BC: Sticking with FPTP

I thought it would at least be close. It was not.

61.3% of voters in British Columbia voted to keep the FPTP system.

In the (now moot) second ballot question, MMP was favored over the other options, on 41.2%, with DMP a (surprising?) second on 29.5% and RUP on 29.3%. A total of 831,760 votes were cast in the second question, versus 1,380,753 in the main question. So fully 40% of voters did not answer the “what if” question.

The second question permitted a ranking of choices on the three alternatives. In the redistribution of preferences, MMP won with 63.05% (of 779,698 votes).

In 2009, I wrote a post entitled “BC: FPTP forever?” And then the question of change came up again a mere nine years later. But this is a pretty decisive defeat. I know forever is a long time. But it seems unlikely for proportional representation to get another chance anytime soon.

Is AV just FPTP on steroids?

In debates over electoral systems in Canada, one often hears, from otherwise pro-reform people, that a shift to the alternative vote would be worse than the status quo. It is easy to understand why this view might be held. The alternative vote (AV), also known as instant runoff (IRV), keeps the single-seat districts of a system like Canada’s current first-past-the-post (FPTP) system, but replaces the plurality election rule in each district with a ranked-ballot and a counting procedure aimed at producing a majority winner. (Plurality winners are still possible if, unlike in Australia, ranking all candidates is not mandatory. The point is that pluralities of first or sole-preference votes are not sufficient.)

Of course, the claim that AV would be FPTP on steroids implies that, were Canada to switch to AV, the current tendency towards inflated majorities for a party favored by less than half the voters would be even more intensified. This is plausible, inasmuch as AV should favor a center-positioned party. A noteworthy feature of the Canadian party system is the dominance, most of the time, by a centrist party. This is unusual in comparison with most other FPTP systems, notably the UK (I highly recommend Richard Johnston’s fascinating book on the topic). The party in question, the Liberal Party, would pick up many second preferences, mainly from the leftist New Democratic Party (NDP) and so, according to the “steroids” thesis, it would thus win many more seats than it does now. It might even become a “permanent majority”, able to win a parliamentary majority even if it is second in (first-preference) votes to the Conservatives (who thus win the majority or at least plurality of seats under FPTP). The “steroids” claim further implies that the NDP would win many fewer seats, and thus Canada would end up with more of a two-party system rather than the multiparty system it has under FPTP.

There is a strong plausibility to this claim. We can look to the UK, where AV was considered in a referendum. Simulations at the time showed that the Liberal Democrats would stand to benefit rather nicely from a change to AV. While the LibDems are a third party, heavily punished by the FPTP electoral system even when they have had 20% or so of the votes, what they have in common with the Canadian Liberals is their centrist placement. Thus, perhaps we have an iron law of AV: the centrist party gains in seats, whether or not it is already one of the two largest parties. An important caveat applies here: with the LibDems having fallen in support since their coalition with the Conservatives (2010-15), the assumptions they would gain from AV probably no longer apply.

On the other hand, we have the case of the Australian House of Representatives, which is elected by AV. There, a two-party system is even stronger in national politics than in the FPTP case of the UK, and far more so than in Canada. (When I say “two party” I am counting the Coalition as a party because it mostly operates as such in parliament and its distinct component parties seldom compete against one another in districts.)

It is not as if Australia has never had a center-positioned party. The Australian Democrats, for example, reached as high as 11.3% of the first-preference votes in 1990, but managed exactly zero seats (in what was then a 148-seat chamber). Thus being centrist is insufficient to gain from AV.

Nonetheless, the combination of centrism and largeness does imply that Canada’s Liberals would be richly rewarded by a change to AV. Or at least it seems that Justin Trudeau thought so. His campaign promised 2015 would be the last election under FPTP. While he did not say what would replace it, he’s previously said he likes a “ranked ballot” and he pulled the plug on an electoral-reform process when it was veering dangerously towards proportional representation.

Still, there are reasons to be somewhat skeptical, at least of the generalization of the Australian two-party experience. The reasons for my caution against the “steroids” view are two-fold: (1) the overlooked role of assembly size; (2) the ability of parties and voters to adapt.

