Deviation from Proportionality in the 2011 Election

So once again Canada finds itself with a majoirty government elected by a distincly non-majority number of voters. We`ve been here before, of course, but being here again merely serves to remind us of the degree to which our electoral system produces disproportionality.

The simplest way to calculate deviation from proportionality is to take, for each party, the difference between total percent of votes and total percent of seats. Then you add the differences together and divide by two.

For 2011, this gives us a number of 0.17. This compares unfavourably with 0.14 for 2008, 0.13 for 2006 and 0.14 for 2004, and matched the 0.17 of 2000 exactly, suggesting of course that a minority government is likely to be more proportional than a majority. But let's face it - these numbers are pretty similar.

And pretty deceptive, too, as it turns out. 2011 is unique not only in being the first federal election perhaps ever where the NDP have actually gotten a higher percentage of seats than votes but also being the first election in which the BQ didn't, and the first in as far back as I care to look when the Liberals didn't. Seeing the Liberals on the losing end of FPTP disproportionality is a real shock.

The thing is, though, that this not-bad 0.17 number is largely a question of luck. When the same quotient is calculated for each province, it turns out that the federal total is more proportional than the results for every province except two. How is that even possible? Well, it's largely an accidental balance of disproportionalities: the NDP get a disproportionately high number of seats in Québec and the Conservatives a disproportionately low number, but these values are inverted for most of the rest of the country, so there's a kind of correction happening. Said differently, the 30.6% of the vote that went NDP and the 33.4% of the seats that did may seem quite similar, but they're located in very different parts of the country.

Party-by-party, the disproportionality looks like this:

• The Conservatives got 14.3% more seats than votes.
• The NDP got 2.8% more seats than votes.
• The Liberals got 7.9% fewer seats than votes.
• The BQ got 4.7% fewer seats than votes.
• The Green Party got 3.6% fewer seats than votes.

 I realise I haven't really worded that properly: the difference in percentage points between the percent of votes that the Conservatives got nationwide and the percentage of seats that they got nationwide is 14.3. For the BQ in particular, that masks the overall difference, since they didn't run in what is effectively the vast majority of ridings. For that, we need to look at the results by province, from best to worst:

1. Nova Scotia, with a DV score of 0.07. This is surprising, in that the party that came third in votes tied for first in seats: not a shining example of proportionality, really. But individual errors fail to hide the fact that Nova Scotia remains a roughly even three-way split, reflected both in their seat tallies and their overall votes, this time out.
2. British Columbia, with a DV of 0.13. It's not just that BC is the only place where the Greens got any seats at all - after all, the Greens' individual DV for BC was second-worst of all the provinces (since they got a higher overall share of votes). The NDP were remarkable here, with 33.3% of seats for 32.5% of the vote. The remaining deviation, as we'll see elsewhere, was the Conservatives getting seats at the Liberals' expense.
3. Newfoundland & Labrador, with a DV of 0.19. Already we're above the national average, but we ain't seen nothin' yet. Newfoundland bucked the national trend, giving the Liberals 37.9% of their vote and 57.1% of their seats. This is more or less the national trend inverted, as the Liberals benefit from the disproportionality to the Conservatives' expense. Though I doubt they're complaining about that too much.
4. Ontario, with a DV of 0.24. How quickly things are getting bad now: The seat count is 24.5% up on its overall vote, and the Liberals' is short by 14.9%. The NDP came closest to the mark than they tend to do in Ontario, but still this is an embarrassment. And it's still 'better than average'.
5. Manitoba, with a DV of 0.25. Similar to Ontario overall, but with a ten percent boost in both columns for the Conservatives: over half of the vote, over three-quarters of the seats. That difference of 25% was taken from the other three parties, each in rather painful amounts.
6. Alberta, with a DV of 0.29. It's a strange country where fully four provinces could do worse on proportionality than Alberta, where the Conservatives got 96.4% of the seats. That came from 66.8% of the vote, a number much lower than the first one but still amazingly high. The other one-third of the vote got a single seat out of the bargain.
7. Prince Edward Island, with a DV of 0.34. This should be the benchmark for disproportionality: the party that got 75% of the seats didn't even win the overall vote, getting fewer votes than the party that got the other 25% of seats. But its very size, and the fact that the whole province is merely four ridings, means its disproportionality tends to get overlooked. Plus, there are three provinces worse.
8. Québec, with a DV of 0.35, shows the phenomenon of the 'winner's bonus' in a FPTP system. Well, it pretty much always has: down the years, the party that 'wins' Québec wins big. After this paragraph is a list of the 'winner's bonus' given in Québec down the years to one of four different parties since 1980. This time, of course, it's the NDP who threw the numbers completely out of whack, with a seat count 35.8% higher than their vote percentage. All other parties suffered at the NDP's hands in Québec, worst of all the BQ, who walked away with a measly 5.3% of seats from 23.4% of the vote.
1. 1980: The Liberals win 98.7% of the seats with 68.2% of the vote.
2. 1984: The PCs win 77.3% of the seats with 50.2% of the vote.
3. 1988: The PCs win 84.0% of the seats with 52.7% of the vote.
4. 1993: The BQ win 72.0% of the seats with 49.3% of the vote.
5. 1997: The BQ win 58.7% of the seats with 37.9% of the vote (just 1.2% higher than the Liberals).
6. 2000 is the exception: the Liberals got 48.0% of the seats, fewer than the BQ, with 44.2% of the vote: indicating that the 'winner's bonus' decreases if the race is close.
7. 2004: The BQ win 72.0% of the seats with 48.9% of the vote.
8. 2006: The BQ win 68.0% of the seats with 42.1% of the vote.
9. 2008: The BQ win 65.3% of the seats with 38.1% of the vote.
10. 2011: The NDP win 78.7% of the seats with 42.9% of the vote.
9. New Brunswick, with a DV of 0.36. The phenomenon is similar in New Brunswick, where all but two ridings went to a party that got a mere 43.9% of the vote. The NDP and the Liberals polled at about their national average, but got a single seat apiece for their troubles.
10. Saskatchewan, with a DV of 0.37. Ah, Saskatchewan. I've written before about the ridings in Saskatchewan, which are set out in a strange fashion such that there is not a single 'urban riding' in the whole province: both Regina and Saskatoon are divided into four and stuck onto otherwise-rural ridings. What this means is that the NDP polled 32.3% in the province - effectively in a three-way tie with BC and Newfoundland for highest NDP vote outside of Québec - without managing a single seat - with a similar vote, the NDP carried a third of BC's seats. The Liberals got barely a quarter of the NDP's vote but walked away with a seat, while the Conservatives got 92.9% of the seats with 56.3% of the vote. Strange indeed.

The phenomenon effected each party differently, and while I haven't included the Greens and couldn't include the Bloc, I've put together three graphs to show how each party was effected. This graph shows the difference in percent - plus or minus - between number of seats and percentage of votes.A positive number means they were rewarded with more seats than their votes justified (looking at strict proportionality) and a negative number means they were punished with fewer. Let's look:

This is how the Conservatives won their majority. West of the Ottawa River, it's winner's bonus all the way down. BC does okay by comparison, but in the other provinces - and New Brunswick too - the Conservatives got seats well in excess of what their overall vote justified. Québec and Newfoundland, the only two provinces that voted for another party in larger numbers than they did for the Tories, balance the numbers a bit, and PEI is just an outlier here.

The Liberals have reaped the benefits of the winning-side of the FPTP system on many occasions in the past, but here the numbers hurt them in every province not an island or a peninsula. Only in Newfoundland, in PEI and to a smaller degree in Nova Scotia do the numbers look good for them.

