Yesterday, Election Canada released the transposition of the 2011 votes on the new electoral map. This one adds 30 ridings to the existing 308 and will be used for the next general federal election (scheduled for 2015). The 30 new ridings are in Ontario (15), Alberta (6), BC (6) and Quebec (3) (note however that even in provinces where the total number of ridings hasn't changed, the electoral boundaries were also modified).

Using the transposition of the votes, we can see that, had the new map been in effect in 2011, the Conservatives would have won most of the new seats, increasing their MPs from 166 to 188. The NDP would only have won 6 additional ridings and the Liberals 2. Looking at these numbers, medias and journalists were quick to write headlines and commentaries such as "Tories stand to benefit from electoral map" (and similarly in French).

The main problem is that this kind of analysis is, to say the least, too short sighted. In particular, the numbers presented yesterday by Election Canada show more the effects of the electoral system than the new map. With the current system (that we should change, but this is for another time), the party who finishes first in a region/province usually wins the most seats. And the system actually rewards this party with a disproportionate share of seats (compared to the share of votes). In 2011, the Tories won 54% of the seats with only 40% of the votes. Therefore, if we increase the number of seats, the winning party will receive most of them. It doesn't show a bias or effect of the map, but rather the impact of the outdated electoral system.

The main thing to notice is that since 2011, the vote intentions have changed drastically. In particular, most of the polls of the last 6 months show the Liberals of Justin Trudeau ahead. The good fortune of the Grits is particularly visible in Ontario. Given that half of the new seats are from this province, it's quite possible the new map will actually give the Liberals an edge. This could be particularly the case given that most of the new seats are in the south of Ontario (where the population growth occured), a region usually favorable to the Liberals (people are quick to forget how dominant the Liberals had been in this province for a decade before Harper won the most seats in 2011).

I decided to run an experiment to try to establish the actual effects of the new map. Using the transposition of the votes from Election Canada, I modified the seat projections model. Then I ran my usual simulations (read the FAQ page if you are not familiar with them) on the old and new map. The starting point for both sets of simulations was the same: the averaged numbers of the two recent spolls from Ekos and Abacus. The two polls show mostly the same situation: the Liberals ahead nationwide, with the Conservatives not far behind and the NDP around 24-25%. Both polls also have the LPC first in Ontario, although by different margins. All in all, these polls are consistent with most polls of the last few months (with the lead of the Liberals slowly decreasing).

What I was interested were mostly two things: which party would increase/decrease its share of seats (with the same, constant, share of votes) and would there be an effect on the probabilities of winning the next election. The results are presented below.

		CPC	LPC	NDP	Green	Bloc
old map	seats	103	123	78	1	3
	share of seats	33.4%	39.9%	25.3%	0.3%	1.0%
	chances of winning	13%	87%	0%	0%	0%
new map	seats	111	137	86	1	3
	share of seats	32.8%	40.5%	25.4%	0.3%	0.9%
	chances of winning	8%	92%	0%	0%	0%

As you can see, the party that is actually favored by the new map is indeed the Liberal Party of Canada, not the Conservative Party. But the impact is quite small. In term of seats, we can see that the Grits would receive the biggest increase, similarly to the fact the Conservatives were benefiting from the increased number of seats in 2011 in the transposition. The biggest effect is however on the chances of winning. Harper and his party drop from 12% chances to only 8%. As a reminder, these probabilities accont for the uncertainity due to the polls (i.e: we are not sure of the actual vote intentions) as well as the one due to the electoral system (and where the vote is).

Let's be clear here: with the same vote intentions (the current ones based on the polls), the new map increases the chances of winning for the Liberals by 5 points. If anything, it should be clear that the new map actually benefits Justin Trudeau. Why is it the case? One answer is of course in Ontario where the Liberals, currently ahead, would win most of the new seats. People are quick to point out the 6 additional seats in Alberta where the Tories have dominated for a long time. That is true, but let's not forget that 24 of the new 30 seats are in Quebec, Ontario and BC. These three provinces hardly qualify as safe lands for the Tories.

At the end of the day, what you should take from these numbers is the following:

- Who benefits from the increased number of seats is essentially a question of which party finishes first in term of votes.

- The effect is therefore mostly due to the electoral system, not the map itself.

- Even in cases where one party is almost guaranteed to win most of the new seats (like in Alberta), let's remember that the new map only corrects for the changes in demographics. In other words, Alberta deserves the added seats and if the Tories (or any party) win them, it's only because they are popular in this province. Winning seats because you are the favote option is only natural. If anything, we should be talking of the bias of the 2011 map where some provinces were under-represented at the House of Commons.

