Fruits & Votes is the Web-log of Matthew S. Shugart ("MSS"), Professor of Political Science, University of California, Davis.
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The biggest surprises in the Canadian election–for me, at least–were the extent of Conservative gains and Bloc Quebecois losses in Quebec. As I noted in my post before the election about estimating the seats, there is a tendency in Canada for the largest party nationally to obtain fewer seats that would be predicted based on the size of the two leading parties (and given the size of parliament and voting population). However, in 2000 and 2004, the estimation procedure worked quite well for all non-Quebec seats. In 2006, the estimation procedure overestimated the Conservative seats even outside of Quebec. Nonetheless, my estimates of the seats based on votes totals for the leading parties that were closest to what actually resulted on election day were pretty close. Why? Because while the Conservatives underperformed (according to the model) outside Quebec, they performed substantially better than I expected within Quebec.
I based my Quebec estimates on a riding-by-riding analysis, rather than on any equations. I expected the Conservative party to go from zero seats in 2004 to 3-7 seats in 2006, and I thought the upper range of that estimate was too optimistic from the Conservatives’ perspective. Instead, the party won ten seats in Quebec.
Meanwhile, I expected the BQ to gain seats even if it lost votes. While I did not anticipate the BQ’s vote falling as much as it did, I expected the biggest result of Conservative gains in the province to be to take seats held by the Liberals and put them into the BQ column. While my pre-election estimates were based on riding-level analysis, and not the seat-vote equation, it is worth entering the now-known provincial votes distribution into that equation to see if the actual Quebec seat allocation is what we should have expected, or if the result was indeed anomalous.
The seat-vote equation’s basic premise is that the ratio of the two largest parties’ seats will tend to equal the ratio of those parties’ votes raised by an exponent that is calculated as the log of the number of voters over the log of the number of single-seat districts. For Quebec, that exponent is 3.5. This means that with the two largest parties—here the BQ and Conservatives—having a votes ratio of 1.71, they should have a seat ratio of 6.54! Using the extended form of the seat-vote equation, the rough estimate—using known votes shares in the 2006 election—would be for the BQ to win 57 seats, the Conservative party 12, and the Liberals 6.1
So, the seat-vote equation expects the Conservative party to have more seats than the Liberal party—hardly remarkable, given that the Conservative party (24.6%) had more votes than the Liberal party (20.7%)! Instead, the Liberals won 13 seats (17.3%) and the Conservatives only 10 (13.3%). The actual ratio of BQ to Conservative shares of the seats was 5.1 instead of the estimated 6.5.
Of course, the reason the Liberals held their own in seats despite a collapse in votes is that they are concentrated. Just as the BQ is overrepresented nationally because its small (10-12% in recent elections) share of the national votes is all concentrated in one province, so within that province the Liberals are overrepresented because most of its voters are concentrated in English-speaking Montreal ridings.
So the surprise, from the standpoint of both the seat-vote equation estimates and my own riding-by-riding analysis is that the Conservatives won seats at the expense of the BQ rather than at the expense of the Liberals.
I said above that I expected the Conservative seat gains to be small because the main effect of their surge would be to displace seats from the previous number two party (the Liberals) to the far larger BQ. That is, just as the seat-vote equation “thinks,” I thought that the main pole of competition was between the two smaller parties in the province, from which the big party would benefit, given the plurality system.
Such expected swings from the Liberals to the BQ on account of Liberals and Conservatives splitting the federalist vote did indeed occur in six ridings2 The BQ lost votes in all six (an average of 1.4 percentage points), but won these seats anyway because it faced divided competition.
However, the Conservatives did extremely well elsewhere in Quebec by appealing to former BQ voters. Eight of the Conservative party’s ten seats gained came in former BQ ridings in which there was an almost wholesale flip of the votes totals of the Liberal and Conservative parties, but also a large decline in the BQ vote. In only one of these ridings (Levis-Bellechasse) could the Conservative candidate have won without the benefit of BQ defections.
Drawing inferences about individual voters from aggregate votes is fraught with peril, but it is not too much of a stretch to say that the Conservatives gained votes in Quebec mostly at the expense of their federal rival, the Liberals. Nonetheless, they gained seats primarily because in districts where a combination of disaffected federalist voters and former sovereigntists could oust the Bloc, many Bloc voters obliged and joined their federalist counterparts in giving a boost to the Conservative candidate.