Assembly size is the most important predictor of the size of the largest party, disproportionality, and the effective number of seat-winning parties in countries that use single-seat districts. (It is likely relatively less important when there are two rounds of voting, as in France, but still likely the most important factor.) This is a key conclusion of Votes from Seats. It is thus important not to overlook the fact that Australia has an assembly size considerably smaller than Canada’s. In the book, Taagepera and I show that Australia’s effective number of seat-winning parties and size of largest parliamentary party are almost what we would expect from its assembly size, even if FPTP were used. (See also this earlier post and its comment thread; how close it is to expectation depends on how we count what a “party” is.) The data are calculated over the 1949-2011 period, and the effective number of parties has been just 1.10 times the expectation from the Seat Product Model (which is based only on assembly size when single-seat districts are used). Similarly, the average largest party has been 93% of the expected size (averaging 54.2% of seats when we would expect 50.5%).

Thus we do not need to invoke the alleged steroids aspect of AV to understand the dominance of two parties in Australia. But this does not mean it would not make a difference in Canada. Consider that the current effective number of parties and size of the largest party in that country, averaged over a similar period, are also just about what we should expect. The multipartism, including periodic minority governments, that characterize Canada are not surprising, when you use the Seat Product Model (SPM). They are surprising only if you think district magnitude is all that matters, and that FPTP is FPTP. But it isn’t! An electoral system using the FPTP electoral rule with an assembly of more than 300 seats is a different, and more multiparty-favoring, electoral system than one with 150 seats. Replace “FPTP” in that sentence–both occurrences–with “AV” and it is surely still true.

But what about the centrist party, the Canadian Liberals? Surely AV would work differently in this context, and the Liberals would be a much more advantaged party. Right? Maybe. If so, then it would mean that the SPM would be overridden, at least partially, in Canada, and the largest party would be bigger than expected, for the assembly size, while the effective number of parties would be lower than expected. Of course, that’s possible! The SPM is devised for “simple” systems. AV is not simple, as we define that term. Maybe the SPM is just “lucky” that the one country to have used AV for a long time has the expected party system; or it is lucky that country has the “correct” assembly size to sustain two-party dominance. (Australia is the Lucky Country, after all, so if the SPM is going to get lucky one place, it might as well be Australia.)

This is where that other factor comes in. While no one has a crystal ball, I am going to go with the next best thing. I am going to say that the SPM is reliable enough that we can predict that, were Canada to have AV, it would have an effective number of parties around 2.6 and a largest party with around 48% of seats. In other words, just about where it has been for quite some time (adjusting for the House size having been a bit smaller in the past than it is now). Note these are averages, over many elections. Any one election might deviate–in either direction. I won’t claim that a first election using AV would not be really good for the Liberals! I am doubting that would be a new equilibrium. (Similarly, back in 2016 I said my inclination would not be to predict the effective number of parties to go down under AV.)

Parties and voters have a way of adapting to rules. Yes the Liberals are centrist, and yes the Conservatives are mostly alone on the right of the spectrum (albeit not quite as much now, heading into 2019, as in recent years). But that need not be an immutable fact of Canadian politics. Under AV, the Liberals might move leftward to attract NDP second preferences, the NDP center-ward to attract Liberal and even Conservative second preferences, the Conservatives also towards the center. It would be a different game! The Greens and other parties might be more viable in some districts than is currently the case, but also potentially less viable in others where they might win a plurality, but struggle to get lower ranked preferences. The point is, it could be fluid, and there is no reason to believe scenarios that have the largest party increasing in size (and being almost always the Liberals), and correspondingly the effective number of parties falling. With 338 or so districts, likely there would remain room for several parties, and periodic minority governments (and alternations between leading parties), just as the SPM predicts for a country with that assembly size and single-seat districts.

As I have noted before, it is the UK that is the surprising case. Its largest party tends to be far too large for that huge assembly (currently 650 seats), and its effective number of seat-winning parties is “too low”. Maybe it needs AV to realize its full potential, given that the simulations there showed the third party benefitting (at least when it was larger than it’s been in the two most recent elections).