Overall, it seems to me the new map doesn't have a real effect. In particular, I don,t think we can speak of an advantage for the Tories simply because they would have won most of the new seats in 2011. The results of my simulations show relatively small effects, especially in term of seats. I'll of course re-run them if the vote intentions change drastically between now and the next election.

Les sondages sont plutôt bons pour QS. Ce parti pointe en effet aux alentours des 10% dans la plupart des sondages. Est-ce que cela se produira vraiment lors d'une élection générale? C'est une autre question. Imaginons que ce soit le cas. Est-ce que QS peut remporter plus de deux sièges?

Oui, plus que deux, car je considère que Gouin est définitivement prenable pour ce parti. Cela ne signifie pas qu'il est 100% assuré que Françoise David rejoigne Amir Khadir à l'Assemblée Nationale, mais c'est possible et fort probable. Non je parle ici d'autres circonscriptions.

Selon les projections actuelles, avec le PQ au-dessus des 30% et QS à "seulement" 10%, il ne semble pas y avoir d'autre comté prenable pour QS. Cependant, ce parti peut être très efficace pour concentrer son vote dans 1 ou 2 circonscriptions. Comme je l'ai souvent mentionné, en regardant la variation provinciale entre 2007 et 2008, il est quasiment impossible de prédire la victoire dans Mercier. Or, cette victoire est belle et bien arrivée. La question est donc de savoir quel genre de "bonus" QS peut obtenir quand cette formation cible un comté.

Une façon de répondre à cette question est d'estimer le bonus reçu par Khadir et David dans Mercier et Gouin. Par "bonus", je parle du pourcentage de votes supplémentaire obtenu, au-delà de ce que la variation provinciale de ce parti pouvait prédire. Voici ces estimations, obtenues en incluant une variable dichotomique dans la régression de QS (la méthode statistique que j'utilise afin d'estimer les coefficients régionaux de chaque parti pour mes projections).

Mercier 07: +7 points

Mercier 08: +8 points

Gouin 07: +17

Gouin 08: +5

Comme on peut le voir, les deux chefs de QS ont tous les deux bénéficié de boosts majeurs lors des deux dernières élections. Sans son 15-points de bonus, Amir Khadir ne serait pas député aujourd'hui. Encore une fois, soyons clairs, ces bonus sont le nombre de points de pourcentages de voix que le candidat a reçu en plus de ce qui était prévisible en utilisant les coefficients régionaux et la variation provinciale. Donc cela tient compte du fait que QS augmente davantage à Mtl lorsque ce parti augmente de 1-point provincialement.

Fait intéressant, le plus gros bonus est revenu à Françoise David en 2007. Mais malgré cela, pas de victoire pour elle. Cela signifie simplement que son comté est plus dur à prendre.

Pourquoi ces bonus? Plusieurs raisons. Tout d'abord, on parle ici des chefs de ce parti, donc ayant une forte présence médiatique. Deuxièmement, QS voulait avoir un député et a investi beaucoup d'efforts et de ressources dans ces circonscriptions afin de gagner.

Naturellement, nous parlons ici de pourcentages. Ainsi, si QS obtient 7-points de plus dans Mercier, ces 7-points proviennent d'un ou d'autres partis. Dans le cas présent, l'estimation révèle que c'est en grande partie du PQ (ce qui n'est pas vraiment surprenant) et dans une moindre mesure du PLQ/ADQ.

Regardons donc les quelques circonscriptions où QS est projeté relativement élevé. Dans Laurier-Dorion, QS pointe à 19%, derrière le PQ et PLQ qui sont respectivement à 31% et 35% (en ayant ces partis à 32% et 33% provincialement). QS n'est donc pas trop loin derrière et pourrait profiter du fait que le pourcentage requis pour gagner est faible (vu que plusieurs partis sont compétitifs dans ce comté). Ainsi, en ayant un candidat vedette et en se concentrant fortement dans Laurier-Dorion, QS pourrait gagner si ce parti arrive à récolter environ 10-points de plus, pris au PQ et PLQ. Même là, la lutte serait serrées mais c'est dans l'ordre du possible. Remarquez cependant que le bonus nécessaire est supérieur à celui obtenu par Khadir cependant.