Consider some average vote-swing data. In the province as a whole, the party percentage-point swings were as follows:
Lib, -13.2
Cons, +15.8
BQ, -6.7
NDP, +2.9
However, in the eight districts that swung from BQ to Conservative,3 the vote swings were:
Lib, -19.3
Cons, +29.9
BQ, -13.5
NDP, +2.1
Yes, Tories plus thirty! Again, we need to be cautious about drawing inferences about individual action from aggregate data, but consider that the NDP gains almost certainly were votes “lent” to the party by Liberals knowing their party was doomed. That leaves around 17% Liberal voters defecting elsewhere. Add that 17 points to the BQ’s 13-point loss and you have 30 for someone else. That someone is the Conservative party. A thirty-point average swing, nearly twice what the party gained provincewide, concentrated in districts that were winnable for the party only if it could attract both federalists and sovereigntists!
This is the stuff realignments are made of, or even the stuff floor-crossings are made of. Could the BQ be cracking up? Are there BQ members elected in 2006 whose ridings are trending Conservative? Actually, no. Or at least I can’t identify any. It looks to me as though every district in which the Conservative party was within twenty points of the winner in 2004 was a district that it won in 2006. There were no near-misses.
There were at least seven other seemingly vulnerable ridings in which the BQ won the district in 2004 with less than 50% of the vote. However, these seven ridings had a very different pattern of swings in 2006 from the eight that flipped from BQ to Conservative:
Lib, -14.4
Cons, +15.0
BQ, -3.4
NDP, +2.4
I do not know enough (or anything, really) about these specific constituencies to draw firm conclusions, but (with again those caveats about inferences drawn from aggregate data) these ridings look like shifts within the federalist vote. The BQ vote losses here were less than in the province as a whole, notwithstanding that some of them could have swung to the Conservatives if more of the BQ vote had been ready to defect, as it was in the eight that actually did swing. In fact, these seven BQ holds all had a Bloc lead of less than twelve percentage points in 2004 and now all but one have a Bloc lead of from 14.7 to 22 percentage points. (The one, with a lead of only 9.3, is Chicoutimi-Le-Fjord.)
This latter group of ridings looks more like the full set of ridings in which the BQ and Liberals were close (less than ten percentage points)—a set that includes BQ holds, Liberal holds, and the six seats that swung from Liberal to BQ. In this expanded set of relatively close Lib-BQ contests from 2004, the Conservatives gained, on average, 11%, the Liberals lost 11%, and the BQ lost just under 3% of the vote.
In other words, while the BQ lost votes throughout the province, its greatest losses were concentrated in a set of districts where many of their voters “lent” the Conservatives their votes. Whether this proves to be a long- or short-term loan will say much about the future of Quebecois politics, as well as about the potential for further Conservative gains. In this context, an early post-election poll4 that shows plummeting support in the province for separatism could be significant. If that holds, the Conservative gain could be sustainable, though as I noted, it would take a far bigger loss of BQ support for the Conservatives to gain much more, given the dynamics of three-way competition, which benefit the BQ in seats even as it loses votes.
(An aside. There is one interesting riding, Hull-Aylmer, across the river from Ottawa. It was one of the NDP’s strongest districts in Quebec in 2004, with 11.9%. But in 2006, the NDP candidate obtained only 5.5%. Perhaps it was the candidates. Or perhaps NDP voters voted strategically, trying to save their local Liberal incumbent. If so, it worked. Without the decline in the NDP vote, the BQ candidate very likely would have won, despite less than 30% of the vote. However, the Liberal candidate squeaked by, winning 32.7%. The riding is in no way representative of any pattern. In fact, it is one of the very few in the province in which the NDP vote declined from 2004 to 2006.)
Footnotes:
1. It is worth emphasizing that the purpose of the s-v equation is not to predict a specific election—which would be pretty worthless after the results are in—but to identify elections that deviate from a pattern; the deviating elections are far more interesting than those that are properly estimated, or even ‘predicted’!
2. Ahuntsic, Brome-Missiquoi, Brossard-La-Prairie, Gatineau, Jeanne-Le-Ber, and Papineau.
In one of India’s largest states, West Bengal, where elections are due in the spring, the upcoming budget session of the state legislative assembly is expected to see a no-confidence motion put forward by the opposition All-India Trinamool Congress, which won 60 seats in the 2001 election. The governing Communist Party of India (Marxist) won a large plurality (143)–but not a majority–of the 294 assembly seats in that election. The significance of West Bengali politics for the federal government can hardly be overstated: Not only is the state large and important in its own right, but also the CP(M) is one of the Congress Party’s formal support partners in the multiparty minority government at the national level.
