Choosing Between Proportional Systems Part 4: Rural Urban Proportional

Between October 22nd and November 30th British Columbians will vote on whether to adopt a new electoral system.  In a series of posts, I am looking at the level of proportionality and the level of regional representation that each system produces.  In previous posts I looked two versions of mixed member proportional (here and here) and dual member proportional.  In the post I will look at rural urban proportional.  Rural urban proportional systems produce results that match parties’ votes in different regions reasonably well.  The extent to which they are proportional varies from election to election.  Like in mixed member proportional systems that use only region-wide vote shares, these systems have the potential to create province-wide disproportionality.

Rural urban proportional representation is really two systems instead of one.  Under this system, urban areas of the province would use single transferable vote (STV).  In this system, multi-member ridings are created.  For my simulations, I created multi-member ridings in the Victoria area, Vancouver, the Lower Mainland, and the Okanagan.  The ridings that would be created in reality if this system were adopted would be decided by a boundaries commission and have yet to be determined.  The more members each riding has, and the larger each riding is, the more proportional the result will be.  I created ridings with between 4-7 members by putting together existing BC ridings.  For a breakdown of which first past the post ridings fit into which STV ridings see the PDF below.  Parties can run as many members in a riding as there are seats, though it is often not in their strategic interest to do so.  Voters then rank order candidates and are allowed to either rank members of the same party together (for example a Liberal, another Liberal second, and so on) or intersperse candidates from different parties.  It is, however, in the strategic interest of voters that wish to see a particular party do well to rank candidates from their preferred party together.

STV Ridings

To be elected under STV, candidates must win enough votes to cross a threshold determined by the follow formula: threshold =(votes/(number of seats in the riding +1))+1.  If a candidate crosses the threshold, any votes beyond what they needed to cross the threshold get redistributed to their voters’ second choices.  If that does not lead any other candidates to get elected the last place candidate is eliminated and that candidates’ voters are redistributed to those voters’ second choices.  This process repeats until all seats are filled.  For the CGP Grey video explanation of how this system works, check out this link.

In rural urban proportional, rural areas of the province would use a mixed member proportional system.  A province-wide rural list system would produce a more proportional result, but the Attorney General’s report suggests that seats in the system would be assigned based on the share of the vote each party wins in each region.  For a more thorough discussion of mixed member proportional check out the first two posts in this series (here and here).  In my simulations*, I break the province into two rural regions, Vancouver Island (outside of Victoria) and the Interior.  I worry that making the Interior a single region is problematic because of the differences between the North of the province and the South.  At the same time, I worry that breaking the province down into smaller regions will produce results that are highly disproportional.  In small regions there will not be enough list seats available to compensate for the disproportionality in the riding seats awarded on a first past the post basis.

I run simulations based on vote totals from the 2017, 2013 and 2009 provincial elections.  It is important to note here that voters will vote differently and different parties will run under different electoral systems.  These simulations are meant to illustrate proportionality at the province-wide and regional levels, not to predict what would have happened in previous elections had they been run under a different electoral system.  I have a particularly low level of confidence in my predictions regarding the results of the STV urban ridings.  Without second or third choice votes, it is impossible to know with any certainty how many seats each party would have won in each riding.  I make estimates by calculating the threshold in each new STV district.  I then subtract the threshold multiplied by a multiplier for a certain number seats (I start with 0, then 1, then 2, and so on) from the parties share of the vote to estimate the vote share for each of the parties’ candidates.  The first candidate from a party gets the vote share for the party in the region, the second candidate gets the vote share minus the threshold, the third candidate gets the vote share minus the threshold x 2, and so on.  I award seats to the candidates with the most votes until all seats are filled.  It is important to note that this produces a rough estimate and is not actually reflective of how seats are assigned under STV.

The graph below shows that this system produces results that are the most part reasonably proportional, but that do vary in their proportionality.  The Liberals are very proportionally represented in 2009, while the NDP’s seat share in 2017 is quite close to their vote share.  The system can also produce some disproportionate results, though.  The NDP ends up over-represented by 5 points 2013, while the Liberals are over-represented by 5 points in 2017.  This disproportionality can have some significant effects on elections results.  In 2013 the Liberals get close to a majority on 44% of the vote.  In 2017 the system takes a vote difference between the NDP and Liberals that is within a point and gives the Liberal a 6-point edge in seats over the NDP.  In each election I simulate the Greens end up under-represented, but never by very much.

Votes and Seats Under Rural Urban PR

The three graphs below show that the system produces quite proportional within-region results.  Like in every system, the Liberals are consistently over-represented in the Interior relative to their vote share.  The 2017 results on Island are really close to their vote share, but there are gaps in most other regions in most other years.  Most notably, the Liberals end up under-represented in Vancouver/Burnaby in 2017 by around 8 points.

2017 Rural Urban PR Regional Breakdown

2013 Rural Urban PR Regional Breakdown

2009 Rural Urban PR Regional Breakdown

Rural Urban PR Riding Breakdown

The cause of this variation in representation in each region is the low number of list seats and seats in STV ridings.  The fewer the seats in an STV riding, the less proportional the result.  There are only so many ways you can split 4, 5 or 6 seats amongst parties.  Such systems can distinguish between 20 percentage point differences in the vote, but they struggle to accurately reflect differences of 5 or 10 points.  The same problem exists with the limited number of list seats in rural districts.  The fewer the list seats, the harder it is to balance out any disproportionality in the first past the post seats awarded in MMP.  The result is the potential for significant disproportionality within regions.

It is possible for this disproportionality to add up to a quite significant province-wide disproportionality.  There is nothing stopping a party from being slightly disproportionately over or under-represented in each region.  This in turn would lead to significant over or under-representation in the province as a whole.  For the most part in the simulations the regional disproportionalities cancel each other, but there is no reason that they should have to.  When they do not, the somewhat problematic results noted in my discussion of overall provincial proportionality occur.