Il y a également Sainte-Marie-Saint-Jacques (SMSJ) où le PQ domine avec 42% contre 22% à QS. Ici aussi, il faudrait un bonus de 10-points, mais pris entièrement au PQ, afin de rendre ce comté compétitif. On peut trouver 1-2 autres circonscriptions où QS est "haut" mais trop loin du PQ pour vraiment espérer gagner.

Au final, je dirais que Laurier-Dorion semble être la meilleure chance pour QS. En faisant une forte campagne ciblée, en faisant sortir le vote étudiant, QS peut légitimement espérer un 3e siège. Mais cela ne sera pas facile. Surtout que je crois que QS sera déjà fort occupé à garantir son second (ou deuxième si vous êtes optimistes) dans Gouin.

The same way polls are provided with margins of error, it would make sense to provide seats projections with some sort of uncertainty. But how to proceed? I'll explain here how I proceed and why.

1. Using the MOE in each province.

One logical solution would be to make projections using the MOE of the polls, or the average of polls since this is what I'm using for the "official" projections. It should be noted that projecting a federal election is more difficult than a provincial one because we need to estimate and apply the model in many provinces. And because pollster usually have a 1000 observations sample size, the polls are much more accurate when these 1000 observations are from one province only (like from Quebec) than from the entire Canada. Therefore, even by using an average of polls, we are still left with really big MOE in some provinces like the Atlantic or the Prairies. Here is an example.

Let's focus on BC, a province with 36 ridings. The Nanos polls have around 150 observations for this province, meaning MOE of 8-points. Let's see how much we can shrink this MOE by averaging most recent polls. The last Ekos poll had 302 observations for this province, thus a 5.6-points MOE. We also had a recent Leger poll, with 349 observations and a 5.6-points MOE. Finally, we also had a Harris-Decima poll with MOE of 6.2-points for BC. Those are the four most recent polls (note: I consider the Nanos as one poll only since every day, the update consists of adding around 400 new observations only. Hence, Nanos has one new full poll every 4 days). If we average these four polls, we get a MOE much smaller of course (here, a big assumption is that the only difference between these polls is the sampling size. In reality, we know that other things matter as well, such as the methodology (online or by phone for instance). But I'm not taking that into account). The MOE for the "meta poll" is 3.2-points only (if you wanna know how to do this calculation, simply sum the square of each MOE, take the square root of the sum and then divide by the number of polls). So basically, at 95% confidence interval, the percentages for BC look like this (note: technically the MOE is NOT the same for every party, it depends on the level of support. But pollsters and media usually use the approximation and give the same MOE to everybody):

CPC: 40.2% ±3.2%

LPC: 22.3% ±3.2%

NDP: 24.1% ±3.2%

Green: 11.3% ±3.2%

If you do the same calculations, you get a meta MOE of 3.8% in the Atlantic, 2.3% in Quebec, 1.9% in Ontario, 3.6% in Alberta and 3.4% in the Prairies. Therefore, to calculate the upper bound for the Conservatives, we should input the upper bound of the confidence interval in every province. What we are supposed to do with the other parties is not that clear. Should I also input the Liberals at the lower bound? It would make sense since if one party is doing better, it means the other ones are doing worse (in each province, the votes for the 4 four (5 in Quebec) main parties usually sum to 96% or even more, leaving very little space for the "others" parties). Let's try first to simply input the Tories at the max, leaving the others at the average.

Using the last 4 fours polls mentioned, the projections would change from 148 to 157 seats. Inputing them at their lower bound for the percentages, they would get 136 seats. This means that the 95%-confidence interval for the Conservatives is 136 seats to 157 seats.

The best case scenario for the Liberals would increase their seats from 75 to 82. The worst case scenario would be 71 seats, meaning the 95% CI is 71-82.

So overall it makes sense. It requires a lot of calculation of course. But is there a simple way to find these confidence intervals? Let's look at solution number 2.

2. Using the "close races".

What I call a close race is what others might call a marginal seat. This is a riding won by a margin of less than 5-points. Using the four polls mentioned, the Tories are projected to win 131 safe seats and be involved in 38 close races. For the projections, they would win 17 out of those 38 races. For me, a 100%-confidence interval would be 131-169. It is way bigger than the 95% CI calculated above. So what can we do? Well, there is no way that a party would lose ALL the ridings where this party was close. Neither is there a chance to win them all. If you look at the past elections, parties usually win between 30% to 70% of close races. Let's apply this here. If the Conservatives were to win only 30%, they would win 131+30%x38=143. If they were to win 70%, they would be at 158. That would give us a CI of 143-158, not so far from the above calculations. For the Liberals, the same interval would be 58+12=70 and 83. Here we are even closer.