I should also note that the votes of those top two parties in 2001 split 36.6%-30.7%, or almost precisely how the Conservative and Liberal parties split this week in Canada. But the West Bengal result, while, like Canada’s, not giving one party a majority of seats, resulted in a much wider disparity between the two parties in seats: 48.6-20.4. In terms of the seat-vote equation that I discussed with respect to Canada, the West Bengali state assembly is an almost perfect comparison: almost identical in assembly size and the top two parties vote shares, but about two-and-a-half times as many voters. The West Bengali result was a greater divergence in seats between the two leading parties than we would expect, whereas the Canadian result was a smaller divergence. The reason is most likely that West Bengal (and India more generally) is a more extreme version of Canada: party fragmentation and regionalization beyond the norm for FPTP systems. All the parties in West Bengal are quite concentrated in their support, but the CP(M), as a largely urban party, has strongholds that comprise more of the districts in India’s most urban state.
How did the seat-vote equation perform in the 2006 Canadian election? To determine that, I repeated the methodology outlined in my pre-election post about seat estimation, entering the now-known votes distribution into the equation. The answer is: Not all that well. The divergence between the model and the actual translation of votes to seats only underscores a point I made in introducing the seat-vote estimations: Canada’s electoral system does not behave like a ‘normal’ first-past-the-post (plurality) system. This is not really surprising, for I noted that the normal seat bonus expected to be enjoyed by the largest party in FPTP is rarely realized in Canada (see the graph in the pre-election post). However, in the preceding two Canadian general elections, the seat-vote equation estimates were largely correct for the votes cast and seats allocated outside Quebec. In 2006 they were not.
The Conservative party–the party with, as expected, the largest share of the votes nationally, would be predicted by the seat-vote equation to have won a large majority of the seats allocated in provinces other than Quebec: 143/233 (61.4%), based on its 40.2% of the votes won outside that province. Instead, it won only 114 (48.9%), thus benefiting much less than might have been anticipated from the normal FPTP tendency to over-represent the largest party even when we exclude Quebec from the results.
Added to the known outcome in Quebec (where Conservatives won 10 of 75 seats), the Conservatives’ winning 61.4% of the non-Quebec seats would have put the party at 49.7% of the total seats, or two seats short of a majority. In other words, allowing for error of estimate, the party would have had either a commanding position despite being short of a majority, or would have had an exceedingly narrow majority. Instead, however, the party won a mere 40.3% of the total seats in the House of Commons–which is the smallest share of seats for a leading party in Canadian history (a point I will take up in greater detail in a separate post).
What this all means is that the Canadian electoral system has crossed a threshold of sorts, where it is no longer performing as a FPTP system is expected to perform, according to its own normative justification. That is, the claimed advantage of such a system is ‘governability.’ FPTP systems in parliamentary democracies are not supposed to deliver seat allocations that mirror the distribution of citizens’ votes. They are supposed to produce clear winners, either ‘manufacturing’ a majority for the party with the plurality of the votes, or at the very least giving the largest party a sufficiently large plurality of the seats that it is in a commanding positions vis-a-vis parliament even if it lacks a majority of that body. The Canadian electoral system has failed miserably this time, by the standards of the family of electoral systems of which it is a part. The Canadian FPTP system is, in a word, dysfunctional.
The Conservative party won 36.3% of the votes nationwide, with a 6.1 percentage-point margin over its nearest competitor, the Liberal party. So, where the votes split 36.3-30.2, the seats percentages split 40.3-33.4. Considering only these two parties, this is not a result far divergent from what many proportional representation systems might produce. PR systems with many districts of small to medium magnitudes–Spain or Norway, for example–often produce similar votes-to-seats relationships for the two leading parties.*
Where the Canadian system does not resemble a PR system, of course, is in how it treats the smaller parties. For instance, the Bloc Quebecois won in this election 51 seats (16.6%) on 10.5% of the votes, whereas the NDP won just 29 seats (9.4%) on 17.5% of the votes. Any small-district PR system of the sort that would give the largest two parties results similar to what they actually obtained on January 23 might continue to over-represent the BQ (because its votes would remain concentrated in several smaller multi-seat districts within Quebec) and under-represent the NDP (because it is less concentrated), but it would bring the results for these two smaller parties closer to their votes. So, even if Canada had a PR system about as proportional as those of Norway and Spain and an allocation of seats for the top two parties about like what actually resulted in the just-concluded election, under such a system the NDP probably would have had about 45-50 seats**, but the BQ more like 30-35–reversing the actual outcomes for these two parties in a way that matches their ranking in the national votes.***
It is a result of the regional distribution of party voting support that the seat-vote equation does not handle the Canadian seat allocation as well as it handles other FPTP systems. For instance, if all of the five leading parties were national, parties the size of the NDP and BQ might have been expected under FPTP to get less than 20-25 seats combined. A leading party with 36.3% of the votes against such a fragmented field of contenders might have been expected to win 57% of the seats. If that sounds high, consider that the Labour party in the most recent British election won 55% of the seats on just 35% of the vote.§
The largest party in Canada under-performs its seat-vote equation estimate for the same reason that the smaller parties over-perform: geographic concentration. This is obvious in the case of the BQ, which is absolutely not a national party (contesting elections only in one province, where it is by far the leading party). But as I noted before the election, the NDP can also be expected to out-perform its seat-vote estimate because it, too, is concentrated (although far less so than the BQ). It is quite obvious that if two parties have the votes concentration to exceed their estimated seat allocations, then larger parties will fall short of their estimates. Such was the case with the Conservative party, which wound up with barely over 40% of the seats despite a votes share that would be expected to result in something between 48 and 54% of the seats in the House of Commons.