Bottom line: I do not buy the “FPTP on steroids” characterization of AV. I can understand were it comes from, given the presence in Canada of a large centrist party. I just do not believe Liberal dominance would become entrenched. The large assembly and the diversity of the country’s politics (including its federal structure) both work against that.

I agree with electoral reformers that PR would be better for Canada than AV. I also happen to think it would be better for the Liberals! But would AV be worse than FPTP? Likely, it would not be as different as the “steroids” claim implies.

Is rural-urban PR gaining on MMP?

In the British Columbia mail-in referendum, the most likely option to win, should change from FPTP be endorsed, has seemed to be Mixed-Member Proportional (MMP). However, a poll from Mainstream BC, released on Nov. 8, suggests that one of the other options could be gaining.

The one that looks close, at least in this poll, is Rural-Urban PR (RUP). I reviewed all of the proposals before, and so will only briefly describe the RUP system here: It would be Single Transferable Vote (STV) for most of the province, but MMP in rural areas. The proposal is meant to address concerns that rural districts (ridings) would have to be too large if STV were used in the entire province, while still giving the rural interior a reasonable degree of proportionality.

This poll shows that on the critical first question, whether to keep FPTP or move to PR, the BC Interior prefers the status quo, 53.3% to 46.7%. Metro Vancouver voters only narrowly favor PR (50.1%), while Vancouver Island favors PR by a slightly wider margin (52.7%). The regional samples are small, so should be treated with caution. Nonetheless, they are suggestive of skepticism of PR in rural areas, exactly what the RUP proposal is meant to address. Overall, it is way too close to call: 50.5% for keeping FPTP, 49.9% for PR.

It is on preference over PR systems that we see the most interesting divide. According to this poll, MMP leads by a wide margin in Metro Vancouver: 50.4% to 32.2% for RUP and 17.4% for the third option, Dual-Member PR (DMP). On Vancouver Island, it is similar, but tighter: 40.4%, 38.3%, 21.3% (this is just 86 respondents). In BC Interior, however, the poll gets RUP on 49.5%, then MMP 37%, and DMP just 13.5%.

Overall, this still puts MMP in front, given the greater population of Vancouver: 44.8%, 38.2%, 17.0%.

It could be that RUP is gaining, as earlier polls had it and DMP both far behind MMP. There is an on-line presence for a specifically pro-RUP effort (“YUP for RUP”). There is some expressed support for RUP, for instance by Andrew Coyne in the National Post. He says he favors it “mostly for the STV part.”

It would be very interesting if RUP ended up winning, but on the strength of rural voters who, were it chosen, would vote by MMP, while Vancouver voters (who would vote by STV) had majority-preferred MMP but would get STV. OK, that was convoluted, but that is the point. It is not a likely outcome, but it is at least possible, provided it is really close in Vancouver and there is a decisive turn towards RUP in rural areas. And would be interesting!

The choice of PR model, if PR defeats FPTP in the first question, will be determined by province-wide alternative vote (the second question is a ranked ballot). So, it would be good to know what DMP supporters’ second choice tends to be. I would guess MMP, but that is just that–a guess. It probably depends on which feature of DMP that minority likes best–all members elected in local districts (for which STV would seem to beat MMP) or province-wide proportionality (for which MMP is clearly better than RUP).

A final note from the poll: It has 963 total respondents, but only 440 for the second question. So lots of voters may be planning to skip the question on choice of models. It is unclear whether that is because those who want FPTP are not weighing in at all, or because of pro-PR canvassers saying things like “if you are confused about the second part, you can skip it” (which I heard in my brief observation of campaigning).

Correction on BC’s MMP proposal

I realized only today that I had misread the proposal for the Mixed-Member Proportional (MMP) system in the British Columbia Attorney General’s report on the options. [Or maybe not, after all: See Wilf’s comment.]

I had thought the compensation would play out only in regions, as is the case in Scotland. I based this on the phrase in the report that says, “the List PR seats are allocated on a regional basis rather than a province-wide basis.” However, somehow I missed the clear statement in the preceding paragraph of the report, where it says, “The overall share of seats each party holds in the Legislative Assembly is determined by the party’s share of the province-wide vote it receives.”

In other words, the regions would affect only which specific candidates are seated from the compensatory (“top-up”) lists, and thus the regional balance of each party’s caucus. They would not affect the number of such seats a party wins overall.