The graph below shows regional breakdown of party caucuses based on the 2017 results.  The NDP and Greens are quite well represented, with NDP caucus mirroring the regional disproportion of their vote share very closely.  The Greens are over-represented by a bit in Vancouver Island and on the Lower Mainland and under-represented in Vancouver/Burnaby, but in neither case is the difference that large.  The Liberals face the problem they face in every simulation I have run.  They are over-represented in the Interior, and under-represented on Vancouver Island and in Vancouver/Burnaby.

2017 Rural Urban PR Within Party Breakdown

Rural urban proportional does regional representation reasonably well, but also has cases where parties’ regional representation do not match their vote share.  It does province-wide proportionality less well.  In some cases, it gets parties’ seat shares quite close to their vote share, in other cases it can be off by as much as 5 percentage points.  The system is quite complex, not just in the way that it counts votes but also in what it requires of voters.  Voters in STV districts need to learn about multiple candidates from multiple parties.  They also have to understand the strategic implications of ranking candidates from the same party together or splitting them up.  On top of all of this, voters moving from rural BC to urban BC (or vice-versa) would have to learn a new electoral system.  The complexity coupled with the potential disproportionality of the system likely make it inferior to the two other proportional options being put to the referendum.

*Like with the boundaries for ridings under STV, how the rural parts of the province would be divided into regions would be decided by a boundaries commission after the system is adopted.



Choosing Between Proportional Systems Part 3: Dual Member Proportional

Between October 22nd and November 30th British Columbians will vote on whether to change their electoral systems.  In a series of posts, I am looking at the way that the different proportional systems being voted on will affect proportionality and regional representation.  In my last two posts I looked at mixed member proportional if seats were assigned on a province-wide basis and if seats were assigned on a regional basis.  In this post I will look at dual member proportional systems.  Dual member proportional (DMP) has tendencies that are similar to the regional mixed member proportional systems.  It leaves some disproportionality at the regional level, but ensures proportionality province-wide.

DMP works by assigning two members to most ridings.  In order to double the number of MLAs elected in each riding without increasing the number of MLAs, one must double the size of most ridings.  There are a number of ridings in Interior BC, especially in the North, that are already very large geographically.  To keep the ridings from becoming so big that they are impossible to represent, these ridings would likely be left as they are and only elect a single MLA.  Parties are allowed to nominate up to two candidates in each riding, specifying a primary and a secondary candidate.  The first MLA in each riding is elected in the same way that they are elected under first past the post, the candidate with the largest number of votes wins.  Parties are then assigned extra seats so that the total number of seats they win equals their province-wide share of the vote.  For example, if a party win 10% of seats elected through first past the post and 15% of the vote province-wide they get extra seats until their total seat share equals 15%.  Unlike in mixed member proportional though, these seats are not filled from a party list.  Rather, they are filled by having a second candidate elected in each riding.  Parties get their extra seats in the ridings where their candidates won the greatest number of votes.  If the NDP, for example, needs 3 extra seats, and their three strongest candidates who are not yet elected are in Vancouver Quilchena, Vancouver Langara, and Surrey Cloverdale, they would get the second seat in each of those ridings.  The ridings would then be represented by a Liberal member and an NDP member (assuming those ridings elected a Liberal member through first past the post).

Two complications need to be noted with respect to the way this system works.  First, there can only be two members elected from each riding.  This raises the issue of what to do if two parties have their strongest losing candidate in a particular riding.  In that scenario the candidate with the greater number of votes would win the second seat and the other party would get an extra seat from the riding they were next strongest in.  For example, if both the NDP’s and Green’s strongest candidates for extra seats came from Vancouver Quilchena, and the NDP candidate had more votes than the Green candidate, the NDP would get the second seat in Vancouver Quilchena and the Greens would get the second seat in the riding they were next strongest in.

A second complication comes about in that a measure needs to be taken to ensure that parties do not win all of their extra seats in ridings they won based on the first past the post count.  Otherwise parties would be highly over-represented in regions where they are strong and under-represented in regions where they are weak.  To avoid this, a party’s vote share in a riding is cut in half for the count determining extra seats if that party wins the first seat in the riding.  It is thus possible, but not likely, that a party will win the second seat in a riding where it already has the first seat.  For example, if the Greens win in Oak Bay Gordon Head with 20000 votes on the first past the post count, their second candidate would be given only 10000 votes.  If the Greens also had a candidate in Victoria Beacon Hill who lost on the first past the post vote with 15000 votes, that candidate would be able to keep all of their votes for the count assigning second seats.  As a result, the candidate from Victoria Beacon Hill would be ahead of the second candidate from Oak Bay Gordon Head in the line for extra Green seats.  It is finally worth noting that if the primary candidate from a party wins the first past the post count, the secondary candidate is considered for the party’s extra seats.  If the primary candidate loses the first past the post count, they are considered for extra seats, and the secondary candidate is eliminated.

In simulating results for this proportional model based on 2017, 2013, and 2009 election results I use the same ridings that I did for the mixed member proportional simulations in the previous two posts.  The way this breaks down in terms of vote can be found here.  It is important to note here that voters would have voted differently and different parties may have run had this system actually been used in the 2017, 2013, and 2009 elections.  This should not be taken as a claim about what would have happened had those elections been run using a DMP system.  Rather, this is only an illustration of how this system affects proportionality and regional representation.

This system produces results that are quite proportional on a province-wide basis.  The graph below shows the seat share each party would have won under DMP, their proportion of the province-wide vote, and their seat share under first past the post.  This graph will be familiar to readers of my two previous posts.  The number of seats each party would win province-wide is the same as it would be in a province-wide mixed member proportional system.  It is also the same as each party would get under a system of MMP that assigns the number of list seats to a party based on province-wide vote share and then tries to allocate those seats to regions after they are assigned to parties.  However, DMP will produce a more proportional result than an MMP system that only takes into account regional vote share and ignores the province-wide share of the vote.  The BC government has not released (to my knowledge) a detailed accounting of how they will allocate list seats to regions under MMP*.  As such, a vote for DMP over MMP would ensure that BC adopted the most proportional system being considered in the referendum.

