Canada and UK 2019: District level fragmentation

With two of the big Westminster parliamentary democracies having had general elections in 2019, we have a good opportunity to assess the state of district-level competition in FPTP electoral systems.

(Caution: Deep nerd’s dive here!)

Before we turn to the district level, a short overview of what is expected at the national level is in order.

As noted previously, Canada’s election produced a nationwide seat balance that was extremely close to what we expect from the Seat Product Model (SPM), yet the nationwide votes were exceedingly fragmented (and, anomalously, the largest seat-winning party was second in votes). The UK election, on the other hand, was significantly less fragmented in the parliamentary outcome than we expect from the SPM, even if it was in key respects a “typical” FPTP outcome in terms of manufacturing a majority for a party with less than a majority of the vote.

In general, over decades, Canada tends to conform well to the SPM expectation for the shape of its parliamentary party system, whereas the UK is a more challenging case from the SPM’s perspective.

The SPM states that the effective number of seat-winning parties (N_S) should be the seat product, raised to the power, 1/6. The seat product is the assembly size, times the mean district magnitude. The SPM predictions for N_S explain around 60% of the variance in actual outcomes for elections around the world under a wide variety of electoral systems. SPM predictions for other output quantities also explain in the neighborhood of 60%. So the SPM is both successful at explaining the real world of seat and vote fragmentation, and leaves plenty of room for country-specific or election-specific “other factors” (i.e., the other 40%). The SPM is based on deductive logic, starting from the minimum and maximum possible outcomes for a given number of seats at stake (in a district or an assembly). The logic is spelled out in Votes from Seats.

In the case of a FPTP system, the SPM makes the bold claim that we can understand the shape of a party system by knowing only the assembly size. That is because with district magnitude, M=1, the seat product is fully described by the country’s total number of seats, S, which is also the number of districts in which the voting is carried out. Thus we expect N_S=S^1/6. Let’s call this “Equation 1.”

For Canada’s current assembly size (338), this means N_S=2.64, as an average expectation. Actual elections have tended to come pretty close–again, on average. Of course, individual elections might vary in one direction or the other. (The assembly size was also formerly smaller, but in recent times, not by enough to concern ourselves too much for purposes of this analysis.) For the UK, the corresponding expectation would be 2.94 based on a seat product of 650.

The actual Canadian election of 2019 resulted in N_S=2.79; for the UK it was 2.39. Thus for Canada, we have a result very close to the expectation (ratio of actual to expected is 1.0578). For the UK, the actual result was quite short (ratio of 0.8913). As I said, the UK is a challenging, even aberrant, case– at least at the national level.

What about the district level? A national outcome is obviously somehow an aggregation of all those separate district-level outcomes. The SPM, however, sees it differently. It says that the districts are just arenas in which the nationwide election plays out. That is, we have a logical grounding that says, given a national electoral system with some seat product, we know what the nationwide party system should look like. From that we can further deduce what the average district should look like, given that each district is “embedded” in the very same national electoral system. (The logic behind this is spelled out in Votes from Seats, Chapter 10).

The crazy claim of the SPM, district-level extension, is that under FPTP, assembly size alone shapes the effective number of votes-earning parties in the average district (N’_V, where the prime mark reminds us that we are talking about the district-level quantity rather than the nationwide one). (Note that for FPTP, it must be the case that N’_S=1, always and in every district).

The formula for expected N’_V under FPTP is: N’_V=1.59S^1/12 (Equation 2). It has a strictly logical basis, but I am not going to take the space to spell it out here; I will come back to that “1.59” below, however. It is verified empirically on a wide set of elections, including those from large-assembly FPTP cases like Canada, India, and the UK. So what I want to do now is see how the elections of 2019 in Canada and UK compare to this expectation. (Some day I will do this for India’s 2019 election, too.)

If the effective number of seat-winning parties at the national level (N_S) is off, relative to the SPM, then it should be expected that the average district-level effective number of vote-earning parties (N’_V) would be off as well. They are, after all, derived from the same underlying factor–the number of single-seat districts, i.e., the assembly size (S). We already know that N_S was close to expectation in Canada, but well off in the UK in 2019. So how about the districts? In addition to checking this against the expectation from S alone, we can also check one other way: from actual national N_S. We can derive an expected connection of N’_V to N_S via basic algebra. We just substitute the value from one equation into the other (using Equations 1 and 2). If we have N_S=S^1/6 then it must be that S= N_S⁶. So we can substitute:

N’_V=1.59(N_S⁶)^1/12= 1.59√N_S (Equation 3).

In a forthcoming book chapter, Cory L. Struthers and I show that this works not only algebraically, but also empirically. We also suggest a logical foundation to it, which would require further analysis before we would know if it is really on target. The short version suggested by the equation is that the voting in any given district tends to be some function of (1) the basic tendency of M=1 to yield two-candidate competition (yes, Duverger!) in isolation and (2) the extra-district viability of competing parties due to the district’s not being isolated, but rather embedded in the national system. The 1.59, which we already saw in Equation 2, is just 2^2/3; it is the expected N’_V if there were exactly two vote-earning parties, because it is already established–by Taagepera (2007)–that the effective number tends to be the actual number, raised to the power, two thirds. And the square root of N_S suggests that parties that win some share of seats (i.e., can contribute more or less to the value of N_S) tend to attract votes even though they may have no chance of winning in any given district. By having some tendency to attract votes based on their overall parliamentary representation, they contribute to N’_V because voters tend to vote based on the national (expected, given it is the same election) outcome rather than what is going on in their district (about which they may have poor information or simply not actually care about). If the parliamentary party system were fully replicated in each district, the exponent on N_S would be 1. If it were not replicated at all, the exponent would be zero. On average, and in absence of any other information, it can be expected to be 0.5, i.e., the square root.