Lastly, the NDP. Down the years the NDP has certainly suffered at the hands of FPTP, regularly getting fewer seats than they deserve. While this is the first time in perhaps ever that they've come away with a higher seat percentage than a vote percentage, we can see that that's all Québec's fault. A significant majority of the NDP's current MPs are from Québec, but this doesn't mean a majority of their voters are. In every province except Québec and BC, the NDP remain punished by FPTP - it just so happens that in one province this time out they were greatly rewarded by the same system. One does wonder what being on this side of the proportionality gap will do for the NDP's long-term commitment to electoral reform. We'll have to wait and see, I suppose.

Post-Election Numbers: The Highs and the Lows

So I'm looking at Elections Canada's results. One thing that intrigues me, and has always intrigued me, about Canada's electoral system is how far from consensus we ever are: a party can come as close as possible to acclamation in one riding and be a complete non-entity in another riding. I realise this is just a reality of the federation we happen to call home, where disparate interests are brought together in a union that, for better or worse, is frequently more pragmatic than ideological. We might even come, one day, to see these schisms as positions of strength.

The Bloc Québécois were, of course, beaten pretty heavily this time out, squeaking ahead of the competition in only four ridings in the province. Yet in most of Québec, they still managed to come in second, and their overall vote tally remained second as well - where the Liberals and the Conservatives both managed more seats int he province than the BQ, that's because they rely on certain pockets of support. The BQ is now a victim of their broad across-the-board appeal.

Well, mostly across the board. It should come as no surprise that Mount Royal (excluding of course the 233 ridings where they did not field a candidate) is the riding where they performed worst, with a laughable 2.9% of the vote. It's one of ten ridings, however, where they failed to obtain even ten percent of the vote - and not all of those ridings are in Montréal. While their best performance was, not surprisingly, one of the four ridings that they took, Bas-Richilieu--Nicolet--Bécancour with 38.3% (still nowhere near 50%, I hasten to add), their second-best turnout of 36.4% was in a riding they lost to the NDP, Verchères--Les Patriotes. Their four victories came in their first, third, seventh and twelfth-best contests.

With the Liberals, the real extent of their current predicament is visible in these riding-by-riding results. As of this most recent election, there are currently a rather horrifying 91 ridings where Liberal support is in the single-digits. Not for the first time, Jonquière--Alma takes the cake for 'worst Liberal performance', with a horrid 1.98% of the vote representing barely a thousand votes (in second-worst-performing Saskatoon--Rosetown--Biggar, their 2.3% was less than 700 votes). This is fringe-party-level support, and indicates that the Liberals will have to do a lot of work to be seen as a truly 'national' party again.

The only real glimmer of light in the Liberals' disastrous May 2nd was the one that came first - Newfoundland, the only province they 'won' in terms of popular support. It should come as no surprise that the Liberals' three best performances in the country are all on the rock, including Bonavista--Gander--Grand Falls--Windsor and Humber--St. Barbe--Baie Verte, at 57.7% and 57.0% respecively the only ridings in the country, two of 308 contested, where the Liberals took a majority of votes. That's two more than the BQ managed, but that must be small consolation for them.

The NDP, by comparison, have to be looking at these riding-by-riding results with a certain degree of satisfaction. There's a tendency at the moment to see the NDP's breakthrough as strictly a Québec thing, but consider this: of 308 ridings, there are only two, Crowfoot and Portage--Lisgar, where the NDP managed less than ten percent of the vote - 9.1% and 9.8% respectively - two is a smaller number and 9.1% is a higher number than any other party in the country, meaning that when they turn to 2015, they'll find a higher basement than the other parties regarding room-for-growth on a riding-by-riding level. The fact that their two worst performances are in the Prairies ought to give them an idea of how to progress as well.

The toplines are satisfying too for the NDP, I imagine, with king-of-the-hill being Jack Harris in St. John's East, where his remarkable 71.2% actually represents a drop from 2008. Jack Layton's own performance of 60.8% was merely fifth-best, though satisfyingly the top five are all from different provinces (Newfoundland and Labrador, New Brunswick, British Columbia, Québec and Ontario, respectively). All-in-all thirty-six of their 102 seats were won with bare majorities of 50% or more - a decent number but by no means sensational. As regards local hegemony, for sensation we must look elsewhere.