At the end, this method of simply attributing more or less close races is of course less scientific. You can't use MOE to back this method. But it seems to provide a good approximation of the uncertainty in the projections and they require way less calculations. On top of that, one could argue it is more reality-based (as opposed to being based on some theoretical statistical concept).

For the final projections, I will probably do the two calculations. But for now, I'll simply mention the number of safe seats and close races.

Everyone pretty much assumes that the Conservatives have to make big gains in Ontario if they want their majority. Indeed, Quebec seems like a dead end for this party and Harper will likely settle for 9-11 MPs there. As for the Prairies, Alberta and BC, the Tories have pretty much maxed out over there. BC has a couple of seats around Vancouver where Harper and its party wish to make some gains, but that's all.

One region I personally think we don't give enough attention is the Atlantic. I'll try to explain here why I think the Conservatives can actually make some important gains over there. Recent polls consistently show that the CPC is higher in this region than it has ever been since 2004 and, more importantly, usually enjoy a decent lead over the Liberals.

This region has traditionally been very liberal. Even Stéphane Dion finished first over there in 2008, with 17 seats, while the Tories got 9 and the NDP 4. But of course, the key for this analysis is to determine if the ABC (Anything But Conservatives) effect of Danny Williams is still there in NF-L. The former Premier was very successfull in building a movement against the Conservatives and effectively managed to wipe them out of his province. So before looking at some scenario, depending on how much of the effect is still present, we need to estimate this ABC effect.

I admit that I worked very hard to estimate my model using the data for the Atlantic. It took me many tries before reaching a model that made sense. The real problem is of course that I have to design my model at the regional-level since polls are not provided at the province-level. One issue with that is that the overall swing a party experiences in the region can be the result of many different swings provincially. It was the case in 2008 where the Conservatives dropped from 32.6% in 2006 to 29.6%. But if you exclude NF-L, the Tories actually experienced a positive swing of 2.2%, with a particularly big increase in NB. Therefore, the huge drop in NFL where the Tories collapsed from 42.7% to 16.6% skewed the regional swing. On the other hand, the boost the Liberals got in NF-L allowed them to partially hide a lackluster performance in the Atlantic.

After some fancy tricks, I manged to estimate the coefficients to translate the regional swing AND estimate the NF-L specific effects. Namely, I found that the ABC effect was -32.7-points for the Tories, + 16.5-points for the Liberals and +8.3-points for the NDP (and virtually 0 for the Gren). If you are surprised to see the boost for the NDP to be so low, you need to remember that I also included a riding-specific effect for St-John-East where the NDP got a giant boost of like 46-points. So this effect alone accounted for a lot of the provincial swing of the NDP.

So whether those effects are still there is crucial in analyzing the current regional swing. Let's look at some scenarios to see that more in details.

1. The effects are still 100% there.

If this is the case, then it means the regional swing is really big. The current projections have the Tories standing at 39.2% in the Atlantic. That would mean a swing of 10-points, applied in all four provinces. With this swing and the effects still there, the current projections would give the Conservatives as many as 21 seats. Don't forget the Liberals are currently projected around 34%, thus slightly below 2008.

2. The effects are completely gone.

If this is true, then it means a large part of the observed regional swing is coming only from the increase in NF-L. Indeed, by jumping 32-points in NF-L and staying stable everywhere else, the Conservatives would now stand at 35% in the Atlantic. Therefore, the provincial swing would be only around 4-points, and not 10-points. With this scenario, the Tories would win 15 seats. Some might be surprised that the party of Stephen Harper is better off having the ABC still there, but it makes sense if you think about it. With the effect still there, it means the CPC is enjoying a big swing everywhere. Thus, big potential gains in NS, IPE and NB.

3. The effects are halfway gone.

This is the scenario I'm currently using. I see it as a compromise. I understand the Conservatives are saying the ABC is gone, but it doesn't mean it's true as some have commented in the past on this site. With this assumption, the CPC is projected to win 18 seats, right in the middle of the two other scenarios. I really like this compromis since it allows me to spread the observed increase of the Conservatives equally between the ABC effect being gone and a regional swing.