How does this hold up in the two elections we are looking at in 2019? Spoiler alert: quite well in the UK, and quite badly in Canada. Here are graphs, which are kernel density plots (basically, smoothed histograms). These plots show how actual districts in each election were distributed across the range of observed values of N’_V, which in both elections ranged from around 1.35 to just short of 4.5. The curve peaks near the median, and I have marked the arithmetic mean with a thin gray line. The line of most interest, given the question of how the actual parliamentary outcome played out in each district is the long-dash line–the expected value of N’_V based on actual N_S. This corresponds to Equation 3. I also show the expectation based solely on assembly size (light dashed line); we already have no reason to expect this to be close in the UK, but maybe it would be in Canada, given that the actual nationwide N_S was close to the SPM expectation, based on S (Equation 2).

Here is the UK, then Canada, 2019.

What we see here is interesting (OK, to me) and also a little unexpected. It is the UK in which the actual mean N’_V is almost the same as the expectation from nationwide N_S (i.e., Equation 3). We have actual mean N’_V=2.485 compared to expected N’_V from actual N_S of 2.45; the ratio of actual to expected is 1.014. We can hardly ask for better than that! So, the nationwide party system (as measured by N_S) itself may be well off the SPM expectation, but the vote fragmentation of the average district (N’_V) closely tracks the logic that seems to stand behind Equation 3. Voters in the UK 2019 election tended to vote in the average district as if parties’ national viability mattered in their choice.

In Canada, on the other hand, even though national N_S was very close to SPM expectation, the actual average district’s N’_V (2.97) was really nowhere near either the expectation solely from S (the light dashed line, at 2.58) or the expectation from the actual N_S (2.66). The average district was just so much more fragmented than it “should be” by either definition of how things ought to be! (The ratio of actual to that expected from Equation 3 is 1.116; the Equation 3 expectation is almost exactly the 25th percentile of the distribution.)

The Canadian outcome looks as if the exponent on actual N_S in Equation 3 were around 0.64 instead of 0.5. Why? Who knows, but one implication is that the NDP (the third national party) performed far better in votes than the party’s contribution to N_S implies that it should have. Such an overvaluing of a party’s “viability” would result if voters expected the party to do much better in terms of seats than it did. This is probably a good description of what happened, given that pre-election seat extrapolations implied the NDP would win many more seats than it did (and the Liberals fewer). The NDP also underperformed its polling aggregate in votes (while Liberals over-performed), but it held on to many more voters than it “should have” given its final seat-winning ability would imply. That is, the actual result in votes suggests a failure to update fully as the parties’ seat prospects shifted downward at the very end of the campaign. In fact, if we compare the final CBC poll tracker and seat projections to the ultimate result, we find that their actual votes dropped by 13.6% but their seats dropped by 31.7% (percent change, not percentage points!). In other words, this was just an unusually difficult context for voters to calibrate the expectations that Equation 3 implies they tend to make. (I am assuming the polls were “correct” at the time they were produced; however, if we assume they were wrong and the voters believed them anyway, I think the implications would be the same.)

It should be understood that the divergence from expectation is not caused by certain provinces, like Quebec, having a different party system due to a regional party, as some conventional expectations might point towards. While Quebec’s size is sufficient to exert a significant impact on the overall mean, it is not capable of shifting it from an expected 2.6 or 2.7 towards an observed 3.0! In fact, if we drop the Quebec observations, we still have a mean N’_V=2.876 for the rest of Canada. The high fragmentation of the average district in the 2019 Canadian election is thus due to a Canada-wide phenomenon of voters voting for smaller parties at a greater rate than their actual viability would suggest they “should”. In other words, voters seem to have acted as if Trudeau’s promise that 2015 would be the last election under FPTP had actually come true! It did not, and the electoral system did its SPM-induced duty as it should, even if the voters were not playing along.

On the other hand, in the UK, voters played along just as they should. Their behavior produced a district-level mean vote fragmentation that logically fits the actual nationwide seat balance resulting from how their votes translated into seats under FPTP. There’s some solace in that, I suppose.

Canada 2019: Results and a good night for the Seat Product Model

Add Canada 2019 to the set of plurality reversals. As anticipated before the election, the two largest parties each ended up with around one third of the vote. This is the lowest vote percentage for a governing party in Canada ever, I believe. The seats are somewhat less close than the CBC’s Poll Tracker estimated they would be. Instead of 133 seats to 123, the seats split 157 to 121. The Liberals are indeed that largest seat-winner, despite trailing the Conservatives in votes percentage, 34.4 – 33.1.

The NDP was either overestimated by polls or, more likely, suffered some late strategic defection. Instead of the near 19% of the vote in the final Poll Tracker, the party ended up with only 15.9%. More importantly, its seats stand at only 24, well below where estimates late in the campaign had them (per the CBC Poll Tracker).

As excepted the BQ had a good night, with 32 seats. The Greens picked up one new seat to augment the two they already held. The new seat is Fredricton, New Brunswick, whereas the other two are both on Vancouver Island.

In what I will call the two best pieces of news form the night (other than there being no single-party majority), the People’s Party crashed and burned, winning only 1.6% and seeing its leader lose his seat. That and the fact that Jody Wilson-Raybould, the former Attorney General who was kicked out of the Liberal caucus, retained her seat, Vancouver-Granville, as an independent.

 

Anomalous FPTP

I will certainly use this result often as a demonstration of how the first-past-the-post (FPTP) system can produce strange results.