Votes and Seats Under DMP

Comparing results under DMP to those under FPTP, the NDP sees little difference in their seat share in 2009 and 2013, and a decrease in seat share in 2017.  This reflects the fact that their first past the post seat shares were pretty close to their vote share in 2009 and 2013 and higher than their vote share in 2017.  The Liberal seat share drops in each election, reflecting the way that the parties’ seats share under first past the post exceeded its vote share.  Finally, the Greens see their seat share increase as they won fewer seats than votes in each election.

The regional breakdown of parties’ seats would come reasonably close to their vote share in each region.  These breakdowns are shown in the three graphs below (for a seat by seat breakdown, click on the PDF below the graphs).  In 2017 and 2013 the NDP are over-represented on Vancouver Island and in the Vancouver/Burnaby region while in 2017 they are under-represented in the Interior.  In 2009 the NDP’s regional seat shares are very close to their regional seat shares.  In 2013 and 2017 the Liberals are over-represented in the Interior.  Consequently, they are under-represented on Vancouver Island in both years and in Vancouver/Burnaby in 2017.  In 2009 the party is over-represented in the Northern Interior, but its seat shares in the rest of the province are pretty close to its vote shares.

2017 DMP Regional Breakdown

2013 DMP Regional Breakdown

2009 DMP Regional Breakdown

DMP Seats by Party

As I discussed in my previous post, the Northern Interior is a problem for proportional systems.  Ridings in the region under first past the post are already very large geographically.  Enlarging them further is difficult to justify as it would create ridings that would be very difficult for MLAs to represent.  This means, however, that there are no extra seats to add in the region either by using a party list under MMP or having two members elected by riding under DMP.  If one wants to maintain province-wide proportionality, parties that are over-represented in Northern BC have to be under-represented in the rest of province.  If one throws out province-wide proportionality in favour of regional proportionality, whichever party does best in Northern BC (in the 2000s the Liberals) will have an advantage over parties that do well in the rest of the province.

The Green party’s regional breakdown is also worth noting.  The Greens tend to be over-represented in the Southern Interior, and at times in the Lower Mainland or in Vancouver/Burnaby (though in 2013 they do not win any seats in the city).  This oddity is a result of the Greens finishing third in most ridings.  As a result, either the NDP or Liberals are usually ahead of the Greens when it comes to deciding who gets its second seat.  This means that the extra seats for the NDP and Liberals come from the ridings in which they are strongest while the Greens get their extra seats in whichever ridings are left over.  This would change if Green support grows and they start to finish second in more ridings.  It would, however, be an issue that affects any party with a relatively small share of the vote.

The breakdowns of caucus support for 2017 votes shows that the NDP and Green caucuses would be reasonably reflective of its voters but that the Liberals would have similar problems to those discussed in the previous systems.  Like in both MMP systems, that Liberals are over-represented in the Interior and under-represented on Vancouver Island and in Vancouver/Burnaby.  The party wins 47% of its seats from the Interior despite winning just 32% its vote there.  Conversely, just 14% of its seats come from Vancouver Island, Vancouver, or Burnaby despite the fact that the party wins 30% of its vote in those regions.  As noted above, the Greens are oddly over-represented in the Interior (with a third of its seats coming from the region on 23% of its vote), but the rest of its caucus is reasonably representative of the regions it gets votes from.

2017 Within Party DMP Regional Breakdown

Of the different proportional systems being looked at in the BC referendum, DMP comes out reasonably well.  It provides proportionality using a system that is likely to be simpler than the regionalized variants of MMP discussed in the previous post.  It will produce province-wide results that will be at least as proportional as MMP, and probably more if the BC government opts to assign MMP list seats with reference only to regional and not to provincial vote shares.  With respect to proportionality within regions, DMP has the same problem as MMP.  The over-representation of parties that are strong in Northern BC requires that party to be under-represented in the rest of the province.  That is a problem is that is impossible to solve without throwing off province-wide proportionality.  In my next post I will look at rural-urban proportional representation, showing that the level of proportionality it produces is more variable than the other two systems being voted on.

*The Attorney General’s report on electoral reform and the Elections BC voter guide seem to differ on the way that MMP would be designed.  The Attorney General’s report suggests that list seats will be allocated to regions with no reference to province-wide vote share.  This would produce a result less proportional than DMP. The Elections BC guide suggests that parties will receive seats based on their province-wide share of the vote and that these seats would be allocated to regions.  This would produce a result as proportional as DMP.


Choosing Between Proportional Systems Part 2: Regional Versions of MMP

In my last post I looked at how adopting a mixed member proportional (MMP) electoral system would affect proportional and regional representation in British Columbia.  For that post I ran simulations based on the assumption that list seats would be assigned province-wide vote.  It was pointed out to me in the comments that the BC Attorney General’s report on electoral report puts forward a version of MMP that would assign list seats on a regional basis, though it is unclear on exactly how it would do so.  Indeed, the Elections BC voter’s guide states both that list seats will be assigned based on province-wide vote and that list MLAs will represent regions.  In this post I look at two ways that list seats could be assigned on a regional basis.  The first method assigns list seats to parties based on the province-wide share of the vote and then places those seats in regions where the party is underrepresented.  The second ignores province-wide vote and instead adds seats to parties based on their region-wide vote.  The first method is a little bit less regionally representative than the second but leads to closer province-wide proportionality.  For both methods, the small number seats in Northern BC presents a problem.

As a caveat to all of this analysis, it is important to note that the way voters vote and the parties that run will change under different electoral systems.  I use past results to provide a sense of how proportional (both at the province wide and at the regional level) the results different electoral systems produce.  These should not be taken as a claim about what would happen had previous elections been run under an MMP system.