In any case, as I said before, Harper can still expect to make as many as 9 gains in the Atlantic. That alone would put the Tories almost in majority territories. Do not think this is negligeable. Yes Ontario is the real battleground, but we might well know whether Harper got his majority after seeing the results of the Atlantic alone. This is also a key region for Michael Ignatieff. It seems he can simply take the Atlantic as granted and a sure source of seats.

Elizabeth May is a puzzle for me. In 2008, she had an unique deal with Stephane Dion in that he agreed not to run any liberal candidate versus her. Yet, where did she decide to run? In the riding of Peter McKay! While she did get a pretty decent score of 32%, it wasn't enough to win and quite honestly, there was no way she would win this riding. In 2006, the Green party only got 1.59% in this riding! So why would she choose to run there? I understand this is where she lives, but still, the Green party is at the point where having an elected MP matters more than that.

So you would think May learned from her mistake and would run in a riding that she can win. But no, instead of running in Ontario where the Green did pretty good in two ridings (Guelph at 21% and Bruce-Grey at 27%), she decided to go to BC and run on Vancouver island in the riding of Saanich-Gulf-Island, a riding where the Green party only got 10.46% of the votes, well behind the Tories and the Liberals.

But can she win this riding? After all, it is clear there is a May effect. But how big is this effect? Let's estimate it using the results of 2008 and the by-election of London North/Centrer where she ran in 2006 and got a surprising 26%.

According to my estimates, in 2008, the Green party was in Central-Nova 29-points above what it should have been! Of course, this is the combine effect of Elizabeth May running AND having no Liberal candidate. Surprisingly, using the same estimation, I find that the NDP was down 15-points in this riding, while the Tories were up 8-points. Again, see those numbers as what would have happened if May wasn't the candidate and the Liberals had a candidate. It's interesting to see that some NDP voters decided to switch in order to give the Green party a chance. It isn't completely surprising given that a lot of NDP voters have the Green as second choice. It's also worth noting the little boost that CPC got. I'm guessing some Liberals voters were upset with the deal and switch to the Tories. As for the Liberals, if they had ran a candidate, I estimate they would have got 21%. So without May and with a liberal candidate, the results would have been:

CPC: 38%

LPC: 21%

NDP: 35%

Green: 3%

Instead of respectively 47%, 0%, 20% and 32%. Note how the maths sum up: the 21% of the Liberals were split into +8 for the CPC and +13 for the Green. Therefore, May got 13+15=28 points more than if it was a regular Green candidate.

So what about the May effect in the by-election in 2006? In the 2006 general election, the Green party got 5.49%. Then, during the by-election, May got 26%! So, at the end, it seems Elizabeth May does benefit of a huge boost in term of votes whenever she runs in a riding. Quantitatively, I would say she can get a jump as high as 20-points. Mostly at the expense of the NDP. Indeed, the Liberals were barely affected in the by-election. In both cases, I would say the May effect was: 5-8-points taken from the Liberals, 10-15-points taken from the NDP. (yes she got around 13-points from the Liberals in 2008, but there was no candidate. It's not the same as having liberal voters deciding to switch simply because it was Elizabeth May).

So let's be generous and give May a 20-points boost, taken at 1/3 from the Liberals and 2/3 from the NDP. Does it allow her to win her seat in BC? Using the latest Ekos poll who puts the Green as high as 19.7% in BC, we have the following projections for Saanich-Gulf-Island:

CPC: 36%

LPC: 42%

NDP: 0.1%

Green: 21.5%

Let's add the May effect. One problem is that this riding has already a low percentage for the NDP, so not so much votes to take from them! At the end, May would need to steal as much as 11-points from the Liberals. It's more than what we have observed in the past. And remember, I'm using a poll very favourable to the Green!

So back to my question: why running in a riding where the Gren party was low in 2008 and where the NDP is low as well? That doesn't make any sense. On the other hand, the current projections place the Green at 36% in Guelph and 28% in Bruce-Grey. In both case, if you add the May effect, you would get a win for her and her party (especially in Guelph). So why did she decide not to run in one of those ridings? I don't know. Let me know if you have a theory.

I'll modify the model to take into account of this May effect of course.

Ok so here we are, in election! I know most people are not happy about that, but I'm sure that most of my readers are, as any political junkie. Today, I'll not post new projections based on one or two polls. Instead, I would like to justify a little bit my model and why I think it is valid. Of course, you can get more details if you read the methodology under the tab FAQ.

