Overview of ERRE Constrained Simulations
Introduction
I presented my modelling work to the House of Commons Special Committee on Electoral Reform (ERRE) on 19-Oct-2016. The next day they passed a motion asking for more work within three constraints:
- Keep the composite Gallagher index as low as possible.
- Each projection must maintain the total number of Members for each Province and Territory, unchanged from the number allocated through the 2015 redistribution
- If any of the projections require a redistribution, the redistribution must be capable of being executed on an expedited basis, and as a result the only method of redistribution employed should be to merge existing ridings in sets of two, three, or more.
These are significant constraints, cutting to the core of the most common techniques for obtaining proportionality. Pure multi-member systems such as STV meet these constraints easily, but anything that requires a top-up layer such as MMP or RU-PR is hard.
This page summarizes the systems developed for ERRE.
The report submitted to the Committee is here.
This page:
Proportionality
| Alternative Vote-2015 | 338 | 0 | 21% | -7% | -6% | -4% | -3% | 16.8% | 21.9% | 48% | 94% | 2015 |
| Alternative Vote-2019 | 338 | 0 | 17% | -1% | -8% | 0% | -6% | 13.8% | 19.4% | 49% | 88% | 2019 |
| Alternative Vote-2021 | 338 | 0 | 16% | 0% | -9% | 1% | -2% | 13.3% | 18.4% | 48% | 91% | 2021 |
| First-Past-The-Post-2015 | 338 | 0 | 15% | -3% | -7% | -2% | -3% | 12.0% | 17.2% | 48% | 94% | 2015 |
| First-Past-The-Post-2019 | 338 | 0 | 13% | 1% | -9% | 2% | -6% | 12.2% | 18.1% | 49% | 89% | 2019 |
| First-Past-The-Post-2021 | 338 | 0 | 14% | 1% | -10% | 2% | -2% | 13.2% | 18.8% | 48% | 91% | 2021 |
| Single Transferable Vote (Medium-sized Regions)-2015 | 338 | 0 | 3% | 0% | 1% | -0% | -3% | 3.0% | 4.1% | 96% | 97% | 2015 |
| Single Transferable Vote (Medium-sized Regions)-2019 | 338 | 0 | 3% | 1% | -0% | 0% | -2% | 3.2% | 4.4% | 95% | 97% | 2019 |
| Single Transferable Vote (Medium-sized Regions)-2021 | 338 | 0 | 3% | 3% | -0% | 0% | -2% | 4.2% | 5.4% | 94% | 96% | 2021 |
| Single Transferable Vote (Small Regions)-2015 | 338 | 0 | 6% | -0% | -2% | -1% | -3% | 5.2% | 6.4% | 90% | 93% | 2015 |
| Single Transferable Vote (Small Regions)-2019 | 338 | 0 | 5% | 3% | -2% | 1% | -5% | 5.8% | 8.9% | 85% | 90% | 2019 |
| Single Transferable Vote (Small Regions)-2021 | 338 | 0 | 4% | 5% | -1% | 0% | -2% | 6.1% | 9.0% | 85% | 89% | 2021 |
Footnotes
- Number of Local MPs is the total number of MPs representing specific ridings. Those ridings may be either single-member ridings or multi-member.
- Number of Regional MPs is the total number of MPs that represent multiple ridings. This happens in systems with top-up seats such as MMP and RU-PR.
- Over-Representation by Party is the percentage of MPs in Parliament minus the percentage of the popular vote. For example, in 2015 under FPTP the Liberals received 54.4% of the seats but only 39.5% of the vote for an over-representation of (54.4 - 39.5) = 14.9%. Negative numbers mean the party was under-represented.
- Gallagher Index is a measure of disproportionality. It combines both over and under-representation for each party into a single number. Gallagherindicies less than 5 are excellent.
- Gallagher Index 2015 is the Gallagher Index for the simulated 2015 election.
- Gallagher Index Composite is the average of the Gallagher Indices for each province and territory, weighted by its number of seats. This corrects for a problem in calculating the Gallagher Index for the nation as a whole, which can can hide regional disproportionalities such as the significant over-representation of Conservatives in the Prairies offsetting the over-representation of Liberals in the Maritimes.
- % Voters with Preferred Local MP is the percentage of voters who have an MP representing their riding from the same party as their first choice candidate. Systems with multi-member ridings will do better under this measure.
- % Voters with Preferred Regional MP is the percentage of voters who have an MP representing their region from the same party as their first choice candidate. Systems with top-up seats will do better under this measure.
- Short System Name is a very consise abbreviation of the key parameters for this simulation.
Model Summary
Proportional electoral systems have many design parameters that can be tweaked. This table has two rows for each model. The bottom row applies to the riding; the top row applies to the region.