In follow-up posts, I am going to look at the within-Quebec results and in somewhat more detail at the significance of the minority government that was just elected, given the distribution of votes and seats for other parties.
*For example, the leading party in Norway’s PR system in 1997 had 35.0% of the votes and 39.4% of the seats. In 2005, the leading party in Norway had 32.7% of the votes and 36.1% of the seats. Spain’s PR system–a better referent for Canada, given the presence of many regional parties–produced a result in 2004 of 46.9% of the seats for the leading party, which had 42.6% of the votes. The runner-up in that election had 42.3% of the seats on 37.7% of the votes. These allocations for the larger parties in small-district PR systems are strikingly close to those of the just completed Canadian FPTP election: The PR examples just given feature an advantage ratio (%seats/%votes) for the largest party of at least 1.10. The Conservatives’ advantage ratio in this election was 1.11.
**It is worth noting that 103 seats for the Liberals and close to 50 seats for the NDP would have put them on the cusp of a majority, and thus possibly put the center-left, with combined votes of almost 48% even without including the Greens, in a position that the actual outcome did not give it: An ability, within the existing conventions on government-formation, to prevent the Conservative minority from forming a government on its own. In other words, governability, the supposed advantage of FPTP, would have been improved by PR!
***I am assuming, of course, that the actual votes would not have changed under PR. Given that there was apparently no large-scale strategic desertion of the NDP (contrary to widely reported expectations of pundits), I think that is not a terribly unreasonable assumption.
§Added Jan. 25: Well, a clear majority of seats on 35% of the vote is unusual. In fact, UK 2005 was the second smallest share of votes ever (within my data) to have resulted in a parliamentary majority. The lowest was a few percentage points lower in New Zealand’s last FPTP election (1993). But several seat majorities have resulted in other elections in various countries or provinces from around 36% of the vote.
REVISION (Jan 22 at 1030 Pacific): My estimates based on a closer national result should also assume it would be closer in Quebec. I have changed them accordingly below, with the new or altered text in italics. (Jan 22 at 1507 Pacific: adding links at the bottom of this post to other projections.)
How big will the Conservative victory plurality be in Monday’s Canadian election? That is the only remaining question, barring some dramatic reversal of current fortunes of the parties in voter opinion. A reversal is not out of the question, as the undecided vote is still substantial and the parties seem to be trending closer to one another in recent polls, but it looks like the Conservatives will win the most votes and seats. The question is, will they have a majority of seats in parliament, or will the next Canadian government be a second consecutive minority cabinet (only of a different party)?
An average of four recent polls suggests the Conservatives lead with between 35.5 and 38% of the vote, with the Liberals at 26-29%. This is a significant swing from 2004, when the Liberals led with 36.7% of the vote, and the Conservatives had 29.6%. It is also quite a turnaround from polls as recently as mid-December, which implied a votes distribution not greatly different from the 2004 result.
But in Canada, there is no direct relationship between votes and seats at the national level, because it is a first-past-the-post (FPTP) system complicated by multiparty competition and significant regional variations in the four largest parties’ votes.
Ipsos-Reid published a seats forecast today: Conservatives, 143-147, Liberals 59-63, New Democrats (NDP) 39-43, Bloc Quebecois (BQ) 59-63. A majority in the House of Commons is 155 seats, so this projection says Canada will continue to have minority government as it has had since the 2004 election, only this time with Conservatives replacing Liberals. (For a discusion of an Ipsos-Reid projection from a few days earlier, see Election Canada 2006.)