Not only the plurality reversal for the top two, but the differential treatment of the next three parties, show anomalies of the sort that are inherent to FPTP. The BQ is only somewhat larger in votes than the Green Party, but will have more than ten times the number of seats. Under FPTP, it is good to have efficient regional distribution of support, and getting all your votes in one province, where you perform exceptionally well, is really efficient. The Greens, on the other hand, gained in almost all provinces, but it was good enough to add only one seat.

The NDP’s situation is one of a quite strong third party, but also inefficient regional distribution: 7.1% of the seats on 16% of the votes is a punishing result, but nothing at all unexpected, given the electoral system.

For that matter, the plurality reversal is itself a signal of the problem of inefficient vote distribution. The Conservative Party mostly gained votes where they could not help the party win seats, whereas the Liberals were much more successful winning close contests.

In his victory speech, PM Justin Trudeau was bold enough to use the M-word (mandate), but this most certainly is not one. For the moment, he can be pretty happy he broke that promise on 2015 being the last FPTP election. His party remains in position to form the government, and has a substantial seat bonus. The advantage ratio (%seats/%seats) is 1.40. (How does that compare with past elections? Click to see.)

Canada would be well served by at least some degree of proportionality. In fact, so would the Conservatives, given their tendency to run up margins where they are already strong. (Note that they are only barely over-represented in seats, with 35.8%.) However, this result is unlikely to advance the cause of reform, as the Liberals’ position–46% of the seats and a 36-seat (more than ten percentage point) edge over the runner-up–looks quite solid.

The other reason the country could really use electoral reform is the map. There is no Liberal red to be seen from central Ontario westward, except around Vancouver (and two northern territories). The party lost some of its ministers’ reelection bids in Alberta and Saskatchewan. With even a minimally proportional system, the situation of a governing party without members of its caucus in nearly every province would not happen.

While a PR system would be beneficial, the country is stuck with FPTP at least for now. So how did this result compare to what we should expect from the electoral system actually in use?

 

The Seat Product Model and the outcome

The Seat Product Model (SPM) performed better than the CBC Poll Tracker’s seat estimator. For an assembly of 338 and districts with magnitude of 1, we should expect the largest party to have, on average, 48.3% of the seats, which would be 163 seats. So the actual result (46.4%) misses the expectation by 6 seats, or 1.78 percentage points (compared to the a 20-plus, or 6 percentage point, miss by the Poll Tracker).

Of course, the SPM has one advantage in its favor: it does not “know” that the seat-winning party would have under 33.3% of the vote, whereas the Poll Tracker must work with this expectation (and, as it turned out, reality). In fact, when a party wins 48.3% of the seats, the formulas of SPM (collected in Table 9.2 of Votes from Seats) expect it to have won 43.3% of the votes. (Theoretically, we do not expect the SPM to perform as well with votes as with the seats that are at its core; but in Votes from Seats, we show that, on average, it performs about equally as well with both.) The Liberals underperformed this expectation by more than ten percentage points! The voters genuinely voted for something their electoral system could not deliver, even if the system indeed delivered what should be expected solely on institutional grounds.

In terms of the effective number of seat-winning parties (N_S), the actual result was 2.79. This is slightly higher than the SPM expectation, which is 2.64. The miss is minor, with a result only 1.057 times expectation.

On the other hand, the effective number of vote-earning parties (N_V) was 3.79. The SPM expects 3.04. Let me pause and emphasize that point. Because Canada uses FPTP in a 338-seat assembly, we should expect the votes to resemble a “three-party system” and not the two-party system that all the conventional “Duvergerian” wisdom claims. If we calculated expected N_V based on the known N_S=2.79, we would expect N_V=3.17. However, neither the SPM nor Duverger’s “law” expects that the largest party nationwide should have only around a third of the votes. That is the really remarkable thing about this outcome.

 

The district level

At the district level, there were numerous non-Duvergerian outcomes, as would be expected with the known distribution of nationwide votes among parties. According to an extension of the SPM (in a forthcoming book chapter), we should expect the effective number of vote-earning parties at the average district (N’_V) to be 1.59 times the square root of the nationwide N_S. That would be 2.66. It will be a while before I am able to calculate what it actually was, but it would not surprise me if it was a fair bit higher than that. But, again, let me pause and say that a Duvergerian two-party competition at the district level is NOT to be expected, given both the nationwide electoral system and the actual aggregate seat outcome. (If we went off expected nationwide N_S, instead of the known outcome, the district-level mean still would be predicted to be 2.58; see Chapter 10 of Votes from Seats.) Canadian elections of the past several decades have tended to conform closely to this expectation for district-level N’_V.

The country does not tend to have two-party contests at district level, nor should it (when we have the Seat Product Model to guide our expectations). In other words, voters do not tend to vote in order to “coordinate” their district outcome around the two most viable candidates. They tend to vote more towards their expectation (or desire) about what the nationwide parliamentary outcome will be. This is so even in Quebec where, in this election, many Francophone voters returned to the regional party, the Bloc Québécois. Quebec has numerous district contests that feature three or four viable parties.

So if your image of Canada’s party system is that in Quebec districts it is BQ vs. Liberal, with other parties barely registering, while elsewhere it is Liberal vs. Conservative, except where it is one of those vs. NDP, it is well past time to update. Canada does not have nationwide multiparty politics because it has separate regional two-party systems (as many folks, even political scientists, seem to believe). Canada has district-level multipartism because it has nationwide multipartism. (See Richard Johnston’s outstanding book for a rich “analytic history” that supports this point.) And this may be even more true in the one province in which there is (again) a strong regional party. Consider the aggregate provincial outcome in terms of vote percentages in Quebec: Liberal 34.2% (slightly higher than nationwide), BQ 32.5%, Conservative 16.0%, NDP 10.7%, Green 4.5%. This gives a provincial-level N_V of 3.82, a bit higher than nationwide.