The Conservatives arguably have less across-the-board consistency than the NDP at the moment, with much more embarrassing bottom-of-the-barrel numbers. Yet their peak performances are that much higher - the Conservatives won this election not by being 'Canada's party' so much as by having extraordinary levels of success in certain parts of the country. And, of course, by squeaking by in many others.

The Conservatives' worst performance is a rather horrid 3.5%, in Gilles Duceppe's own former riding of Laurier--Sainte-Marie, where fewer than 1800 people cast their vote for the party who now has a majority government in the country. That the basement is in Québec should come as no surprise: amazingly their forty-two worst ridings are all in La Belle Province, with my own riding of Davenport the worst in the so-called 'RoC'. Only 23 of those are less than 10%, though, a much smaller number than the Liberals currently have to contend with.

Their best performance nationwide should come as no surprise: it's Kevin Sorenson's fiefdom of Crowfoot, where the only two times since the creation of the riding in 1968 that the conservative candidate has won less than 70% of the vote were two elections in which the conservative vote was split in two. United, they anaged this time out to award Harper's party with a shocking 84.0% of the vote. In fact, 13 of the top 16 Conservative victories were all located within Alberta, and they were all more than 70%.

There were a stunning 107 ridings in 2011 in which the Conservatives got more than 50% of the vote - almost two-thirds of the ridings that they won. Anyone wanting to blame 'vote-splitting' or a disunified opposition for the Conservatives' victory needs to consider this very important fact: where the Conservatives are strong, they are very strong indeed, and it's tough to imagine any other party forming a proper national government in Canada without making very serious inroads into those 107 ridings. At the moment, there are more ridings where a completely united opposition would still not shake the Tories' victory than there are ridings won in total by any other party in the country. The NDP managed an impressive 102 seats, squeaking by with less than 50% in two-thirds of those ridings. And yet the Tories' fortress ridings actually amount to a larger number than that. And they actually managed to obtain at least one of these bare-majorities in every province in the country except Newfoundland and Labrador: one in PEI, two in Nova Scotia, four in New Brunswick, one in Québec, 40 in Ontario, nine in Manitoba, ten in Saskatchewan, 25 in 28-seat Alberta, and 15 in British Columbia.

That's a remarkable coast-to-coast victory, and it indicates the breadth of Harper's current mandate, which is much deeper than a popular vote of less than 40% might indicate.

The 2011 Colours of the Ridings: Toronto

So in the lead-up to the election, I played with an idea of looking at election returns in primarily tripartisan Conservative-Liberal-NDP ridings and, by converting voting percentages to hexadecimal RGB values, come up with a unique 'colour' for each riding. RGB means 'red, green and blue', and since the Liberals and the Conservatives happen to use those very colours, I had to rebrand the NDP green in colour, and then we're off.

A riding, then, that voted very strongly for one party would find its 'colour' very close to that party's colour, while a party that split pretty evenly between, say, the Liberals and the Conservatives would be a deep purple. A three-way race, by comparison, would be a grey colour.

Colourwise, here's what Toronto looks like as of May 2. A click will make this bigger.

The first thing one notices is how 'green' (i.e. orange) downtown Toronto suddenly is. This is not only because seven of the eight NDP ridings in Toronto are side-by-side in the heart of the city (save the ex-NDP Bob Rae's Toronto Centre) but also because those ridings tended to have more decisive victories: of 23 Toronto ridings, only three returned their MPs with over 50% of the vote, and all three were NDP (Davenport's Andrew Cash is the only Toronto MP elected with a majority not to be moving into Stornoway, unless Jack and Olivia are letting him bunk). Outside of the NDP, the Liberal elected with the strongest mandate was York West's Judy Sgro with 47.0% of the vote, and the Conservative with the strongest mandate was her neighbouring riding of York Centre, where Mark Adler upset Ken Dryden with 48.5% of the vote.