The provision also makes workable the possible open list, which is given as an option to be worked out post-referendum, but which the Premier has said he will ensure is chosen rather than a closed list. If the lists were province-wide, open lists would make for more cumbersome ballots and arguably excess choice (as well as failing to ensure regional balance in the assembly).

The details of how one balances province-wide proportionality with open regional lists are complex. It is the system in Bavaria, however, so it is not unproven.

I have corrected my two previous entries on this accordingly:

1. BC electoral reform options for referendum

2. What can we expect from electoral reform in BC?


Open lists in MMP: An option for BC and the experience in Bavaria

One of the options for electoral reform in British Columbia is mixed-member proportional (MMP) representation. The criteria for the potential system allow for a post-referendum decision (if MMP is approved by voters) on whether the party lists should be open or closed. The guide that was sent to all BC voters shows a mock-up of a ballot that looks like New Zealand’s, with closed lists. However, the provincial premier has stated that, if MMP is adopted, lists will be open.

When it comes to lists, it is my opinion that citizens will elect all of the members of the legislature. They will select names that are representative of their communities.

I remain uncertain about the value of open lists under MMP. Is it worth the extra ballot complexity? What additional gain does one get from having preference votes determine order of election for those winning compensatory seats? The MMP Review in New Zealand after the 2011 referendum (in which voters voted to keep MMP) looked at this question extensively. It came down firmly on the side of keeping lists closed.

Nonetheless, the statement by the premier suggests he believes the system is less likely to be chosen if voters expect the lists to be closed. And, given regional districts on the compensation tier, as explicitly called for in the system proposal, the lists would not be too long and thus the ballots not too complex.

It happens that there is one MMP system in existence in which the lists are open. Such a system has been used in Bavaria for quite some time. I actually proposed such a model in a post way back in 2005, quite early in the life of this blog. At the time I had no idea that what I had “invented” was, more or less, the existing Bavarian model.

Of course, Bavaria just had an election. In the thread on that election, Wilf Day offered some valuable insights into how the open lists worked. I am “promoting” selections from Wilf’s comments here. Indented text in the remainder of this post is by Wilf.

The Bavarian lists are fully “open,” and the ballot position has no bearing on the outcome, except to the extent the voters are guided by it, especially seen in voting for the number 1 candidate.

Of the 114 list seats, 31 were elected thanks to voters moving them up the list, while 83 would have been elected with closed lists.

Did the first on the list always get elected? Almost. In the region of Lower Bavaria, the liberal FDP elected only 1 MLA, and he had been second on their regional list.

Did the open lists hurt women? I did not check most results, but the SPD zippers their lists, and I noticed in Upper Palatinate the SPD elected 2 MLAs, list numbers 1 and 3 (two women). Conversely, in Middle Franconia the SPD elected 4 MLAs: 1, 2, 3, and 5 (three men).

Little known fact: a substantial number of voters in Bavaria, being used to voting in federal elections where their second vote is just for a party, blink at the Bavarian ballot, look for the usual space to vote beside the party name, it’s not there, so they put an X beside the party name anyway. A spoiled ballot? No, they count it as a vote for the party. Not a vote for the list as ranked, it does not count for the ranking or for any candidate, but it does count in the party count. Just like Brazil, where a vote for the party is not a vote for the list ranking, except Bavaria does not publicize the option of voting for the party.

Among the more interesting new Free Voter MLAs:

Anna Stolz, lawyer, Mayor of the City of Arnstein; she had been elected Mayor in 2014 as the joint candidate of the Greens, SPD, and Free Voters; the local Greens said they were very proud of her as Mayor. The Free Voter delegates meeting made her number 5 on the state list, but the voters moved her up to second place as one of the two Free Voter MLAs from Lower Franconia.

From Upper Bavaria, the capital region, list #12 was Hans Friedl, with his own platform: “a socially ecologically liberal voice, an immigration law based on the Canadian model, no privatization of the drinking water supply, a clear rejection of the privatization of motorways”). The voters moved him up to #8, making him the last of 8 Free Voters elected in that region.

