs:227227
Gallagher Index:17.9817.98

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
Lib517,64743.6%2578.1%34.5%2578.1%34.5%
Con374,44431.5%721.9%-9.7%721.9%-9.7%
NDP200,91816.9%00.0%-16.9%00.0%-16.9%
PPC51,7314.4%00.0%-4.4%00.0%-4.4%
Grn37,7423.2%00.0%-3.2%00.0%-3.2%
Total Number of MPs:3232
Gallagher Index:28.2928.29

Ontario

Statistics on Ontario.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib2,532,44639.3%7763.6%24.4%7763.6%24.4%
Con2,249,48534.9%3629.8%-5.1%3629.8%-5.1%
NDP1,151,78817.9%75.8%-12.1%75.8%-12.1%
PPC352,0765.5%00.0%-5.5%00.0%-5.5%
Grn143,2182.2%10.8%-1.4%10.8%-1.4%
Total Number of MPs:121121
Gallagher Index:19.9819.98

Quebec

Statistics on Quebec.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Lib1,361,29133.6%3747.4%13.8%3747.4%13.8%
Bloc1,301,75832.1%2835.9%3.8%2835.9%3.8%
Con755,54818.6%1114.1%-4.5%1114.1%-4.5%
NDP395,9599.8%22.6%-7.2%22.6%-7.2%
PPC109,0462.7%00.0%-2.7%00.0%-2.7%
Grn61,7301.5%00.0%-1.5%00.0%-1.5%
Oth59,3411.5%00.0%-1.5%00.0%-1.5%
Total Number of MPs:7878
Gallagher Index:12.0412.04

Alberta

Statistics on Alberta.

Ridings OnlyRidings + Top-up
PartyPopular VotesPct VotesElected MPsPct Elected MPsOver RepElected MPsPct Elected MPsOver Rep
Con1,073,10355.3%2985.3%30.0%2985.3%30.0%
NDP370,34419.1%25.9%-13.2%25.9%-13.2%
Lib300,09915.5%38.8%-6.6%38.8%-6.6%
PPC142,6737.3%00.0%-7.3%00.0%-7.3%
Oth30,1831.6%00.0%-1.6%00.0%-1.6%
Total Number of MPs:3434
Gallagher Index:24.2624.26

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 211 km2 and 90% of our population live in ridings smaller than 29,982 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
1338
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
013
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
421
781
1211
Average:26.0

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→BlocCHPComConGrnIndLbtLibM-LNDPOthPPC
Bloc23142010
CHP
Com
Con610121812
Grn1581622
Ind
Lbt
Lib2178462
M-L
NDP21218393
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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