I will offer a few striking examples of multiparty contests at district level, just to illustrate the point. The new Green Party MP from Fredericton, Jenica Atwin, won 32.8% of the vote. The Conservative had 31.1%, the Liberal 27.3%, and the NDP 6.0%. There may indeed have been strategic voting happening here, with some NDP voters–the party had 9.9% in 2015–switching to Atwin to stop the Conservative (and perhaps some who don’t like the Greens boosting the Liberal). But the outcome here is N’_V=3.53!

The change from 2015 in Fredericton is really striking, as the Liberal candidate was an incumbent who had won 49.3% in 2015 (against 28.4% for the Conservative, meaning this party gained a little here in 2019). Clearly many Liberals defected from their party to the Green following that party’s success, including a local win, in the recent provincial election. In doing so they only narrowly avoided the serious “coordination failure” that would have been a Conservative win.

Another Green MP, the reelected Paul Manly in Nanaimo-Ladysmith, won 34.5%. This was actually a pretty clear victory despite being barely over a third of the vote; Manly had been elected in a by-election this past May with 37.3%. The runner-up Conservative had only 25.9% in the general election contest, the NDP 23.7%, Liberal 13.6%. N’_V=3.83!

Wilson-Raybould’s win in Vancouver-Granville as an independent was also with under a third of the vote. She had 32.3%, beating the Liberal’s candidate (26.6%) and the Conservatives’ (22.1%). The NDP candidate had 13.1%. The Greens, who tried to recruit Wilson-Raybould to be their candidate, put up their own against her, who got 5.0%. It should be noted that the NDP candidate in this riding last time won 26.9%, so it would appear there was ample strategic voting here in Wilson-Raybould’s favor. (She won 43.9% as the Liberal candidate in 2015.) The Green voters, on the other hand, did not seem to warm to their near-candidate; the party’s actual candidate did better in this district in 2019 than in 2015 (when the party got 3.1%).

One of my favorite cases is Sherbrooke, in Quebec. The winner was Liberal Elisabeth Briere with 29.3%, edging out an NDP incumbent who won 28.3% in this election. He had won the seat with 37.3% in 2015. Close behind in this year’s contest was the BQ candidate who had 25.8%. Following behind them was a Conservative (10.7%), and Green (4.5%). N’_V=4.06!! The Liberals won this by basically standing still in vote share, having lost this district by a wide margin in 2015 when their candidate had 29.8%.

A few interesting tidbits from candidate backgrounds. Bernier’s defeat in his own riding of Beauce was at the hands of a dairy farmer, Richard Lehoux. The Conservatives recruited him because of Bernier’s opposition to supply management policies in the dairy sector. (Info found in the CBC’s Live Blog.) Lehoux won only 38.6% of the vote, but it was sufficient to beat Bernier rather badly, as the latter (elected as a Conservative in 2015 and previously) had just 28.4%.

There were several mayors recruited to run, including a case in Quebec where the Conservatives hoped the candidate’s local popularity would overcome the party leader’s unpopularity. (The specific case was Trois-Rivières; the Conservative finished a close third in a riding the BQ candidate won with 28.5%.) There was also an Olympic medal-winning kayaker, Adam van Koeverden, whom the Liberals recruited in Milton (in Toronto, Ontario) to run against the Conservative Deputy Leader, Lisa Raitt. He defeated her–easily, winning 51.4% to her 36.5%. Presumably his celebrity (and perhaps his local roots, which he made a point to emphasize in an interview after his victory was confirmed) helped him win despite a nationwide swing against the Liberals and in favor of the Conservatives. (She had won 54.4% in 2015.) In other words, while I may emphasize that district politics under FPTP in a parliamentary system is mostly national politics, there is still plenty of room for local and personal factors to matter.

 

What it means for the near term

As to the shape of the government to result, it should be a reasonably stable minority government, although it may not last full term. It can form legislative majorities with either the BQ or the NDP, and thus need not be tied to either one in a coalition. And the NDP certainly is not strong enough to demand a coalition (even if it wanted to try). Nor is it likely strong enough to demand action on electoral reform, even if an election in which two thirds of the voters voted against the governing party, and various other aspects of the outcome can be seen as anomalous, suggests that reform is needed more than ever.

Canada 2019

It is the final Friday before Shemini Atzeret, also known as Election Day in Canada this year, And what an interesting campaign it has been! The polls have moved quite a lot, especially recently. The New Democrats (NDP) seem to be enjoying a surge. Not on anything like the scale of 2011, but still something notable, as it was not long ago that there was talk about the Greens possibly passing them for third place. The Greens have slipped somewhat, as has been the case in past campaigns. No longer do they look likely to win as many as four seats; two (which is their current number) looks most likely.

The striking thing is that the poll aggregate at CBC (compiled by Éric Grenier) shows both major parties–incumbent seat-majority Liberal and opposition Conservative) barely above 30% of the vote (31.7-30.8 at my latest check). From 1949 to present, the largest party has never had a vote percentage below 36.3% (in 2006). So if there is not a late surge of strategic voting, this will be quite a record-breaker.

Projecting seats under FPTP is always a challenge. The CBC Poll Tracker currently has the Liberals significantly favored, despite being marginally behind in votes, 133 seats to 123 (but with wide confidence bands on both).  That would be 39.3% of the seats for the largest party, which would also break the record (from 1949 on) set in 2006 (40.3%, or 124 in what was then a smaller parliament).