Note: the comments are excerpted, and the order of ideas is a little different from where they appear in the thread. I thank WIlf for his comments, and for his permission to make them more prominent.

Canadian provincial elections and the SPM: Those assemblies are too small

After posting my earlier overview of expectations from possible electoral reform in British Columbia, I was wondering how well the Seat Product Model has performed over time in Canadian provincial assembly elections. Spoiler alert: not nearly as well in the provinces as a whole as in BC, and better for votes than for seats. The latter is particularly puzzling; the model works by first estimating seats (which are more “mechanically” constrained by district magnitude and assembly size than are votes). That is why the book Rein Taagepera and I published in 2017 is called Votes from Seats. The key to the puzzle may be the serious under-sizing of Canadian provincial assemblies. As I will show in a table at the end of this entry, many provincial assemblies should be almost twice their current size, if we go by the cube root law.

I have a dataset originally constructed for my “to keep or change FPTP” project (published in Blais, ed., 2008). It has most provincial elections back to around 1960, although it stops around 2011. Maybe some day I will update it. For now, it will have to do.

The first graph shows the degree of correspondence between a given election’s observed effective number of vote-earning parties (NV) and the expectation from its seat product (i.e., for FPTP, the assembly size). The black diagonal is the equality line: perfect prediction would place an election on this line. The lighter diagonal is a regression line. Clearly, the mean Canadian provincial election exhibits NV higher than expected. On the other hand, the 95% confidence interval (dashed curves) includes the equality line other than very trivially near the middle of the x-axis range. Thus, in statistical terms, we are unable to reject the hypothesis that actual NV in Canadian provincial elections is, on average, as expected by the SPM. However, the regression-estimated line is systematically on the high side.

It might be noted that we never have NV expected to be 2.0, and in the largest provinces, the assemblies are large enough that we should expect NV>2.5. (“Large enough” here meaning independent of what they “should be”, by the cube root; this is referring only to actual assembly size.) So the classic “Duvergerian” outcome is really only expected in the one province with the smallest assembly. And such an outcome is more or less observed there, in PEI. Nonetheless, a bunch of elections are very much more fragmented than expected, with NV>3! And several are unexpectedly low; many of these are earlier elections in Quebec.

All individual elections are labelled; in a few cases the label generation did not work well (some elections in 2000s). The regression coefficient is significant, although the regression’s R2 is only 0.15. The basic conclusion is a marginally acceptable fit on average, but lots of scatter and some tendency for the average election to be more fragmented than expected.

Now, for the largest seat-winner in the assembly (s1). Here things get a little ugly.

This might be considered a rather poor fit. There is a systematic tendency for the largest party to be bigger than expected: note that the equality line is essentially never within the 95% confidence interval. When we expect, based on assembly size, the largest party to have 60% of the seats, it actually tends to have more like 68%. More importantly, the scatter is massive. In fact, the regression coefficient is insignificant here; please do not ask what the  R2 is!

The size of Canadian provincial parliaments is never so large that the leading party is expected to have only 50% of the seats (note the reference lines and where the equality line crosses the 50-50 point). Yet there is not a trivial number of elections with the largest party under 50%. More common, however, are the blowout wins, where the largest party has 80% or more of the seats. This has been a chronic feature of Canadian provincial politics, especially in a few provinces (notably Alberta, New Brunswick, and Prince Edward Island).

Why is Nv so much better predicted (even if not exceptionally well) than s1? It is hard to say. It is an unusual situation to have both NV and s1 trend higher than expected. After all, normally the more “significant” parties there are the smaller the largest party should tend to be. In the set of predictive equations, s1 (and the effective number of seat-winning parties, NS) are prior to NV, because the seat-based measures are more directly constrained. This is why the book is called Votes from Seats. In our diagram (p. 149) deriving the various quantities from the seat product, we show NV and s1 coming off separate branches from “Ns0” (the actual number of parties winning seats), which is expected to be (MS)0.25, where M is the magnitude and S the assembly size. Thus for FPTP, it is S0.25. A parliament with 81 seats is expected to feature three parties; the other formulas would predict that NS=2.08, s1=0.577, and NV=2.52. If the parliament had 256 seats, we would expect four parties, NS=2.52, s1=0.50, and NV=2.92.

