Overview of Featured Simulations

Introduction

What's New

2016-10-05: Added a few simulations based on 2006, 2008, and 2011 elections. See the second table on the All Systems page.

2016-10-12: Added AV+ to the list of featured systems. Several changes to the Vote Swing Analysis graphs. Adjusted the Summary Statistics to account for constitutional considerations on provinces for the Proportional MPs column.

2016-10-30: Added a number of systems at the request of the ERRE Committee that meet a specific set of constraints.

2017-07-05:

I've been continuing to work on systems. My new, favourite system is a variant of STV. It
  1. is proportional (of course!),
  2. maintains existing riding boundaries,
  3. does not add any MPs, and
  4. guarantees the election of a locally-nominated candidate in each existing riding.
For more on this system (including models!), see localpr.ca.

This web site presents the results of simulating 61 electoral systems. Others have done individual simulations of their favourite systems, but this is believed to be the first which uses a consistent approach on so many. This page features the 11 systems I view as most interesting. For the full list of 61 simulations, please see the "All Systems" item in the "Overview" menu, above.

Each of these 11 systems is described at the bottom of this page.

There is a lot of data here. It's not for the faint of heart. Perhaps the best way to dive in is to start with the associated submission to the Parlimentary Electoral Reform Committee.

With respect to the Committee's first principle of Effectiveness and Legitimacy, the recommendations based on this modelling is that:

  • the Committee issue a preliminary report stating that the Alternative Vote would be a step backward from FPTP and should not be considered further;
  • the Committee strongly consider Rural-Urban PR, a highly proportional, made-in-Canada system that effectively deals with our diverse riding sizes;
  • if choosing STV, the Committee think carefully about whether having smaller multi-member ridings is worth the decreased proportionality;
  • if choosing MMP, the Committee should stipulate that FPTP (rather than AV) continues to be used in the local riding elections;
  • the Committee avoid MMP-Lite’s substantial increase in complexity for very little gain in proportionality.

It should be noted, of course, that all simulations make assumptions and that any change to the voting system would change how people vote. So actual results will surely be somewhat different from any simulation. Nevertheless, these simulations show us important properties about the systems we are considering that can help guide our decision-making.

Proportionality

Alternative Vote338024%-11%-4%-4%-3%19.0%24.0%48%94%2015
First-Past-The-Post338015%-3%-7%-2%-3%12.0%17.2%48%94%2015
AV+3385317%-7%-4%-2%-3%13.4%15.4%48%90%2015
Mixed Member Proportional
(Lite)		3385311%-2%-5%-1%-3%9.0%11.4%48%91%2015
Mixed Member Proportional
(Small Regions)		2121265%-1%-0%-0%-3%3.8%4.7%47%95%2015
Rural-Urban PR
(More Singles, 389 Seats)		338511%2%-0%-0%-2%1.9%3.4%81%98%2015
Rural-Urban PR
(Few Singles)		338523%-1%-0%-0%-1%2.4%3.3%90%97%2015
Riding Centric Rural-Urban PR338422%-1%0%-0%-0%1.5%2.2%90%99%2015
Rural-Urban PR
(More Singles, 338 Seats)		287513%-1%1%-1%-2%2.7%3.4%80%98%2015
Single Transferable Vote
(Medium-sized Regions)		33804%-0%0%-0%-3%3.3%4.3%96%97%2015
Single Transferable Vote
(Small Regions)		33807%-1%-2%-1%-3%5.6%6.5%90%93%2015

Footnotes

  1. Number of Local MPs is the total number of MPs representing specific ridings. Those ridings may be either single-member ridings or multi-member.
  2. 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.
  3. 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.
  4. 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.
  5. Gallagher Index 2015 is the Gallagher Index for the simulated 2015 election.
  6. 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.
  7. % 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.
  8. % 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.
  9. Short System Name is a very consise abbreviation of the key parameters for this simulation.

Observations

  • FPTP in 2015 gave the Liberals an undeserved 15% over-representation of MPs, just like it did for the Conservatives in 2011. These graphs shows that as the spread in the vote becomes larger, the spread in MPs grows even faster. For every percent the Liberals can increase their vote, their share of MPs goes up by more than 3%.

  • Many commentators have noted that AV favours centrist parties like the Liberals. These simulations illustrate just how true that is. Replaying the 2015 election with AV gives the Liberals 24% more MPs than deserved based on the popular vote.

  • Some MPs might consider keeping the current 338 local ridings and adding 10% - 15% more MPs to give a measure of proportionality. These simulations and the table above show, however, that such a tepid response moves us towards proportionality but doesn't really get us there. With similar design parameters (338 MPs in local ridings; 15% more MPs) the Rural-Urban Proportional (RUP) model does far better.

  • Simulating swings in voter preferences shows that most of the proportional systems remain proportional even as the gap between the first-place and second-place finishers increases. These can be seen in the Vote Swing Analysis graphs produced on the Summary page for each model as well as the "Average Gallagher Index" in the chart above.

    The Gallagher Index is a measure of disproportionality. Numbers below 5% are good. The Average Gallagher Index is the average taken across many simulations done for the voter swing analysis.

    Unfortunately, MMP with only a small top-up layer does not perform well on this measure.

  • All of the parties are currently disadvantaged by FPTP. The Liberals are disadvantaged in the prairie provinces while the Conservatives and NDP are disadvantaged in the eastern provinces and particularly in the Maritimes. The Greens, of course, are disadvantaged nearly everywhere. By the same token, a proportional system would advantage each party in different areas of the country.