Despite being both a plurality reversal and a record low vote percentage (and an extremely close vote margin), the advantage ratio (%seats/%votes) of 1.278 for the largest seat-winner would be just about average. Over 22 elections, the mean advantage ratio has been 1.2897. (Note: I am calculating this as the share of the largest seat-winner over its vote share, not over the share of the largest vote-winner, when those diverge.) For those who know Canadian electoral history, I will note that advantage ratios of around 1.2-1.3 have occurred in 1965, 1968, and 2008 (among others). Thus even if the specific vote totals may be very unusual, the workings of FPTP, given the actual votes, is fairly “typical” for Canada.

As for the other parties, I mentioned the NDP surge. But just as noteworthy is the surge of the Bloc Quebecois, which may turn out (again) to be the single most important factor in preventing a majority of seats. The BQ is currently polling just under 7% nationwide, while the Greens are just over 8%.

Of course, the BQ and Green fortunes will diverge in seats. It is very helpful for votes-seats conversion to be a regional party under FPTP, and not useful to be relatively more dispersed. So the BQ is currently estimated to get 38 seats, about the same as a much larger national party, the NDP (41) and vastly more than the also larger–in votes–Greens (2).

Regarding those surges I mentioned. The BQ was, according to the polling aggregate on only about 20% in Quebec as recently as one month ago. Now it is up to almost 30%, and just behind the Liberals’ percentage in the province (31%, having been 37% a month ago). The Conservatives have really crashed in Quebec, down from 22% a month ago to just under 16% now. The latter puts them not too far ahead of the NDP, who are now on about 14% in the province.

Nationally, the NDP was at only about 13% a month ago, but is approaching 19%. A rising vote share tends to lift the seat share–even for a national third party under FPTP. While a month ago, the Poll Tracker had the party at only 15 seats, its 41 projected now represents an increase by a factor of 2.7 when its votes have increased only 1.27 (19/15). The party would still be significantly under-represented by the electoral system, but it has reached a point where it gains a lot of seats by a small increase in votes (assuming it holds and that Grenier’s swing assumptions are reasonable, etc.).

The NDP has also pulled narrowly ahead of the Liberals in the polling aggregate in British Columbia, although still well behind the leading Conservatives.

As for the Greens, their slide has been quite abrupt. They were over 10% as recently as the first of October and were projected to win 4 seats as recently as 16 Oct.

The sixth party in the picture, the far-right Peoples Party of Canada, looks likely to win only the seat of its leader, Maxime Bernier. The riding (district) is Beauce, in Quebec, in which Bernier has held as a Conservative since 2006 until defecting from that party in 2018. (I see the Rhinoceros Party has found a candidate with the same name to put up against him.) For months, the PPC has been at either zero or one seat in the projection.

As for who will form a government, the Liberals seem best placed, even if the result is as short of majority as the Poll Tracker projects. It is possible that they will be weak enough to have to form a coalition with the NDP, even though probably the Liberals would prefer a minority government. On current numbers, Liberal+NDP would be a very bare majority. The coalition or a minority government might need working arrangements of some sort with the Greens and/or BQ as well.

It is much harder to see how the Conservatives can form government, even if they end up edging out the Liberals for a seat plurality. Conservative leader Scheer has already begun the spin just in case, claiming this week (incorrectly) that the party with the most seats gets the first shot at forming a government.

NDP leader Jagmeet Singh has said he would try to form a coalition with the Liberal Party if the Conservatives have the most seats. And PM Justin Trudeau would have the legal right to attempt to work out such a deal and meet parliament to try to retain office. Presumably, Singh (and the Green leader, Elizabeth May) would attempt to extract a concession that 2019 be the last election under FPTP.

Quebec to have electoral reform referendum

Per CTV News Montreal, the CAQ governing party in Quebec promises a referendum on a specific electoral-reform proposal to be held concurrent with the next general election in 2022.

The CAQ government on Wednesday introduced its electoral reform law, but backed away from its 2018 campaign promise to have it in place in time for the next general election.

The system is a form of mixed-member proportional representation (MMP), but a complex one. And not very proportional.

The number of seats in the National Assembly would remain 125. The new electoral law would divide Quebec into 80 larger electoral divisions that will mainly be the same as federal ridings, and 17 wider regions:

• 80 MNAs would be elected according to the current system

• 45 MNAs on a list of candidates would be divided among the parties, according to the percentage of votes obtained in the 17 regions

Thirty six percent of seats for the list tier is certainly on the small side, and the proportionality would be reduced further by that list tier itself being districted. Note that the mean number of seats per compensation region is only 2.65.

Based on further detail that I learned from Manuel on Twitter (and that I trust he will not mind my sharing here), we can see yet more ways that this proposal is designed to limit proportionality.

…it’s a very constrained implementation of PR, limited by a provincial-level 10% (yes, ten percent) threshold; and districted MMP in seventeen regions, with a new variation of the D’Hondt rule that skews seat distributions in favor of the larger parties.

Regarding the seat allocation method for the compensation seats (which will limit how compensatory it actually will be):

In Scotland and Wales the modified D’Hondt divisors are N+1,N+2,N+3, and so on, where N = number of single-member seats. In the Quebec proposal, they are N/2 + 1, N/2 + 2, N/2 + 3, N/2 being *half* the number of single-member seats, rounded up, and resulting in lower divisors.

One additional detail: the bill provides for separate allocations of single-member and PR list seats among regions – according to the number of registered voters – which guarantee all but one region a minimum of two seats. This would cost Montreal – a PLQ bastion – three seats.

I would still consider this MMP*, as there is a compensation mechanism. I am on record as considering even the Jenkins Commission proposal in the UK to be MMP, albeit with lots of caveats given it was also designed to be about as weak on the P as could be.

Regarding the election of 2018 when the CAQ came into power–surprisingly, with an absolute majority of seats–and the electoral-reform promises made at the time, see this earlier planting.