Other than that, there's a lot of wishy-washiness here. The three neighbouring ridings of Scarborough Centre, Scarborough Southwest and Scarborough-Guildwood all look the very same colour, and indeed in none of the three was the difference in percent between the winner and the third-place finisher greater than ten percent. Yet all three returned an MP from a different party - a wonderfully accidental example of proportional representation.

While Scarborough and 'Old Toronto'are different shades than they used to be, Etobicoke and North York are still reliably the purple of classic Toronto Liberal-Conservative contests, whichever of the two came out on top. In fact, the rumours of the death of the Liberal party in Toronto are greatly exaggerated: even if they lost 15 of the 21 seats they used to hold in the 416, the third-place finishing Liberals came third in only two ridings in the city - the two NDP seats in Scarborough. Otherwise, all nine Conservative ridings featured Liberals in second and NDP in third, while all six Old Toronto NDP ridings featured the Conservatives in (a sometimes-distant) third. Among the six Liberal victories, four featured the Conservatives in second and two featured the NDP in second.

Indeed, this situation reveals a curiosity: while the NDP's strongest performance (60.5% in Jack Layton's Toronto-Danforth) was much higher than the other two parties', their lowest was lower as well - a sad 11.6 in Eglinton-Lawrence, even less than the NDP's paper candidate in Don Valley West. The Liberals and the Conservatives bottomed out, by comparison, at 17.7 and 14.4 respectively - both in Jack Layton's Toronto-Danforth (the most vividly green dot in the city).

A Few Post-Election Numbers

I didn't have much of an opportunity this election to contribute to poll analysis. To be honest, I feel like this site ought to be non-partisan, and in the heat of the battle, I can get rather partisan. No harm done, though. Here are a few quick numbers:

Regarding the talk of 'vote splitting', Elections Canada's current numbers suggest that:

• 107 Conservative seats last night were won by 50% of the vote or more (meaning no combination of opposition support could have won them), while only 59 of them were in some way 'split'.
• Conversely, only 36 NDP seats were sure things. 67 of them could have gone another way if the opposition broke down differently (though the term 'vote splitting' rarely describes such a situation).
• Shockingly, only Gerry Byrne and Scott Simms of the Liberals got over 50% of the vote in their riding. Otherwise, 32 of their 34 ridings - every Liberal victory not on the island of Newfoundland, would have been lost in a conceptually strange 'ABL' combined vote.
• Not a single of the four BQ MPs got a majority of the vote in their riding. The highest, unsettlingly, was 38%.
• Though it was close, Elizabeth May fell short of 50%, and if the people who voted Liberal and NDP in her riding all voted for Gary Lunn instead, he'd still be in the cabinet today.

So with our new party alignment, what are the new two-way races? We know who came first in all the ridings, but who came second? Well, the numbers are truly shocking, and probably tell the real story even more than the baseline:

• Based on who came first or second, 148 of the ridings, just shy of half, are now Conservative-NDP races. The NDP came second in a remarkable 107 of Tory seats, and the Tories came second in 41 NDP wins.
• Quite amazingly, nationwide the NDP are 'competitive' (meaning first or second) in 233 of our 308 ridings - by a whisker, this is even more than the majority-government Conservatives, with 231 of the seats. That paints a shockingly bipartisan picture of our electorate, doesn't it?
• The full numbers, then, are as follows:
• Con-NDP: 107 races (64% of Conservative seats)
• Con-Lib: 56 races (40 of these are in Ontario)
• Con-Ind: 2 (Edmonton-Sherwood Park and Renfrew-Nipissing-Pembroke)
• Con-Green: 1 (Dufferin-Caledon)
• NDP-BQ: 42 races (remarkably, a higher number than the NDP-Con races)
• NDP-Con: 41 races
• NDP-Lib: 19 races (12 in Ontario or Québec)
• NDP-Ind: 1 (Portneuf-Jacques-Cartier)
• Lib-Con: 23 races (oddly only 8 in Ontario; also notice a total of only 79 ridings, barely a quarter of Canada, remain battles between the 'big two parties')
• Lib-NDP: 11 races
• BQ-NDP: 3 races
• BQ-Lib: 1 (Haute-Gaspésie-La Mitis-Matane-Matapédia, the only riding in Québec where the NDP came less than second)
• Green-Con: 1