However, it is worth noting that the Ipsos Reid poll gives the Conservatives the greatest lead of any of the five major polls published on January 19. For the record, these polls show the parties’ likely votes percentages as follows (always listed as Cons-Lib-NDP-BQ-Green):
Also see Charles Franklin’s Canada poll tracker at Political Arithmetik. The trends suggest that the Conservative momentum may have peaked in the last week as it became likely that its level of support would be high enough to give the party a parliamentary majority. Whether this trend will continue–which would imply the Conservatives falling back to 35% or below–or stabilize will determine the size of the plurality the party has in the Commons. A majority remains within reach, but would require a reversal of the last several days’ trends. The party pretty much has to run the table to have a majority.
I have run several simulations based on various polls and other assumptions. Before going further, I want to make a very important disclaimer. What follows are not predictions. They are estimates from a mathematical model that has several assumptions behind it. If any of the assumptions are wrong, the estimate will be wrong. Therefore, I would discourage any Canadian from basing his or her voting on these scenarios or anyone else from taking the following too seriously. I am going to put this out there, explain my assumptions, give a few alternatives, and compare how the model has performed in several past Canadian elections.
If all you care about is the seat estimates themselves, scroll down to the bottom of this post (after clicking on the “more” that appears shortly after the graph, below). However, it makes little sense to show the estimates without explaining the methods first, and indicating the assumptions that underly them.
The estimator model is based on something called the seat-vote equation. The simplest form of this equation is the well known cube law of plurality elections, which states that the ratio of seats for the two largest parties tends to be the cube of the ratio of the votes of those parties. In mathematical notation:
sk/sl = (vk/vl)3,
where s is a party’s seat share and v the vote share and the subscripts refer to parties k and l.
While the cube law is well established, it has also been known for decades that the exponent, 3, is not quite right, at least not for all situations. In 1989, Rein Taagepera and I published Seats and Votes, in which we offer a generalization of the seat-vote equation. The form is the same:
sk/sl = (vk/vl)n (later to be referred to as equation 1)
where the exponent, n, is derived as follows:
n=logV/logE,
where V is the number of voters and E is the number of districts.
For Canada, around 13.5 million voters and 308 ridings (districts) results in an exponent of 2.865 instead of 3. In other words, for the size of Canada’s voting population and the size of its chamber, the expectation is that the two largest parties will be somewhat closer in seat shares than what the standard cube law would predict. (If the two largest parties are at .38 and .28, as Ipsos Reid says, then a cube relationship would predict a seat ratio of 2.499, while the 2.865 exponent would suggest a seat ratio of 2.399.)
How does this model perform? The graph below shows elections over the past 40 years in Canada, each of the Canadian provinces, the U.K., and New Zealand (before its change in electoral system). The horizontal axis shows the actual seat ratio of the two largest parties that resulted from the election, while the vertical axis shows the expected ratio, based on equation 1, with n defined according to the number of votes in the respective election and the size of the assembly. Diamonds indicate elections that produced a majority party; crosses indicate minority situations (such as Canada currently).
(Click on the image for a much larger version; I apologize that even on the large version some squinting is necessary.)
It is clear that most elections fall fairly close to the solid diagonal line that indicates a 1:1 agreement between the estimated and the actual seat ratios. There are some dramatic outliers–especially on the right side of the graph. More on them later, in a future post. For now, what we care about is Canada, at the federal level.
It is noteworthy that of the points that are left of and above the diagonal, many of the elections are Canadian federal elections. In other words, the Canadian electoral system results in a closer ratio of seats for the two largest parties than what would be expected. To put it less clumsily, the Canadian electoral system is relatively more proportional than most FPTP systems. (Note: I said relatively, as in relative to the expected degree of disproportionality inherent in FPTP.) (more…)
If by my laws you walk, and my commands you keep, and observe them,
then I will give-forth your rains in their set-time,
so that the earth gives-forth its yield
and the trees of the field give-forth their fruit.
--Vayikra 26: 3-4
F&V time: This blog's date function is so set as to start a new day at approximately local sunset.
(Why, if we have "day" and "night," should a new "day" start in the middle of the night?)
FRUITS: Support your local, organic growers; and, plant vines and fig trees and pomegranates for the generations to come...
VOTES: For democratization and full representation, for environmental sustainability, social justice, and peace, always sincerely...