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• * UPDATE: I am now not sure about this; I need more time to think it through, and that will have to wait till some time in 5780! In the meantime, see this Twitter thread. I think the issue hinges on whether the “modification” to D’Hondt is actually more like Imperiali. While Taagepera and I list Imperiali divisors in our book as being part of the family of PR allocation formulas, we both now believe that it should not be. We were prompted to this view by an email exchange earlier in 2019 with Steven Verbanck (regular F&V commenter). Anyway, to be continued…

Newfoundland and Labrador 2019

Now, this is a close election! Newfoundland and Labrador held its provincial election on 16 May. The result was the Liberal Party winning exactly half the seats–apparently. One of their losses is by five votes. Not five percentage points. Five votes. The apparent winner is the NDP candidate. There is likely to be a recount.

If the result holds, the NDP has won three seats in the 40-seat assembly, up from two in the previous election. The Liberals had 31 seats last time, so this is some electoral rebuke, even if it ends up back with a majority. The Progressive Conservative Party, which won 15 seats, has not conceded defeat, and the leader has said he will be calling on the NDP and two independents (who are ex-Liberals) to consider a possible bid for power if the Liberals do not win their 21st seat.

The Liberal vote total percentage was 43.9, PCs 42.6, NDP 6.3.

PEI 2019: Provincial assembly election and MMP referendum

Prince Edward Island election day was today. Results appear to be pointing towards a lead in votes and seats for the Progressive Conservatives. Thus the expectation (at least according to some polling) that the Greens might form the government looks unlikely now. The Green Party appears to be in second place, although closer (in votes) to the third place Liberals than to first place. The Liberals are the outgoing governing party, with a seat majority.

It looks like it will be a minority situation, which I think will be a first for PEI.

Voters were also voting in a referendum on whether to replace FPTP with a mixed-member proportional (MMP) system, with the voter brochure showing it as an open-list variant. That looks like a close call at this point, but most likely it has been defeated. To pass, the MMP proposal requires not only a majority of votes, but also a win in 17 of the 27 districts. At the moment, CBC is reporting it will win no more than 15 (and may not have a provincewide majority anyway).

PEI has been here before, having voted in a non-binding ballot (conducted by phone or online) for MMP in 2016, and having defeated an earlier MMP referendum by a big majority in 2005.

Today’s referendum had an odd ballot format: the NO option appears above the YES option. I am not sure I have ever seen that before.

(There is one district that did not vote today in the assembly election; a candidate, of the Greens, died in a canoe accident last Friday, so there will be a by-election at a future date.)

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 50.5%  of seats when we would expect 54.2%).

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 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 somewhere, 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 (N_V) 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 N_V 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 N_V 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 N_V expected to be 2.0, and in the largest provinces, the assemblies are large enough that we should expect N_V>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 N_V>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 N_v so much better predicted (even if not exceptionally well) than s₁? It is hard to say. It is an unusual situation to have both N_V 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, N_S) are prior to N_V, 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 N_V 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 S^0.25. A parliament with 81 seats is expected to feature three parties; the other formulas would predict that N_S=2.08, s₁=0.577, and N_V=2.52. If the parliament had 256 seats, we would expect four parties, N_S=2.52, s₁=0.50, and N_V=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 N_V and s₁. It can be calculated from the formulas displayed in Table 9.2 (also on p. 149). It would be:

s₁=(N_V^1.5 -1)^-0.5.

In this last graph, I plot this expectation with the solid dark line, and a regression on s₁ and N_V 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 N_V>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 N_V>2.92 (in order of increasing N_V: BC91, AB04, NB91, QC70, AB67, BC72; in the last one, N_V=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 N_V 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 s_1cr and N_Vcr. Then I can take ratios of actual s₁ and actual N_V to these “expectations”. The mean ratios are: N_V/N_Vcr=0.994; s₁/s_1cr=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.

New Brunswick 2018

The Canadian province of New Brunswick held its provincial assembly election on 24 September. The result is an assembly with no majority of seats.

The incumbent Liberal government, which won a majority in 2014 but had fallen to minority in the interim, came in second place in seats but first in votes in the 2018 election. The main opposition, Progressive Conservatives (PC), won just one seat more, and are short of a majority.

The Liberals have 21 seats on 37.8% of the vote, the PCs 22 seats on 31.9%, while a previously underrepresented party, People’s Alliance (PANB) and the Green Party each won three seats. The PANB won 12.6% of the vote and the Greens 11.9%. The NDP won 5% of the votes, but no seats.

The district-level results are interesting. The People’s Alliance leader, Kris Austin, won a clear majority (54.6% in Fredricton-Grand Lake, with the runner up being a PC incumbent with only 27.7%; in 2014, Austin had lost to the PC candidate 28.8%-28.5%!). In another riding, Fredricton-York, the PANB candidate defeated another PC incumbent, 33.7%-30.9%. The third PANB winner was in Miramichi and won 57.0% to 35.0% over a Liberal. I counted six other seats in which a PANB candidate came in second, although only one of these was really close (Southwest Miramichi-Bay Du Vin, where a PC has 35.4% over the PANB on 35.0%). The three districts the PANB won and the one where they are very narrowly behind, are all contiguous. It is clearly a regional party; it ran in 30 of the 49 ridings.

As for the Green winners, leader David Coon, who was their first elected MLA (2014) retained his seat easily, 56.3%-20.1% over a Liberal. In Kent North their candidate won 45.9%-37.4% over a Liberal. In Memramcook-Tantramar, Megan “Landslide” Mitton won by 11 votes (38.3%-38.2%) over a Liberal.  It seems there are two districts in which a Green came in second, but neither was close; in both cases the Liberal winner had a majority. The Green wins are not contiguous districts; the leader represents a seat in Fredricton and the other two are geographically large coastal districts. (See results and map at CBC; these are, of course, not necessarily final at this point, and there is even one Liberal lead of just 10 votes over a PC.)