Those are truly dramatic numbers. And for those who talk about 'vote splitting',  the Conservatives won by less than 50% in 35 of the 56 Con-Lib battles (this is a larger number than the number of seats the Liberals actually took), and in 23 of the 107 Con-NDP battles. I don't know how many of those 58 ridings would have turned away from the Tories merely by adding the Liberal and NDP numbers. Of the two Con-Ind battles, the Tories beat Hec Clouthier by a majority but beat James Ford by a mere plurality - although I'm not convnced that the 'vote splitting' in Edmonton-Sherwood Park was between Ford and the Liberals or NDP.

The Colours of the Ridings: Manitoba, 2008

So the previous blog entry explains what 'the colours of the ridings' means. The day I did the map for Saskatchewan, I also did one for Manitoba. Events are rapidly conspiring to make 2008 ancient history, but I did the map, so I might as well get it out there, pre-election. It looks like this:

Manitoba has the urban-rural split that strange riding boundaries have denied Saskatchewan. And there's a clear difference too. Of course, by square kilometres the vast majority of this province is one riding, and a reliably NDP riding it is too. But outside of Churchill, the rural ridings are pretty darn blue. In Winnipeg, though, we see more colours. It never gets overly red, but it gets a pretty deep purple in the south. The north is more reliably green though.

The Colours of the Ridings: Saskatchewan, 2008

Have you ever seen a variation on the colour wheel that you can find on some 'paint'-style computer programmes, that I call a 'colour hive', since it is often a grid of hexagonal cells?

Well, in any case, I was thinking about how to visually represent voting percentages in multiparty elections when it popped into my head. I got thinking about how you could use RGB values to produce a colour that was made up of the relative voting percentages of three parties - one for each primary colour.

Of course, there were no three-party races in Canada in 2008. Outside of Québec, they were four-way, and in Québec they were five-way. I decided to ignore the Green Party, and then be left with the Conservatives, the Liberals and the NDP. It was a no-brainer to call the Conservatives blue and the Liberals red - which left green for the NDP. A far cry from orange, but green is the NDP's secondary colour.

In other words, in a riding that went 50% CPC, 49.9% LPC and 0.1% NDP, the result would be a pretty vivid purple colour: half blue and half red. A riding that went 34%, 33% and 33% would more or less be grey.

I thought it would be a decent way to show the underlying differences that exist between 'a blowout for party A' and 'a narrow win for party A', something that you can't readily observe in areas that are painted as huge swaths of the same colour.

I chose Saskatchewan. I was curious to see how the province, the historical heartland of the NDP, could have elected no NDPs, letting in a Liberal amidst an otherwise uniform blue wave.

Was it really so uniform?

In retrospect, I shouldn't have chosen Saskatchewan for the experiment. Blue-green splits are less dramatic, colourwise, than, say, red-green. But I liked the experiment anyway. Most of these circles are pretty darn blue. Wascana fails to be red at all, since the Conservatives put up a good fight and the NDP were also in the mix - the result is an attractive brown. The NDP's best performance in the province, Saskatoon-Rosetown-Biggar, shows up as that colour, 'cyan', that no-one outside of the world of computers has heard of. And the northern riding showed good Liberal numbers and weak NDP numbers, giving it a purple colour.