The point I want to address today is the following: can we really predict riding-level swings using the provincial swings only? After all, I'm sure some of you are skeptical. Simply because one party increases by 4 points in a province doesn't mean this party will increase by 4-points in every ridings. The 4-points provincial swing is an average, and an average could hide a lot of variation. For instance, it is technically possible that this 4-points increase came from an increase of 12-points in 50% of the ridings, and a decrease of -4-points in the other 50%.

I showed in this post what the swing looks like. It isn't perfectly uniform, nor is it perfectly proportional. Actually there is a lot of variations. Nevertheless, it turns out that the provincial swing is still a good predictor, especially if we interact it with other variables. But before showing you numbers, let's see what kind of information we have about each riding. I'm talking here about information publicly available during an election, so the GDP per capita is not one of them.

-The past results of every party.

-The current incumbent.

-The province and region where the riding is located (ex: Montreal West or Quebec city).

So by using the provincial swing and these other variables, we can get a lot more predictive power. For instance, it is obvious that when the Conservatives increase in the province of Quebec, they increase much more in the region of Quebec city than on the island of Montreal. We know that because we can observe the past elections' swings. We can also look if a party did better or worse in the ridings it won the last election (an incumbency effect). This is really where the use of statistical tools such as a regression (or econometrics in general) helps a lot. Other websites can't take into account so many variables, not at once. I can even differentiate the swing in function of the level of support of the other parties (for instance, when the Tories go up in Ontario, do they take votes from the Liberals or the NDP?).

At the end, the predictive power varies across provinces and political parties. It works really well for Quebec and Ontario, for the two main parties. For instance, I can explain as much as 89% of the riding-level swing for the CPC in Quebec! This number is 86% for the Liberals. The remaining 12-15% could be inputed to riding-specific events, or on an efficient organization (to get the vote out).

On the other hand, it works usually less well for the NDP. The reason being that this party has experienced less variaiton over the last couple of elections (in most provinces, the NDP stayed really flat), so I have less variation to identify (pin down if you prefer) the coefficients. Nevertheless, I can explain around 76% of the swing for the NDP in Quebec, but only 22% in Ontario. When this number is that low, I actually switch to a simple linear-uniform model for this party. This is unfortunate but there isn't much that can be done. And anyway, as shown in my methodology, the linear-uniform model already provides a good approximation.

So, here you go. It seems that we can indeed project riding-level swings using only the provincial ones as the source of new information. In average, we could explain over 70% of the swing. But it works better in big provinces and for political parties that have experience changes over the year. I would say the best scenario for the model would be to have the CPC down a little bit (going closer to its 2006 results) and the Liberals up a bit. On the other hand, if the Tories get closer to 40% and the Liberals keep falling, we could face a problem of extrapolation. Indeed, since we've never observed the Liberals so low, we don't really know what would happen. But as long as the changes are not too big (and let's face it, they usually aren't), it works just fine. In 2006, given the correct percentages, the model would have predicted correctly 286 ridings. In 2008, it was 283. And most of the mistakes were in close races (where the margin of victory was less than 5-points). Better than that, in average, the projections were accurate within around 2-points (so for instance, the model predicted the CPC at 46% and the actual result was 44%.

The election isn't officially started yet, but we're already talking about a possible coalition between the LPC and NDP (and, to a lesser extent, the Bloc). This post is not intended to promote such coalition. Nor do I want to argue whether such coalition is legitimate or a good idea. My objective here is simply to show how many seats such a coalition could grab. And I'm well aware that the scenario studied here is highly unlikely to happen in Canada. So don't fall on me for that lol See that as an academic exercise, nothing more.

I'm talking here about a coalition PRE-election, where the NDP and LPC officially announced that they would do one. If such a situation should occur, then I believe the two parties should actually "exchange" candidates in some key ridings. Indeed, it is the case that in some ridings, the CPC can win, but the total sum of votes for LPC and NDP is actually greater. When it is the case AND those two parties want to do a coalition, then they should be logical and leave only one candidate. That would avoid a split of the "coalition votes". But of course, to really forecast what would happen in such circumstances, we need to take into account the second choices of the voters. Indeed, it is obvious that in the event that the NDP removes its candidate, not all voters will follow the order and give their vote to the Liberals. Some will simply not vote, while other will vote for another party, including the Conservatives.

So here are the details of this experiment:

- I'm using the latest projections, based on the average of most recent polls.

- I'm using the second choices as given in one of the latest Ekos poll.