It is not clear what the government result will be. I’ve been listening to CBC on the post-election discussions, and it seems the Greens have rejected a possible coalition with the Liberals; given that the results revised above suggest the Liberals are the Greens’ main opponent at district level, this reluctance has some (FPTP-based) logic to it. The Conservatives have said they will vote down a Liberal throne speech (not surprisingly). The PCs have declared all of their members are unwilling to stand for Speaker, and the Liberals also do not want any of their own to take the post. Without a Speaker, no other business can be transacted. So, for now at least, we have a stand off. (Update: The Liberal leader and current Premier Brian Gallant has said his party will put forth a candidate for Speaker today.)

It is worth noting that New Brunswick has quite a record of unusual election outcomes, and electoral-reform proposals. Just click “N.B.” at the bottom of this post to see previous entries on this recent history. Of particular interest is the time the Liberals took power thanks to a plurality reversal and promptly called off the previous (Conservative) government’s planned referendum on adopting MMP. Maybe it is time to dust off those proposals. The voters of the province seem unwilling to play the old FPTP game the way “the law” says to play it.

What could we expect from electoral reform in BC?

This week is the beginning of the mail voting period for the referendum on whether to reform the electoral system for provincial assembly elections in British Columbia. The ballot asks two questions: (1) Do you want to keep the current FPTP system or “a proportional representation voting system”: (2) If BC adopts PR, which of three types of PR do you prefer?

The second question offers three choices, which voter may rank: Mixed-Member Proportional (MMP); Dual-Member Proportional (DMP); Rural-Urban Proportional (RUP).

I have reviewed before what these options entails, and will not repeat in detail here. Besides, the official BC Elections site explains them better than I could. What I want to try to get it here is how we might expect BC’s provincial party system to change, were any of these options adopted. To answer that question, I turn, of course, to the Seat Product Model, including the extended form for two-tier systems developed in Votes from Seats.

The punch line is that the various scenarios I ran on the options all suggest the effective number of parties in the legislative assembly would be, on average, somewhere in the 2.46 to 2.94 range, the effective number of vote-earning parties would tend to be in the 2.83 to 3.32 range, and the size of the largest party would be somewhere between 45% and 51% of the seats. Again, these are all on average. The ranges just provided do not mean elections would not produce a largest party smaller than 45% or larger than 51%. Actual elections will vary around whatever is the point prediction of the Seat Product Model for any given design that is adopted. And fine, yet important, details of whichever system is adopted (if FPTP is not retained) will remain to be fleshed out later.

The ranges I am giving are formula-predicted averages, given the inputs implied by the various scenarios. I explain more below how I arrived at these values. The key point is that all proposals on the ballot are quite moderate forms of PR, and thus the party system would not be expected to inflate dramatically. However, coalition governments, or minority governments with support from other parties, would become common; nonetheless, single-party majority governments would not likely disappear from the province’s future election outcomes. As we shall see, one of the proposals would make single-party governments reman as the default mean expectation.

Before going to the scenarios, it is important to see whether the real BC has been in “compliance” with the Seat Product Model (SPM). If it has tended to deviate from expectations under its actual FPTP system, we might expect it to continue to deviate under a new, proportional one.

Fortunately, deviations have been miniscule. For all elections since 1960, the actual effective number of vote-earning parties has averaged 1.117 times greater than predicted. That is really minor. More important is whether it captures the actual size of the largest party well. This, after all, is what determines whether a single-party majority government can form after any given election. For all elections since 1960, the average ratio of actual largest-party seat share to the SPM prediction is 1.068. So it is even closer. For an assembly the size of BC’s in recent years (mean 80.7 since 1991), the SPM predicts the largest party will have around 57.8% of seats. The mean in actual elections since 1991 has been 62.7%. That is a mean error on the order of 4 seats. So, the SPM captures something real about the current BC electoral system.

Going a little deeper, and looking only at the period starting in 1996, when something like the current party system became established (due to the emergence of the Liberals and the collapse of Social Credit), we find ratios of actual to predicted as follows: 1.07 for effective number of vote-earning parties; 1.07 for largest parliamentary party seat share; 0.905 for effective number of seat-winning parties. If we omit the highly unusual 2001 election, which had an effective number of parties in the assembly of only 1.05 and largest party with 96.2%, we get ratios of 0.98 for effective number of seat-winning party and 0.954 for largest party size. The 2017 election was the first one since some time before 1960 not to result in a majority party, and it is this balanced parliament that is responsible for the current electoral reform process.

As for the proposed new systems, all options call for the assembly to have between 87 seats (its current size) and 95 seats. So I used 91, the mean; such small changes will not matter much to the estimates.

The MMP proposal calls for 60% of seats to remain in single-seat districts (ridings) and the rest to be in the compensatory tier (which would be itself be regionally based; more on that later). So my scenarios involved a basic tier consisting of 55 seats and a resulting 36 seats for compensation. Those 36/91 seats mean a “tier ratio” of 0.395 (and I used the rounded 0.4). The formula for expected effective number of seat-winning parties (Ns) is:

Ns=2.5^t(MS)^0.167.

With t=.4, M=1 (in the basic tier) and S=91, this results in Ns=2.81. I will show the results for other outputs below.

For the DMP proposal, the calculations depend on how many districts we assume will continue to elect only one member of the legislative assembly (MLA). The proposal says “rural” districts will have just one, to avoid making them too large geographically, while all others will have two seats by combining existing adjacent districts (if the assembly size stays the same; as noted, the proposals all allow for a modest increase). In any case, the first seat in any district goes to the party with the plurality in the district, and the second is assigned based on province-wide proportionality. For my purposes, this is a two-tier PR system, in which the compensatory tier consists of a number of seats equivalent to the total number of districts that elect a second MLA to comprise this compensatory pool. Here is where the scenarios come in.