I find it interesting that Saskatchewan has a strange riding system that kind of smells like Gerrymandering - though I don't accuse Elections Canada of actually intending it. There are no 'urban ridings' at all in Saskatchewan: four huge ridings, spreading across miles and miles of prairies, happen to intersect into a four-corners located squarely in downtown Saskatoon, and another four do the same thing in downtown Regina. These two cities each encompass part of several ridings, but no riding can claim to be 'Regina only' or 'Saskatoon only'. I wonder what urban dwellers in Saskatchewan think of this - certainly the NDP do best in cities, and were the election map drawn differently, the NDP would have taken a few seats in the province.

Anyway... I think aftert the election, I'll do some of these maps for the whole country. In the meantime, I might try a more competitive area. Manitoba, perhaps?

The Liberals' and NDP's Strategies of Mutual Destruction

Please note: the above graphic requires detail that isn't really visible when it's this small. Please click on it to make it larger.

Jack Layton is criticising Stephen Harper. Michael Ignatieff is criticising Stephen Harper. It's a strange country we live in where the main goal these two men have in attacking Stephen Harper is not to steal votes from Harper but to steal votes from each other.

But it's true. The sad fact is the the NDP sees its best chance for growth in siphoning from the Liberals, and the Liberals see their best chance for growth in siphoning from the NDP. Both parties seem to think that Harper's 35-or-so percent is more or less carved in stone, and as yet they haven't made much of an attempt to take votes from the two seemingly 'single-issue' parties.

As Harper himself seems eager to paint them as natural coalition partners dying for the chance to jump in to bed with each other, it may seem bizarre to see these two 'infighting' so much. It must seem, from the outside, counteractive as hell - and there are many who consider it the surest way to get Harper's Conservatives a majority.

Is it?

Well, what I've done here is looked at the results of the 2008 election. And then what I've done is determined what the composition of the house would look like if we shifted support only between these two parties. So that suggests a scenario where everyone who voted CPC, Green or BQ last time does again this time, and the only fluidity is between the Liberals and the NDP, in a completely consistent and predictable fashion across the country. For the sake of consistency, the graph I've generated looks only at increments of ten percentage points, even though a shift of merely 1% is enough to get seats changing colours. So when it says, for example, "LIB-10%", that imagines a scenario where one in ten Liberal supporters starts voting NDP - in each riding, one-tenth of the 2008 Liberal vote is shaved off the Liberal tally and added to the NDP tally. Obviously this is going to see Liberals lose seats and the NDP gain seats, but it can also effect the other parties too: a riding where the Liberals finished first, the Conservatives finished second and the NDP finished third is likely to turn Conservative sooner than turn NDP as in this scenario Liberal support bleeds to the NDP. To what extent is this a problem?

Well, the results are interesting. The centre column of the graph shows the Commons composition that actually resulted from the 2008 vote. When we start to move left from there, as Liberal support goes, ten percentage points by ten percentage points, to the NDP, we see that the Liberal seat count drops swiftly and the NDP seat count rises. Ten percent gone and the Liberals lose ten seats, another ten percent gone and they lose another seventeen seats. Yet where the Liberals have lost 27 seats, the NDP have picked up only ten. Where have the other seventeen seats gone?

Amazingly, to the Conservatives. With no other factors affecting voting preferences, the defection of one in five Liberals to the NDP gives the Conservatives a majority. That is to say that in my scenario the Conservatives get not a single voter more than they had in 2008, yet this movement on the 'opposition' side gives them their majority.

It continues from there - to a point. If the Liberals shed 30% of their vote to the NDP, then the NDP pick up eleven seats, passing both the Liberals (now down to a mere 33 seats) and the stable BQ to form the official opposition - but to a further strengthened Conservative majority. The NDP's success at the Liberals' expense in this scenario has handed the Conservatives a remarkable 22 seats, which is even more than the NDP themselves have been able to pick up. In these 22 ridings, the Liberal vote has dropped below the Conservatives, but the NDP vote hasn't risen enough to pass the Conservatives. Yet, I hasten to add, though while the model continues, past here I think it really stretches the boundary of 'possibility' into 'strictly theoretical'.