MMP Ridings and Party Lists

Throughout this post I will discuss riding seats and list seats in some depth.  In MMP, voters cast a vote for a local candidate and a party.  Local candidates are elected in ridings in the same way that they are elected in first past the post.  Additional seats are then given to each party until they are represented in proportion to their province-wide (or as I will discuss later) their regional proportion of the vote.  If a party wins 15% of the vote provincially but only 10% of ridings, they get additional seats until they have 15% of the total seats in the legislature.  I refer to these additional seats as list seats because the members that fill them come from a party list.

Determining What a Region Is

In my previous post I broke the province down into 5 regions, Vancouver Island, Vancouver Burnaby, the Lower Mainland, the Southern Interior, and the Northern Interior.  I did this based on my own approximation of how the province can be divided.  In the previous post whether a riding was in one region or another had little impact on the way list seats were allocated.  This is because those simulations did not consider regional representation when assigning list seats.  In a regional MMP system the way the province is divided into regions matters to the way that seats are assigned.  The BC government has yet to determine regional boundaries for MMP, so I stick with the 5 that I use in my previous post.  As a general rule making the regions larger would increase regional proportionality but may weaken the connection voters feel to list MLAs (voters in the Northern Interior may not feel they could be represented by voters in the Southern Interior if those regions were combined).  Making regions smaller strengthens the connection voters have to their list MLAs but reduces proportionality (at least when one looks at whether a party’s seat share in a region is proportional to its vote).

Assigning Regional List Seats While Accounting for Province-Wide Vote

The first approach I modeled assigns list seats to parties based on their share of the provincial vote.  Once one knows how many list seats each party gets, those seats are assigned to regions based on where the party has won fewer ridings than its vote share warrants.  For example, if the Liberals win 3 fewer ridings in the Vancouver/Burnaby than their vote share in Vancouver/Burnaby suggests they deserve, 3 of the list seats that the Liberals received based on their provincial vote share would be allocated to a list of Liberals from Vancouver/Burnaby.  If they won two fewer seats on Vancouver Island than they deserved, an additional 2 of their list seats would be allocated to Liberals from the Island.

In this approach there are two important constraints on the list seats a party receives.  First, a party cannot receive more list seats than is justified by their province-wide proportion of the vote.  This would lead to disproportionate representation within the legislature.  Second, there is a limit to how many list seats can be assigned to any given region.  Otherwise some regions would be over-represented in the legislature relative to their share of the population.  In my simulations I stick to a strict limit where I never allocate more seats to a region than they currently have under first past the post.  One could get a result that more closely reflects each party’s vote within regions, however, by relaxing this rule and adding seats to regions where needed (though to avoid over-representing regions, adding seats in one region would require adding seats in others).*

The graph below shows the impact this system would have on party’s overall seat shares.  This will look very similar to the graph of province-wide seats in the previous post.  Indeed, it is the same graph because this method produces the exact same province-wide result as the approach to MMP used in that post.  Because the Liberals were over-represented under first past the post their seat share drops under MMP.  Because the Greens were under-represented, their seat share goes up.  In 2009 and 2013 the NDP seat share does not change much as their seat share under first past the post was already pretty close to vote share.  In 2017 their seat share goes down a bit, reflecting the fact that their seat share under first past the post was higher than their vote share.

Votes and Seats under ATF MMP

Where this system’s results deviate from the results in the previous post is in the way seats are broken down by region.  In this version of MMP list seats are also regional seats, so I count them as part of a party’s representation in a given region.  The result is that parties’ representation in different regions is closer to their vote share in the region than in the simulations run in the previous post.  The three graphs below show this for 2017, 2013, and 2007 respectively.  For a detailed account of which seats each party would win click on the PDF link below the graphs.

2017 ATF MMP Regional Breakdown

2013 ATF MMP Regional Breakdown

2009 ATF MMP Breakdown

MMP ATF Regional Seats By Party

It is worth noting that parties’ seat shares still do not match their vote share in each region, particularly in 2017.  This is because of the two constraints I noted when describing the system, that parties cannot receive more list seats than their province-wide vote share justifies and that there are a limited number of list seats that can be allocated in any given region.  This is a problem for the Liberals in 2017.  In 2017 they are under-represented by about 4 seats on both Vancouver Island and in the Lower Mainland and by 3 seats in Vancouver/Burnaby.  Their total provincial vote share, however, only justifies awarding them 8 total list seats.  They need 11 to make up for their under-representation in Vancouver Island, Vancouver/Burnaby, and the Lower Mainland.  The corollary of this is that the NDP’s and Green’s province-wide vote shares justify awarding them more list seats than they need to make up for disproportions in their representation in particular regions.  As a result, the NDP and Greens get awarded an extra seat or two in the Vancouver Island and Vancouver/Burnaby regions because they need those seats to ensure their province-wide representation is equivalent to their provincial share of the vote.  I am not sure there is a way to award these extra seats in a way that is not at least somewhat arbitrary.**

The final graph I have for this system shows the proportion of seats each party would have based on 2017 results in each region relative to their vote share in the region.  It shows that NDP caucus looks a lot like their vote share, as does the Greens (though the Greens a little under-represented in the Interior and over-represented in the Lower Mainland).  The Liberal caucus looks more like its vote share than it did in the MMP model used in the previous post.  It is still over represented in the Interior though (47% of their seats come from the Interior, but only 32% of their vote does).  Conversely, the Liberals are under-represented on the Island and in Vancouver/Burnaby (19% of their seats come from the two regions while 30% of their vote does).