I did two scenarios, one with minimal districts classified as “rural” and one with more. The minimal scenario has 5 such districts–basically just the existing really large territorial ridings (see map). The other has 11 such districts, encompassing much more of the interior and north coast (including riding #72, which includes most of the northern part of Vancouver Island). I will demonstrate the effect with the minimal-rural scenario, because it turned out to the most substantial move to a more “permissive” (small-party-favoring) system of any that I looked at.

Of our 91 seats, we take out five for “rural” districts, leaving us with 86. These 86 seats are thus split into 43 “dual-member” districts. The same formula as above applies. (Votes from Seats develops it for two-tier PR, of which MMP is a subset.) The total number of basic-tier seats is 48 (the five rural seats plus the 43 DM seats). There are 43 compensation seats, which gives us a tier ratio, t=43/91=0.473. Ah ha! That is why this is the most permissive system of the group: more compensation seats! Anyway, the result is Ns=2.94.

If we do the 11-rural seat scenario, we are down to 80 seats in the DM portion of the system and thus 40+11 basic-tier seats. The tier ratio (40/91) drops to 0.44. The resulting prediction is Ns=2.61. This does not sound like much, and it really is not. But these results imply a difference for largest seat size between the first scenario (45%) and the second (49%) that makes a difference for how close the resulting system would be to making majority parties likely.

Finally, we have RUP. This one is a little complex to calculate because it is really two different systems for different parts of the province: MMP for “rural” areas and STV for the rest. I am going to go with my 11 seats from my second DMP scenario as my “rural” area. Moreover, I understand the spirit of this proposal to be one that avoids making the districts in rural areas larger than they currently are. Yet we need compensation seats for rural areas, and like the full MMP proposal, RUP says that that “No more than 40% of the total seats in an MMP region may be List PR seats”, so this region needs about 18 seats (the 11 districts, plus 7 list seats, allowing 11/18=0.61, thereby keeping the list seats just under 40%.) That leaves us with 91-18=73 seats for the STV districts. The proposal says these will have magnitudes in the 2-7 range. I will take the geometric mean and assume 3.7 seats per district, on average. This gives us a seat product for the STV area of 3.7*73=270.

In Votes from Seats, we show that at least for Ireland, STV has functioned just like any “simple” PR system, and thus the SPM works fine. We expect Ns=(MS)^.167=2.54. However, this is only part of the RUP system. We have to do the MMP part of the province separately. With just 11 basic-tier seats and a tier ratio of 0.39, this region is expected to have Ns=2.13. A weighted average (based on the STV region comprising 80.2% of all seats) yields Ns=2.46.

The key point from the above exercise is that RUP could result in single-party majority governments remaining the norm. Above I focused mainly on Ns expectations. However, all of the predictive formulas link together, such that if we know what we expect Ns to be, we can determine the likely seat-share of the largest party (s1) will be, as well as the effective number of vote-earning parties (Nv). While that means lots of assumptions built in, we already saw that the expectations work pretty well on the existing FPTP system.

Here are the results of the scenarios for all three output variables:

System	Expected Ns	Expected Nv	Expected s1
MMP	2.81	3.19	0.46
DMP1	2.94	3.32	0.45
DMP2	2.61	3.01	0.49
RUP	2.46	2.87	0.51

“DMP1” refers to the minimal (5) seats considered “rural” and DMP2 to the one with 11 such seats. If we went with more such seats, a “DMP3” would have lower Ns and Nv and larger s1 than DMP2, and the same effect would be felt in RUP. I did a further scenario for RUP with the MMP region being 20 districts, and wound up with Ns=2.415, Nv=2.83, s1=.52; obviously these minor tweaks do not matter a lot, but it is clear which way the trend goes.And whether any given election is under or over s1=0.50 obviously makes a very large difference for how the province is governed for the following four years!

I would not really try to offer the above as a voter guide, because the differences across systems in the predicted outputs are not very large. However, if I wanted to maximize the chances that the leading party would need partners to govern the province, I’d probably be inclined to rank MMP first and RUP third. The latter proposal simply makes it harder to fit all the parameters together in a more than very marginally proportional system.

By the way, we might want to compare to the BC-STV proposal that was approved by 57% of voters in 2005 (but needed 60%, and came up for a second referendum in 2009, when no prevailed). That proposal could have been expected to yield averages of Ns=2.61, Nv=3.0, and s1=.49. By total coincidence, exactly the same as my DMP2 scenario.

Edit: The following paragraph is based on my own misreading of the proposal, which contrary to what I say here, calls for province-wide proportionality if MMP is chosen. What it says about Scotland still applies, so I will leave it here. [Then again, maybe not?]

A final note concerns the regional compensation in the MMP proposal vs. province-wide in DMP. In an on-line appendix to Votes from Seats, I explored whether regional compensation in the case of Scotland produces a less permissive system than if compensation were across all of Scotland. I concluded it made no difference to Ns or s1. (It did, however, result in lower proportionality.) Of course, if it made a difference, province-wide would have to be more favorable to small parties. Thus if this were a BC voter’s most important criterion, DMP might pull ahead of MMP. However, the benefit on this score of DMP is greater under a “low-rural” design. The benefit of DMP vanishes, relative to MMP, if the system adopted were to be one with a higher share of seats marked as rural. I certainly am unable to predict how the design details would play out, as this will be left up to Elections BC.

The bottom line is that all proposals are for very moderately proportional systems, with MMP likely the most permissive/proportional on offer.