- I'm assuming that the coalition would do such a candidate swap only in the ridings where they can potentially beat the Conservatives. Specifically, it has to be the case that CPC is first, and LPC+NDP is greater than CPC. As you'll see, the number of ridings currently in this situation is not that big.

- The "coalition" would remove the candidate from the party that is currently third. In other words, if the Tories are first, the Liberals second and the NDP third, then the NDP candidate would have to go.

- When one candidate is removed, I'm using the second choices of the voters of this party and redistribute the votes.

This redistribution requires some explanations and assumptions. First of all, I'm well aware that some voters would switch even though their first choice is still technically available. For instance, in our previous example, we could expect some Liberal voters to actually change their votes simply because they don't want a coalition with the NDP. That could happen to some voters that are exactly between the Tories and the Liberals. Here, I'm assuming that this isn't the case. This introduces a bias, but hopefully it will be canceled out by the next assumption. The second choices are biased as well. Indeed, it is one thing to not name the Liberals as your second choices when you are a NDP voters (possibly, you don't have a second choice, which happens in around 30% of the cases), but it's another thing to be told by the NDP to vote LPC. We can imagine that some voters that didn't have the Liberals as second choice would still switch their votes, simply because they understand the whole principle of the coalition and the candidates exchange. I don't model that. So at the end, I have two assumptions who both introduce a bias, but in the opposite direction. In the future, I could try to "play" with those assumption and see what it would change (or even better: maybe we'll have one pollster asking specifically how many people would switch or not, in the event of a coalition).

So, enough about the technicalities, let's see if such a deal could actually benefit the Liberals and NDP. Based on the current projections (they are a little bit different from the ones displayed on the right because I added the latest Ipsos poll), here is what such a deal would change:

Number of ridings where the LPC+NDP>CPC: 34

seats	actual	coalition
CPC	153	148
LPC	72	74
NDP	32	35
Green	0	0
Bloc	51	51

So, out of the total of 34 ridings where the coalition votes is higher, such a deal would only take 5 seats away from the Conservatives. The main reason? Well it is the retention rate. Specifically, only 32% of NDP voters have the Liberals as second choice (and 33% of LPC have the NDP). Those numbers are not high enough to warrant such a deal pre-election. However, let me say two things.

1) The current projections are very favourable to the Tories. We'll see what happens during the campaign. Such an exercisee would give different results if the Liberals go up and the Tories go down. For instance, if we were to go back to the levels of support of 2006, you would see that such a coalition would be much more effective.

2) As I've said, maybe one of my assumptions is to harsh. Do you really think that only 32% of the NDP voters would switch to the Liberals, while 23% would prefer to vote for the Green and 25% would simply not vote? I have a hard time believing that. Polls usually showed that the NDP voters were quite pro-coalition, back in 2008 (but in the same time, as I've said, some Liberals voters could be scared off as well). So I might adjust those assumptions. In my simulations, it seems that the coalition becomes effective when the retention rate is at 45% or more.

In any case, as I've said, this is simply meant as an exercise. I will repeat it or modify it during the campaign. In the mean time, let me know what you think. By the way, you might think that "stealing" 5 seats away from the Tories is not that big of a deal, but if those 5 seats are the difference between a majority and minority, it could well be important!

In its latest poll, Ekos asked the second choices, as well as asking who they voted for in 2008. I always find those questions very interesting.

For the retention rate, we see that the Conservatives are the best. They would keep 77.3% of the people who voted for them in 2008. The Liberals would keep only 63.8%, while the NPD and Bloc stand at respectively 61.6% and 73.8%. Surprisingly, the "lost" voters of the Liberals would actually go the the NDP (13.3%) and the Green (14.2%), more than to the CPC (11.5%). This is one of the only good news in recent weeks for Igniatieff: it seems he has a pool of potential voters in the Green and NDP. In case of an election, I think it's likely that those people could quickly come back to the Liberals if te prospect of a Tories majority becomes real. Of course, for the Lib, keeping the voters of 2008 is hardly enough to make some gains in term of seats. But it's a start.

The second choices show how the Conservatives are different. Indeed, they are the party with the most voters that have no second choice at all (as much as 48.6%!), while this number is only around 25% for the Liberals or NDP. I was also surprised to see that among Green voters, the second choices are split almost evenly between the NDP and the Liberals. I was expecting the NDP to have the edge here.