2017 ATF MMP Within Party Regional Breakdown

Allocating Seats Without Reference to Province-Wide Vote

The second way that one can allocate list seats regionally is by ignoring the province-wide vote completely, and instead allocating list seats in regions based on the proportion of the vote a party wins within the region.  For example, if a party wins 15% of the vote in Vancouver/Burnaby but only 10% of the ridings, the party gets list seats for Vancouver/Burnaby until it has 15% of the seats in Vancouver/Burnaby.  This is what is done in German federal elections where list seats are allocated by province (land in German) instead of for the entire country.  This works well in Germany because it has a large population and, as a result, has a large number of list seats in each province to compensate under-represented parties.  Because BC has a much smaller population, there will be far fewer seats list in each region and it will be harder to compensate parties that win fewer ridings that their regional vote share justifies.

This is shown in the graph below, which compares the seat shares each party would have won under regional MMP with 2017, 2013, and 2009 vote shares to their vote share and seat share under FPTP.  The result is better proportionality than under FPTP, but worse than under the first approach to MMP discussed in this post and the system discussed in the previous post.  The Liberals even manage to win a majority of seats in 2009 on 46% of the vote, a result that would have very significant consequences with respect to which party or parties govern BC.

Votes and Seats Under Regional MMP

The three graphs below show what the regional breakdown would like for the vote shares from the 2017, 2013, and 2009 elections.  In most cases parties’ vote shares are quite close to their vote shares in the region.  The Greens tend to be under-represented in the Interior and the Liberals are over-represented in the Lower Mainland and the Interior but otherwise the results are pretty good.  This is somewhat surprising given the small number of list seats in each region.  In 2017 Vancouver Island only has 7 list seats available, Vancouver/Burnaby has 8, and the Southern Interior has 5.  Only the Lower Mainland has a large number of list seats at 15.  The fewer the list seats in a region the fewer seats there are to compensate the parties that are under-represented after the riding votes are counted and the less proportional the result will be.

2017 Regional MMP Breakdown

2013 Regional MMP Breakdown

2009 Regional MMP Breakdown

Regional MMP Seats By Party

The way this affects party caucuses for the 2017 results is shown below.  The make-up of each party’s caucus gets closer to the distribution of its voters than under the other two versions of MMP.  At the same time there are still significant discrepancies.  With only 23% of their caucus (compared to 32% of their vote) coming from Vancouver/Burnaby and the Island, the Liberals still have a disproportionately small share of their caucus from those two regions.  They also still have a disproportionately large share of their caucus from the Interior.

2017 Regional MMP Within Party Breakdown

The Problem With Northern BC

The Northern Interior stands out in all of the above graphs as having the least proportional results.  This is because I did not add list seats to that region.  When I merged ridings together to reduce the number of ridings and make room for list seats I left the boundaries in Northern Interior the same as they were under first past the post (I also did this with some of the ridings in the Southern Interior).  This is because the ridings in that region of the province are already very large geographically.  Merging ridings in the Northern Interior would create ridings that are so big that it is hard to see how an MLA could serve them well.  Even merging the two Prince George ridings (which are on the smaller end relative to the rest of the Northern Interior) would create a riding that stretches as far south as Valemount and as far north as Mackenzie (according to Google Maps driving between the two towns takes 5 hours and 474 km).

Adding list seats without merging ridings would lead to a legislature that disproportionately represents the Northern Interior even more than is the case already.  Ridings in Northern BC already tend to have fewer people in them in ridings in the rest of the province because of the need to keep the ridings to a reasonable geographic size.  Skeena, for example, only has about 23000 people in it despite the fact that ridings in BC are supposed to have 50000.  I cannot see a way in which list seats could be added to the Northern Interior in a way that keeps the distribution of seats in the province relatively close to the distribution of the province.  The region just has too few people living across too large an area.

The disproportionality in Northern BC in turn throws off proportionality in the rest of the province.  If one wants to ensure that parties’ seats match their province-wide vote, parties that are over-represented in Northern BC (usually the Liberals) need to be compensated with under-representation in the rest of the province.  If one is willing to ignore province-wide vote share in favour of looking at regional vote share, a party that is over-represented in Northern BC will have a larger share of seats in the legislature than their province-wide vote justifies.  This is how the Liberals win a greater share of seats that province-wide votes in the second set of simulations in this post.

One solution to this problem is not to have separate regions for the Northern and Southern Interior.  This raises a creates a different problem, though.  The issues important to people living in the North are likely very different from people living in the South.  A voter from Prince George might not feel well represented by an MLA from Kelowna or Kamloops elected off a list.  Advocates of an MMP system with list seats assigned to regions may simply have to live with the problem that the low population density in Northern BC creates.


This post looks at a couple of ways to design MMP systems to allow for regional representation on party lists.  Both systems are messy and both still leave some discrepancies in regional representation.  They do, however, do better than first past the post or a province-wide list MMP system with respect to regional representation.  An approach to party lists that looks only at regional vote shares (the second system) leaves room for a reasonable amount of disproportionality and is only slightly better at regional representation.  As a result, it probably makes sense to allocate list seats to parties based on their province-wide vote share first and then try to allocate them to regions (the first system).  The complexity of these systems highlights an important thing with respect to electoral reform.  The more one tries to account for both proportionality and regional representation, the more complicated the electoral system has to get.

*The Elections BC guide sets out a limit for total seats in the legislature of 95, just 8 more than there are currently.  It also sets out a limit where only 40% of total seats can be allocated as list seats (while at least 60% must come from ridings). This puts additional constraints on any attempt to add seats to regions in order to make regional results more proportional

**It is hard to know whether to give the Greens their extra seat in Vancouver/Burnaby and the NDP their extra seat on Vancouver Island or vice-versa.

*** Data for calculating the seat breakdowns in this post can be found here.


Choosing Between Proportional Systems Part 1: Mixed Member Proportional

Between October 22nd and November 30th British Columbians will vote by mail on whether to adopt a proportional representation electoral system, and if so, which one to adopt.  In a series of posts, I will compare the three proportional systems on the ballot in the referendum, mixed member proportional (MMP), dual member proportion (DMP), and rural urban proportional.  In doing so I will run simulations using past vote totals to look at the extent to which each system is proportional and way each system would affect the regional diversity within parties.  In this post I will look at mixed member proportional.  I argue that while mixed member proportional increases proportionality, it also decreases the regional diversity of each party’s caucus.