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% SeatsAvg # Seats/RegionAvg #Reg/ProvAvg Adjust Seats / Region
RidingYear# Tot Seats% SeatsAvg # Seats/Riding% Single% MultipleComp. Gallagher
fptp00%0.01.0
MMP_AV2015338100%1.0100%0%24.0%
fptp00%0.01.0
MMP_FPTP2015338100%1.0100%0%17.2%
mmp_enlargeP5314%9.24.2
MMP_AV201533886%1.0100%0%15.4%
mmp_enlargeP5314%9.24.2
MMP_FPTP201533886%1.0100%0%11.4%
mmp_small12637%8.04.2
MMP_FPTP201521263%1.0100%0%4.7%
ru_enlargeP5113%21.41.8
FptpList201533887%2.362%38%3.4%
ru_multiples5213%13.82.8
STVplus201533887%4.15%95%3.3%
ru_multiples_rc24211%29.01.3
RcRUPR2201533889%4.25%95%2.2%
ru_singles5115%18.61.8
AvList201528785%2.159%41%3.4%
stv_med00%0.01.0
STV2015338100%10.910%90%4.3%
stv_small00%0.02.8
STV2015338100%4.15%95%6.5%

Representation

The Representation table focuses on how voters are represented by MP.

Alternative Vote33803381.099,034368
First-Past-The-Post33803381.099,034368
AV+338533911.01.39.299,034368
Mixed Member Proportional (Lite)338533911.01.39.299,034368
Mixed Member Proportional (Small Regions)2121263381.03.08.0157,8941,495
Rural-Urban PR (More Singles, 389 Seats)338513892.32.821.499,0343,048
Rural-Urban PR (Few Singles)338523904.11.913.899,0345,894
Riding Centric Rural-Urban PR338423804.23.229.099,0346,704
Rural-Urban PR (More Singles, 338 Seats)287513382.12.818.6116,6323,787
Single Transferable Vote (Medium-sized Regions)338033810.999,03441,667
Single Transferable Vote (Small Regions)33803384.199,0345,894

Footnotes

  1. Number of Local MPs is the total number of MPs representing a specific riding. That riding may be either a single-member riding or a multi-member riding.
  2. 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.
  3. Number of MPs is the sum of the local and regional MPs, or how many seats in Parliament is assumed by this model.
  4. Average Local MPs/Riding is the average number of MPs representing a local riding. Forsystems that have single-member ridings everywhere such as FPTP and MMP, it will be 1.0. For systems that have at least some multi-member ridings such as STV and RU-PR it will be largerthan 1.0.
  5. Average Top-up Seats/Region is useful for systems like MMP and RU-PR where it gives the average number of seats in the top-up region.
  6. Average Total MPs/Region is the average number of MPs representing a region -- the sum of all the local MPs in that region plus the MPs in top-up seats for that region.
  7. Population/Local MP is the total Canadian population divided by the number of local MPs.
  8. Area Represented by Median Local MP is a measure of the area covered by a local MP. In this case 50% of the ridings are smaller than the area (given in square kilometeres) and 50% of the ridings are larger.
  9. Short System Name is a very consise abbreviation of the key parameters for this simulation.

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.

mmp_enlargeP

MMP with the 338 existing single-member ridings. Enlarge parliament to get the top-ups.

mmp_small

MMP with small regions

ru_enlargeP

A total of 338 single and multi-member ridings. Additional compensatory seats come from enlarging Parliament.

ru_multiples

A Rural-Urban design with an emphasis on using multi-member ridings as often as is practical. It gains compensatory seats by enlarging the House.

ru_multiples_rc2

A mash-up of Rural-Urban and Riding-Centric. This design started life as erre_ru_multiples_15pct. All the adjustment seats were added back to the multi-member ridings and explicit made top-ups by enlarging the House.The numbers of top-ups follow as suggestion by Ryan Campbell.

In addition, the STV rules were tweaked to force the election of one MP in each riding that makes up the multi-member ridings.

ru_singles

A Rural-Urban design with an emphasis on preserving sparsely populated areas as single-member ridings. It combines existing ridings and parts of existing ridings to free up compensatory seats. The total number of seats in the House is maintained at 338.

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.

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→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:

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.

AvList

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→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:

Calculate the number of votes for each party and from that the determine the number of seats won by each party using a highest averages method -- specifically as described in "Quota system". After calculating the number of seats for each party, make a list of all the candidates for the party, ordered by number of votes in the 2015 election, and choose the first n candidates as the winners.

Top-up or Adjustments:

Iteratively choose the most disadvantaged party.

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.

FptpList

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:

Calculate the number of votes for each party and from that the determine the number of seats won by each party using a highest averages method -- specifically as described in "Quota system". After calculating the number of seats for each party, make a list of all the candidates for the party, ordered by number of votes in the 2015 election, and choose the first n candidates as the winners.

Top-up or Adjustments:

Iteratively choose the most disadvantaged party.

MMP_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→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:

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

Top-up or Adjustments:

Iteratively choose the most disadvantaged party.

MMP_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:

Iteratively choose the most disadvantaged party.

RcRUPR2

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→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:

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.

The multi-member riding typically has at least one of its seats designated as an adjustment seat. The topup algorithm selects a candidate from an empty old riding (ie the adjustment seat).

Top-up or Adjustments:

Iteratively choose the most disadvantaged party.

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→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:

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

Top-up or Adjustments:

A placeholder election strategy for where no top-up strategy is applicable.

STVplus

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→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:

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

Top-up or Adjustments:

Iteratively choose the most disadvantaged party.