But let's carry on: an extra ten percent reduces the Liberals to an eight-party rump, and this time it's just the NDP who benefit: the Conservatives and the Bloc stay more or less the same, while the NDP seat count vaults from 58 to 83. When we reach the 50% mark, the point were one in two 2008 Liberals have left the party and are now voting NDP, the Liberals have disappeared from Commons altogether and the NDP have now hit the 100 mark. One hundred MPs and a turnaround where the Conservative numbers are now starting to drop again - but at this 50% point, even if the 100-person-strong NDP caucus unites with the essentially-unchanged 50-strong Bloc caucus, and even in the unlikely event that Bill Casey and André Arthur side with them, the opposition is still not enough to topple Harper. The Conservatives still have a majority.

As we preside over the final destruction of the Liberals here, as we watch 60%, 70%, 80%, 90% and finally every last Liberal vote cross over to the NDP, these numbers switch. At 60%, the Conservatives lose their majority. At 80%, the NDP passes the Conservatives and we finally see the spectacularly unlikely face of Prime Minister Layton (provided Harper doesn't form a coalition with Duceppe...). And at the terminus of 100%, we have the point at which the Liberals and NDP have entirely combined to form a new party - a different 'unite the left' scenario - we see the NDP/Liberal party with 152 seats to the Conservatives' 113 and the Bloc's 41, and Casey and Arthur still laughing. But still no majority.

Which raises and entirely different point: that for all the talk of a divided left, that neither the NDP nor the Liberals can sneak to a majority by reaching into each other's pockets. In more than half the ridings in Canada, the theoretical combined Liberal/NDP vote remains less than the actual vote given to the Conservatives or the Bloc - there is simply no way either the Liberals or the NDP can get a majority without stealing votes from the Conservatives or Bloc, and there's no way they can get a functioning coalition without working with either of them. Not based on 2008's numbers, anyway.

Excepting that I've completely ignored the Green vote here. The Green vote could serve as a spoiler in a number of ridings, I don't know. That might be another thing to look at on another day.

However, I've only looked at half of the above graph. As the current Liberal caucus is much larger than the current NDP one, obviously the game of dominoes I've set up tumbles more entertainingly when we watch the Liberal vote shift to the NDP vote. But looking in the other direction, we see a very different story indeed.

Superficially, much is the same: the NDP number drops quickly, to the point where it takes a 50% vote shift to kill of the NDP completely (meaning that if half of all 2008 NDP voters in every riding in the country cast their votes this time out for the Liberals, the NDP would not win a single seat). We have to go all the way to 70% to see the Liberals pass the Conservatives as the party with the largest number of seats - what Harper would like to call 'the winner' (it was 80% for the NDP, though the 70% number was pretty close). And of course the end point is the same - as it should be, since 100% NDP support going to the Liberals is much like 100% Liberal support going to the NDP. The Liberals are as unable to vault to a majority on NDP backs as the NDP are on Liberal backs.

Yet there is a huge difference between these two scenarios: bleeding support from the NDP to the Liberals never pushes the Conservatives into majority territory - in fact, it never results in anything greater than a single seat gain for the Tories. In fact, as an NDP-to-Liberal bleed starts peeling seats away from the Bloc much faster than the other way round (since the NDP were much less of an issue in Québec in 2008 than they're shaping up to be thins time round), NDP-to-Liberal transfer immediately improves the total combined Liberal/NDP seat count.

A million other factors muddy the issue to the extent that nothing here has any value outside of the strictly academic, I concede. Yet when viewed strictly on the basis of this information here, the outcome is tough to overlook: to the extent that 'vote splitting' between the Liberals and the NDP can be seen as a 'key to a Conservative victory', it's really only true whenever the NDP manage to take votes from the Liberals: the Liberals can fearless steal from the NDP as much as they want without risking a Conservative majority, while the NDP can make no such claim.

A surprising result, perhaps. But one with many repercussions for the campaigns over the next month.