MMP is perhaps the simplest of the proportional systems being considered in the referendum.  It works by dividing MLAs in the legislature into two groups, those elected off of a party list and those elected in ridings.  In these systems voters get two votes, one for a local candidate in their ridings and one for a party.  The vote for a local candidate determines who represents a voter’s riding while the vote for a party determines the overall share of each party’s seats in the legislature.  MLAs are first elected in ridings using the same plurality rule as first past the post, whichever candidate wins the largest vote share wins the riding, regardless of how much they win the riding by.  Parties then get additional seats from their party lists until their share of the seats in the legislature equals their overall share of the province-wide vote.  The list seats essentially compensate any party that wins a lower proportion of ridings than their overall share of the provincial justifies.  For example, if a party wins 15% of the vote but only 10% of ridings, that party would get extra MLAs from their party list until the number of seats they had in the legislature equaled 15%.  Because in BC the number of MLAs will stay approximately the same as under first past the post, this requires cutting the number of ridings to create space for MLAs elected off the party lists.

To get at the impact this system would have on proportionality and within party regional diversity, I simulated the 2017, 2013, and 2009 BC elections under a mixed member proportional model.  It is important to remember that these simulations are only done to get at the issue of proportionality and regional diversity, they do not get at what would have happened had those elections been contested under MMP.  Voters would have likely voted differently had the electoral system been different and new parties may have formed.  It is impossible to know what the actual results of those elections would have been had they been run under a different electoral system.

Using past results also means that I have to take the boundaries of ridings under first past the post as given.  To get at what happens to regional representation when one reduces the number of ridings, I went through the electoral maps in the three elections and combined ridings together to reduce the number of ridings to slightly more than half the current number.*  If BC moves to MMP, a boundaries commission will draw new boundaries that will likely make more sense than they ones I was forced to create.  The data for this post, as well as others later in the series can be found here.**

With respect to proportionality, MMP does well.  The graph below shows the share of the vote each party received in 2009, 2013, and 2017, the number of seats each party received under first past the post, and the number it would have received with that share of the vote in an MMP system.  The graph shows that in MMP, parties’ share of seats in much more in line with their share of the vote.  For the NDP this makes little difference to the party in the 2009 and 2013 elections as the party’s seat share was already quite close to its vote share.  In 2017, however, their seat share drops to fall in line with their vote share.  For the Liberals this would mean a drop in their seat share in each election, reflecting the fact that first past post left the Liberals with a greater proportion of seats than votes.  Finally, the opposite is true for the Green party.  Their seat share goes up in each election, reflecting the fact that first past the post often leaves them with fewer seats than their share of the vote.

Votes and Seats under MMP

What is perhaps more interesting is where these seats end up coming from.  The three graphs below show the seat share parties would have in different regions of the province compared to their vote share for the region (for a more detailed breakdown of which ridings each party would have won, click on the PDF below the graphs).  Each graph shows that the seat share of parties in their strongholds goes up dramatically.  The NDP ends up winning 71% of seats on Vancouver Island in 2017 and all of the seats on the Island in 2013 and 2009.  The Liberal party is shut out on the Island in each election despite having close to or above 30% of the vote.  The NDP also outperforms its vote share in the Vancouver/Burnaby region in 2017 and 2013 while the Liberals outperform their vote share in the rest of the Lower Mainland and the Interior region.  The Greens meanwhile are completely shut out of regional ridings in 2009 and 2013 and only win on the Island in 2017.

2017 Regional Breakdown Under MMP

2013 Regional Breakdown Under MMP

2009 Regional Breakdown Under MMP

MMP Seats By Party

Unlike first past the post, none of this affects overall proportionality.  Any province-wide disproportionality is compensated for with seats off a party list.  These list seats are particularly important to the NDP, which wins a plurality of list seats in each election.  They are also important to the Green party, which would have few seats without the party list.  The Liberals, by contrast, would be less reliant on list seats.  This has the potential to have some interesting effects on the way parties behave.  The higher reliance on list seats means that the NDP and Greens would have more MLAs that need to boost the parties’ total provincial vote share to get elected and therefore more MLAs with incentives to be concerned about the province-wide effects of policies.  By contrast, the Liberals would have more MLAs elected from ridings.  These MLAs have an incentive to think in terms of the way policy affects the particular local areas they are elected from.

Similarly, the disproportionality in the regional breakdown of the party caucuses may affect which regions the parties pay most attention.  The large numbers of MLAs from the Island and Vancouver/Burnaby may make the NDP disproportionately responsive to those parts of the province.  The same is true for the Liberals with respect to the large share of seats they have in the Interior and Lower Mainland.  This is the case despite the fact that there are significant number of Liberal voters on the Island and in the Vancouver Burnaby area and significant numbers of NDP voters in the Interior.

A last graph, below, shows what party caucuses would have looked like if seats in 2017 had been distributed through an MMP system.  The NDP caucus’ regional breakdown is fairly close to the breakdown of their vote share, with the party’s voters in the Interior being slightly under-represented as a proportion of their caucus.  The Liberal’s and the Green’s regional breakdowns are not representative of their party’s voters.  Despite the fact that the Liberals won close to 30% of their votes in either Vancouver, Burnaby, or Vancouver Island, just over 5% of their MLAs would come from those three regions (as noted above none would come from the Island).  Meanwhile, 47% of the Liberal caucus would come from the Interior despite the fact that only 32% of its voters are from there.  For the Greens, the discrepancy is starker as the party wins no representation in ridings off of the Island despite winning two thirds of its vote off of the Island.  If the Greens wanted, they could nominate a large number of party list members from off the Island to compensate for their lack of riding representation there, but they would be under no obligation to do so.  With fewer list seats, there is little that the Liberals could do to compensate for regional imbalances in their caucus.