So using those numbers, let's do a little bit of math. In particular, let's see what would happen if the Bloc didn't exist in Quebec, and what would happen if the Green party didn't exist. For each scenario, I will also input those calculated numbers into my model, even though the model is not meant for that. I'm assuming that people without a second choice would simply not vote.

Scenario 1: No Bloc.

	actual	no Bloc	seats
cpc	15.4%	22.3%	20
lpc	21.7%	30.6%	36
ndp	12.5%	23.8%	13
green	11.3%	19.3%	6
bloc	35.9%	-	-
other	3.2%	4.0%	0

In term of percentages, the NDP would be a clear winner. However, in term of seats, the Tories would actually get all the forteresses of the Bloc (in rural Quebec). The Green would get as many as 6 seats, but this is only because in this poll, they were already high. As opposed to the projections using this Ekos poll, the CPC would gain 12 seats, the LPC 19. the NDP 12 and the Green 6.

Scenario 2: No Green Party of Canada

Here I'm assuming that the second choices are the same in every province, since Ekos doesn't provide us with the provincial breakdown.

	actual	no Green	seats	gain
cpc	35.2%	37.9%	137	0
lpc	27.8%	31.2%	84	-4
ndp	14.9%	17.9%	34	2
green	10.1%	-	-	-
bloc	8.8%	9.6%	50	2
other	3.1%	3.5%	0	0

In term of seats, not many changes, even though the Green Party seems to be costing the NDP, 2 seats and 2 other seats to the Bloc, both at the expense of the Liberals. Since the Tories don't suffer any overall loss, it seems the Green party is only affecting the distribution of seats among the other parties. If you want to compare province by province, here is the breakdown:

Ekos projections:

Ekos No Green:

You can see that at the province level, the absence of the Green party would also affect the Conservatives. But at the end, it seems that the Green party is not big enough (yet?) to actually change the colour of the government or cause substantial seat cheanges.

When a party's support increases in a province, how does it translate in each riding? The answer to this question is crucial as to which forecasting model to choose. So let's look at some graphs.

Let's look at the Conservatives (a party who experienced quite a lof of changes at the provincial level during the last 5 year), in Quebec (where the model usually performs at its best, both for the federal and provincial elections) during the last election (2008). The next graphs displays the swing at the riding level, sorted by the level of support during the previous election:

Remember that province-wide, the Conservatives dropped from 24.6% to 21.7%, thus a decrease of 2.9 percentage points, or -11.8%. Therefore, if the swing was uniform, we should see all the dots on the same horizontal line, at 2.9 (red line). On the other hand, if it was proportional, we should see the dots as forming a straight line decreasing (representing -11.9% of the previous level of support) (green line). As we can see, both assumptions would clearly be wrong. There is considerable amount of variation between the riding-level swings. You have an easy-to-understand graphical representation of how those two simplistic models could be wrong.

By the way, you get similar plots if you use other parties and/or provinces. Just to prove that I didn't use the one example that proved my points, here is a similar graph for the Liberals in Ontario, in 2008.

Here, I didn't bother showing the proportional change line, since it is obvious it wouldn't fit the data. Rather, I added the projection of the model. While I agree it isn't very clear that the model is performing better, what I would like you to notice is that the projected values are not on a straight line. Using regional effect, incumbency or the level of support last election, (for each party) my model is able to better forecast the outcome, without having to rely on an arbitrary assumption such as uniform or proportional changes.

Let's go back to the CPC in Quebec. Another aspect that might be surprising is the fact that the Conservatives actually increased their share of votes in some riding, despite a drop at the province-level. How to explain this? Well, first of all, individual effects could play a role, such as a new candidate or other specific events (for instance, what happenned to Maxime Bernier). Second of all, we are looking at shares of votes here, meaning that even though a party lost some votes, it could still increase its share if the other parties lost even more votes. For the model, I project every party and then make sure the percentages sum up to 100%. However, on e downside of the fact that riding sometimes go against the provincial trend is that my model could lead to weird results. Indeed, since I'm estimating my coefficients, the model could give parameters such that the support for one party would decrease in one rding when this party increases at the provincial level. This can be a potential problem but since I'm using more than one election, hopefully those weird effects will not biase the estimates.

At the end, it is really difficult to find evidence that the swing is proportional, especially in Ontario and Quebec. This is the reason the proportional swing model performs significantly worse than any other models, incuding the linear one, as shown in my methodology pdf. And this is why I find it weird when I see some websites basing their model on this assumption.

I'll post soon about how proportional models can even be worse for small of third parties.