The first column of that table gives the name of the riding design (top) and the election algorithm used and the year of the election it's based on (bottom). The riding design specifies a particular mapping from old (e.g. 2015) ridings to new ridings, how the new ridings are gathered into regions, and finally how the regions are gathered by province. Riding designs are described in more detail at the bottom of this page and by following the riding design link.
| Region | # Tot Seats | % Seats | Avg # Seats/Region | Avg #Reg/Prov | Avg Adjust Seats / Region | ||
| Riding | Year | # Tot Seats | % Seats | Avg # Seats/Riding | % Single | % Multiple | Comp. Gallagher |
| fptp | 0 | 0% | 0.0 | 1.0 | |||
| AV | 2015 | 338 | 100% | 1.0 | 100% | 0% | 21.9% |
| fptp | 0 | 0% | 0.0 | 1.0 | |||
| AV | 2019 | 338 | 100% | 1.0 | 100% | 0% | 19.4% |
| fptp | 0 | 0% | 0.0 | 1.0 | |||
| AV | 2021 | 338 | 100% | 1.0 | 100% | 0% | 18.4% |
| fptp | 0 | 0% | 0.0 | 1.0 | |||
| MMP_FPTP | 2015 | 338 | 100% | 1.0 | 100% | 0% | 17.2% |
| fptp | 0 | 0% | 0.0 | 1.0 | |||
| MMP_FPTP | 2019 | 338 | 100% | 1.0 | 100% | 0% | 18.1% |
| fptp | 0 | 0% | 0.0 | 1.0 | |||
| MMP_FPTP | 2021 | 338 | 100% | 1.0 | 100% | 0% | 18.8% |
| stv_med | 0 | 0% | 0.0 | 1.0 | |||
| STV | 2015 | 338 | 100% | 10.9 | 10% | 90% | 4.1% |
| stv_med | 0 | 0% | 0.0 | 1.0 | |||
| STV | 2019 | 338 | 100% | 10.9 | 10% | 90% | 4.4% |
| stv_med | 0 | 0% | 0.0 | 1.0 | |||
| STV | 2021 | 338 | 100% | 10.9 | 10% | 90% | 5.4% |
| stv_small | 0 | 0% | 0.0 | 2.8 | |||
| STV | 2015 | 338 | 100% | 4.1 | 5% | 95% | 6.4% |
| stv_small | 0 | 0% | 0.0 | 2.8 | |||
| STV | 2019 | 338 | 100% | 4.1 | 5% | 95% | 8.9% |
| stv_small | 0 | 0% | 0.0 | 2.8 | |||
| STV | 2021 | 338 | 100% | 4.1 | 5% | 95% | 9.0% |
Riding Design Descriptions
fptp
Canada's current riding design: 338 single-member ridings with no compensatory seats. Thisdesign can be used with either FPTP or Alternative Vote.
fptp
Canada's current riding design: 338 single-member ridings with no compensatory seats. Thisdesign can be used with either FPTP or Alternative Vote.
fptp
Canada's current riding design: 338 single-member ridings with no compensatory seats. Thisdesign can be used with either FPTP or Alternative Vote.
stv_med
STV (Single Transferable Vote) with medium-sized ridings that average 10.9 seats each. The three territories are left as single-member ridings and PEI is of necessity only 4 seats. All other ridings are 7 seats or larger -- ranging up to one with 18 seats.
This particular grouping of ridings is based on work by Antony Hodgson, President of Fair Voting BC.
stv_med
STV (Single Transferable Vote) with medium-sized ridings that average 10.9 seats each. The three territories are left as single-member ridings and PEI is of necessity only 4 seats. All other ridings are 7 seats or larger -- ranging up to one with 18 seats.
This particular grouping of ridings is based on work by Antony Hodgson, President of Fair Voting BC.
stv_med
STV (Single Transferable Vote) with medium-sized ridings that average 10.9 seats each. The three territories are left as single-member ridings and PEI is of necessity only 4 seats. All other ridings are 7 seats or larger -- ranging up to one with 18 seats.
This particular grouping of ridings is based on work by Antony Hodgson, President of Fair Voting BC.
stv_small
STV (Single Transferable Vote) with smaller ridings that average 4.1 seats each. The three territories and Labrador are left as single-member ridings. There are 5 two seat ridings in large, sparsely populated areas. Most ridings have four seats and the largest is eight.
This particular grouping of ridings is based on work by Antony Hodgson, President of Fair Voting BC.
stv_small
STV (Single Transferable Vote) with smaller ridings that average 4.1 seats each. The three territories and Labrador are left as single-member ridings. There are 5 two seat ridings in large, sparsely populated areas. Most ridings have four seats and the largest is eight.
This particular grouping of ridings is based on work by Antony Hodgson, President of Fair Voting BC.
stv_small
STV (Single Transferable Vote) with smaller ridings that average 4.1 seats each. The three territories and Labrador are left as single-member ridings. There are 5 two seat ridings in large, sparsely populated areas. Most ridings have four seats and the largest is eight.
This particular grouping of ridings is based on work by Antony Hodgson, President of Fair Voting BC.
Election Strategy Descriptions
Election strategies are the specifics of how ballots are counted to determine which candidate fills a seat. Each strategy has three parts: how single-member ridings are handled, how multi-member ridings are handled, and finally how top-up or adjustment seats are handled.
AV
Single-Member Ridings:
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:
An election strategy for where none are applicable. For example, for multi-member ridings in a FPTP simulation.
Top-up or Adjustments:
A placeholder election strategy for where no top-up strategy is applicable.
FPTP
Single-Member Ridings:
After collapsing all candidates running for the same party into one virtual candiate, choose the virtual candidate with the most votes.
Multi-Member Ridings:
An election strategy for where none are applicable. For example, for multi-member ridings in a FPTP simulation.
Top-up or Adjustments:
A placeholder election strategy for where no top-up strategy is applicable.
STV
Single-Member Ridings:
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:
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 or Adjustments:
A placeholder election strategy for where no top-up strategy is applicable.