Post publication note: It was pointed out to me in the comments that the Attorney General’s report designs an MMP system that will allocate seats list seats by region.  It is unclear to me exactly how this will work while respecting a province-wide proportional vote.  Allocating seats based on the proportion of the vote in a region will affect the proportionality of a system.  Assigning party list seats allocated based on a province-wide vote to regions after the fact runs the risk that a party will not receive enough list seats to boost its representation in regions that are underrepresented.  I will explore both scenarios in my next post.

2017 MMP Break Down of Party Seats

MMP does well to provide representation in the legislature that is proportional to parties’ votes.  Increasing the size of ridings, however, leads parties to be over-represented relative to their vote share in the regions they are strongest and under-represented in the regions they are weakest.  As I’ve written about in the past this is also something the happens in first past the post, though not quite to the same degree.  Under the current system, the BC Liberals, for example, are under-represented in places where they are weak, like Vancouver Island.  However, unlike under the MMP simulations, they do win the odd seat there.  This within party regional disproportionality is not something that is universal to all proportional systems.  In my next two posts I will look at proportionality and regional party support in dual member proportional and rural urban proportional systems.  The regional breakdown of party caucuses in these systems will get a lot closer to regional breakdowns of party votes.

*I left some large rural ridings as they are under first past the post.  This would likely occur under MMP as there is a limit to how geographically large one can make a riding before it becomes too big for one person to reasonably represent it.

** Data for elections results comes from BC Pundit’s Guide.


Elections Without Parties are No Fun: Why Victoria Municipal Elections Would Benefit from Political Parties

On October 20th Victoria residents, and residents across British Columbia, will vote in municipal elections.  In Victoria 10 candidates are running for mayor and 29 are running for 8 seats on city council.  Unlike in federal or provincial elections (or in Vancouver’s municipal elections) most are running as independents.  No candidates are running as part of a party with an organization that stays consistent from election to election.  One mayoral candidate and seven council candidates are running on one of two different slates (alliances between candidates that are like parties but that tend not to last from election to election).  The lack of parties in Victoria elections is a problem.  It makes it harder for voters to learn about the positions and records of different candidates and to determine which candidates are competitive.

Parties play a central role organizing candidates in elections.  They develop a common platform that voters can use to get a sense of where each candidate stands on the major issues.  In federal or provincial elections knowing that a candidate is running for the NDP, the Liberals, the Greens, or (in federal elections) the Conservatives allows voters to connect a candidate to a particular set of policies even if they do not get the opportunity to interact with a candidate.  Absent parties, voters have to sift through the policy profiles of a wide range of independent candidates trying to make sense of 20 or 30 different sets of policy ideas instead of a more manageable 3 or 4.

It is also useful to voters that parties develop records of passing different policies and delivering on particular policies.  Voters can use these records to get a sense of what parties will do in should their members be elected to office.  The fact that the NDP has a history of investing in government services allows voters to know that if they vote for an NDP candidate they will probably get an MLA or MP that supports such policies.  The same is true with respect to tax cuts and BC Liberal or federal Conservative candidates.  It is harder to make these determinations for independent candidates.  Independent incumbents have a record that can be judged, but tracking the voting records of 8 independent candidates is a much more time-consuming task than tracking two or three parties.  Non-incumbent independents have no record to campaign on, and so are at a disadvantage when trying to demonstrate to voters that they can credibly deliver on their promises.  Non-incumbent parties may have been in government in the past, so voters may still have a record to judge them on even if they are not the incumbent.

Parties can further help voters make decisions by staking out clear ideological positions.  Even if a voter does not know exactly where they stand on tax policy or on housing policy, voters might have an understanding that they generally prefer policies on the centre-left or centre-right of the spectrum.  Parties allow voters to use ideology as a short-cut to determine which candidates will pursue the general policy profile they prefer.  This assumes less knowledge on the part of voters, but that is not unreasonable.  It is likely asking too much to expect voters to become experts on the details of housing and zoning policy, transit policy, or the optimal way to levy property taxes.  These are issues that think tanks and policy analysis devote a great deal of time and expertise to understanding.  It is unreasonable to expect voters who have no training in policy analysis and have their own jobs, family commitments, and other demands on their time to try to distinguish between the often very similar policy commitments put forward by independent candidates.  This is not to say that parties should not put forward detailed policy platforms or that voters should not scrutinize them.  It is to argue, though, that voters should also be provided with short cuts that help them to sift to what is often a lot of reasonably detailed information about policy debates that they have limited expertise in.  A party affiliation gives voters more information about a candidate and that extra information can be useful to those struggling to make a decision.

Parties finally offer a way for candidates to coordinate.  This is particularly important in plurality electoral systems (like Victoria’s) where candidates win simply by having more votes than their competitors (as opposed to based on their proportion of the total vote or on a ranked ballot).  In these systems if too many similar candidates run they can wind up slitting the votes of those who prefer their policies.  This can lead to candidates that advocate a particular set of popular policies losing to candidates who prefer less popular policies if the voters who prefer the less popular policies are better at coordinating their votes.  This is particularly likely if there are a large number of candidates running on the popular policies and a small number running on the less popular ones.  In plurality systems voters need to strategically vote to avoid this vote splitting, but without parties, it is very hard to know who to strategically vote for.

Parties help solve coordination problems.  First, by limiting the number of candidates that they nominate, they reduce the number of candidates on any one side of the political spectrum.  This in turn reduces the likelihood of vote splitting.  Second, voters can use parties’ past results (as well as any polling) to determine which parties are likely to be competitive.  A voter that knows that there are two or three parties that tend to finish first or second from election to election can make a careful choice between those two or three parties.  Knowing that other candidates are unlikely to be successful helps a voter to avoid “wasting” their vote by casting a ballot for a candidate that will finish so far behind the others that a vote for them will have no impact on the election result.