Unfortunately, the dataset I am using does not (yet) have how many parties won seats–actual or effective number. Thus I can’t determine whether this is the point at which the connections get fuzzy in the Canadian provincial arena. Nonetheless, there should be a relationship between NV and s1. It can be calculated from the formulas displayed in Table 9.2 (also on p. 149). It would be:

s1=(NV1.5 -1)-0.5.

In this last graph, I plot this expectation with the solid dark line, and a regression on s1 and NV from Canadian provincial elections as the lighter line (with its 95% confidence intervals in dashed curves).

The pattern is obvious: there are many elections in Canadian provinces in which the leading party gets a majority or even 60% or 70% or more of the seats despite a very fragmented electorate. We should not expect a leading party with more than 50% of the seats when NV>2.92. And yet 17 elections (around 15% of the total) defy this logically derived expectation. Six have a party with 2/3 or more of the seats despite NV>2.92 (in order of increasing NV: BC91, AB04, NB91, QC70, AB67, BC72; in the last one, NV=3.37!).

I think the most likely explanation is Cube Root Law violations! Canadian provincial assemblies are much too small for their populations. So, the cause of the above patterns may be that voters in Canadian provinces vote as if their assemblies were the “right” size, but these votes are turned into seats in seriously undersized assemblies, which inflates the size of the largest party. (Yes, votes come from seats in terms of predictive models, but obviously in any given election it is the reverse!)

There is some support for this. I can calculate what s1 and NV would be expected to be, if the assemblies were the “right” size, which is to say the cube root of the number of voters (which is obviously smaller than the number of citizens, but this is what I have to work with). I will call these s1cr and NVcr. Then I can take ratios of actual s1 and actual NV to these “expectations”. The mean ratios are: NV/NVcr=0.994; s1/s1cr=1.19. If the assemblies were larger, the votes–already with a degree of fragmentation about as expected from more properly sized assemblies–would probably have stayed about the same. However, with these hypothetically larger assemblies, the largest party in parliament would be less inflated by the mechanics of the electoral system.

Canadian provinces would have a greatly reduced tendency to have lopsided majorities if only they would expand their assemblies up to the cube root of their active voting population. Of course, this assumes they stick to FPTP. The other thing they could do is switch to (moderately) proportional representation systems, like BC is currently considering. That would be seem to be a good idea regardless of whether they also correct their undersized assemblies.

Below is a table of suggested sizes compared to actual, for several provinces. (“Current” here is for the latest election actually in the dataset; some of these have been increased–somewhat–subsequently.)

Prov. Current S Increased S
Alberta 83 121
British Columbia 79 152
Manitoba 57 94
New Brunswick 55 91
Newfoundland 48 81
Nova Scotia 52 95
Ontario 107 208
Prince Edward Island 27 55
Quebec 125 197
Saskatchewan 58 95


(By the way, the R2 on that s1 graph that I asked you not to ask about? If you must know, it is 0.03.)


Why “voting system”?

In the earlier entry on the BC referendum, I quoted a passage from the ballot question. It uses the term, voting system.

Yes, “voting system” rather than “electoral system”. Why? What the voters are being asked to decide is clearly what we political scientists mean by electoral system. Is there something objectionable about that term to the general public?

I do not ever use the term, voting system. However, if I did, I would probably understand it to mean the ballot format and other aspects of the process of casting a vote. I would not understand it to include how seats are allocated. An electoral system, as I understand it, is a set of rules that govern voting, counting, and allocation. A whole electoral system is assembly size, district magnitude, tier structure (if not “simple” single-tier), and the specific seat-allocation rule (edit: and the ballot structure). The BC proposals cover all these aspects. It clearly is a referendum on the electoral system. Yet it is officially, “a referendum on what voting system we should use for provincial elections.”

I find it puzzling, although not troubling in any sort of way. (Now, if the term starts creeping into political science, I reserve the right to object.) On the other hand, proponents of change in Canada seem to prefer to call proportional representation “ProRep” rather than PR. I can kind of understand that (“PR” means public relations to civilians). Whenever I see “ProRep” I flinch just a little. But if calling it that helps sell it, I can get over it.