One should not assume that voters have an infinite amount of time and resources to become informed about politics.  The easier it is for voters to become reasonably well informed about the differences between candidates, the more people will vote in elections.  The more people vote, the more representative governments will be.  Parties make it easier for voters to become informed and therefore have an important role to play in our democracy.  Municipal elections in Victoria would be better off with parties.


Sorted Voters: A Look at How Competitive Individual Ridings Were in the Quebec Election

The October 1st Quebec election was a historic one.  The Coalition Avenir Quebec (CAQ) became the first party other than the Liberals and Parti Quebecois to win government in the province since the 1966 election.  The Liberals won a lower share of the vote than in any election since confederation.  Meanwhile, the Parti Quebecois won a lower vote share than any time in their history, ended up with the 4th largest number of seats, and failed to get official party status.  In light of all of this it is worth looking at how competitive the election was at the riding level.  One would think that the rise of two new parties, the CAQ and Quebec Solidaire, would lead to a number of close races.  It did not.  The only election in the 1990s, 2000s, or 2010s that saw fewer close races was the 1998 election.  Also troubling is the disproportionate number of uncompetitive ridings in two parts of the province, Montreal and Outaouais (the region surrounding Gatineau).

Understanding the number and location of competitive ridings is important to understanding parties’ incentives to respond to voters.  In first past the post systems, parties have incentives to be most responsive to voters on the fence in competitive ridings.  Parties have no incentive to be responsive to voters in ridings they are very likely to lose because winning a few extra votes in such ridings will not prevent them from losing.  Similarly, they have only limited incentives to pay attention to voters in the ridings they win by large margins because losing a few extra votes in those ridings will not cause them to lose the ridings.  Because of this, the fewer ridings that are competitive, the fewer voters parties will focus on when campaigning, and the fewer voters’ interests will be taken into account when parties are governing.  Additionally, parties and governments are more likely to be concerned with voters’ interests in a particular part of the province or country if that region has a large number of close ridings.

When it comes to riding competitiveness, the 2018 Quebec result was not encouraging.  One might have expected the increased fragmentation caused by the emergence of the CAQ and Quebec Solidaire to lead to more close races.  Instead, only 18 of the 125 ridings saw margins of victory that were within 5 percentage points.  Only 32 ridings saw margins of victory that were within 10 percentage points.  The graph below shows that the only election between 1989 and 2018 with few ridings with margins of 5 percentage points or less was the 1998 election.  There has not been an election since 1989 with fewer races that had margins with 10 percentage points.

Number of Close Ridings Across Quebec

It is also important to note the extent to which uncompetitive ridings tend to be geographically concentrated.  The graph below shows the percentage of ridings in all elections from 1989 to 2018 that are uncompetitive.  It breaks these ridings down into 10 areas in Quebec.  Which riding fits into which area can be found here.  Graphs at the very bottom of this post show the percentage of competitive ridings in each area broken down by each election.

Percentage of Competitive Ridings (1989 to 2018)

The graph shows that the areas of Quebec with the least competitive ridings are in Montreal and the Outaouais region.  The eastern half of Montreal is less competitive than the rest of the province, though not drastically so.  Between 1989 and 2018 its percentage of ridings with a margin under 5 points is 5 points lower than the province as a whole.  Its percentage of ridings within 10 percentage points is just under 10 percentage points lower.  The western half of Montreal and Outaouais are very substantially less competitive.  In both regions, fewer than 5% of ridings have had races that have been decided by a margin of less than 5 percentage points and just over 10% have seen margins of victory within 10 percentage points.  In Western Montreal that works out to just 5 races out of the 127 that took place between 1989 and 2018 having a margin of victory within 5 points.  In Outaouais there were just 2 out of 45.

The lack of competitiveness in Western Montreal can be underscored by the average margin of victory in the area.  The graph below shows that candidates in Western Montreal have been winning their ridings by an average of 40 percentage points since the 1994 election.  Even uncompetitive Outaouais does not come close to those margins of victory, it only breaks an average margin of 40 percentage points in two elections.  The eastern half of Montreal is much closer to the rest of Quebec, though it rarely has a lower average margin of victory than the rest of the province.

Average Margin of Victory over Time

That these regions stand out as uncompetitive in Quebec is more problematic when one considers the demography of the areas.  Western Montreal is one of the most Anglophone parts of the province.  Montreal as a whole is probably the most ethnically diverse and has the largest immigrant population in the province.  Outaouais’ proximity to Ottawa makes it one of the most federalist regions of Quebec.  Large victories, most often for the Liberal party, mean parties (including the Liberals) have a weak incentive to respond to the interests of voters in these important communities.  The concentration of uncompetitive ridings in these regions not only decreases regional representation within the National Assembly but also hurts the representation of linguistic and ethnic diversity.

It is important to note here that this these effects are not a result gerrymandering.  Quebec’s ridings are relatively square-ish, suggesting little effort on the part of electoral boundaries’ commissions to try to pack Anglophones, immigrants, or Liberal voters in particular ridings.  Rather this a result of the combination of Anglophone and immigrant voters’ geographic concentration coupled with their strong support for the Quebec Liberal party.

There is a general concern in both American and Canadian elections that voters are starting to “sort” themselves geographically in a way that is decreasing the competitiveness of elections.  There is not enough of a pattern over the last few elections to suggest that this is a trend in Quebec, but the large number of uncompetitive ridings in the 2018 election should raise concerns.  The location of these ridings should also be of concern.  Unlike in federal elections, where the high competitiveness of culturally diverse ridings increases parties’ responsiveness to minorities, the low competitiveness of parts of the province with linguistic and cultural minorities is likely to hurt the representation of diversity in Quebec politics.

Ridings Within 5 By Region (2010s)

Ridings Within 5 By Region (2000s)

Ridings Within 5 By Region (1990s and 89)