Thursday, December 11, 2014

What's the threshold for a minority or majority government?

The current federal polling averages give the Liberals 34.5% support against 32.1% for the Conservatives. Yet, the Conservatives are projected to win 133 seats with those numbers and the Liberals just 128. What kind of margin do the Liberals need to win a plurality of seats? How close do the Conservatives need to make the race in order to come out ahead? And what do they need to win a majority?

Let's take a look at this for all three parties. But first, a few words about how I came to these calculations. I started with the current averages and then uniformly lowered or raised each party's support in each region of the country. I based my adjustments on EKOS Research's last 'second choice' poll as follows:

For every one point gained by the Conservatives, 0.7 points were subtracted from the Liberals and 0.3 points from the NDP (in Quebec, the Bloc was subtracted 0.1 point and the NDP 0.2 points). For every one point gained by the Liberals, 0.6 points were subtracted from the NDP, 0.3 points from the Conservatives, and 0.1 point from the Greens (in Quebec, the Bloc was subtracted 0.1 point instead of the Greens). For every one point gained by the New Democrats, 0.7 points were subtracted from the Liberals, 0.2 points from the Conservatives, and 0.1 point from the Greens (in Quebec, it was 0.6 points from the Liberals, 0.3 points from the Bloc, and 0.1 point from the Conservatives).

We'll start with the Conservatives, who have the most efficient vote of the three parties.

The gap might currently stand at 2.4 points, but it could theoretically widen to as much as 4.1 points and the Conservatives would still narrowly come out ahead in the seat count. With 31.1% of the vote against 35.2% for the Liberals, the Conservatives could win 129 seats against 127 for the Liberals.

The party won a majority governing in 2011 with 39.6% of the vote, but it could manage the feat with a little less. With 38.1% support against 30.3% for the Liberals and 20.7% for the NDP, the Conservatives could reach the magic 169 number and form a majority government. The Liberals would take 102 seats and the NDP would win 64.

This assumes, roughly speaking, that the Conservatives have 63% support in Alberta, 45% support in the Prairies, 42% support in Ontario, 38% support in British Columbia, 30% support in Atlantic Canada, and 22% support in Quebec. This is with a uniform swing of the vote, though. The Conservatives could probably win a majority with even less of the vote if, say, they took a greater share in British Columbia and a lot less in Quebec.

Now to the Liberals, who find themselves needing more votes than the Conservatives to come out ahead in the seat count, or to obtain a majority government.

With the Conservatives now above 30%, the Liberals would need about 36% support to ensure a plurality of seats. With that much support, the Liberals could win 131 seats to 130 for the Conservatives if they are at 31.6%. The NDP, at 21.6%, would win 73 seats.

To reach the majority threshold, however, the Liberals need the NDP vote to drop much further. With 41.5% support to 29.9% for the Conservatives, the Liberals would take 172 seats and leave 118 for the Tories. The NDP, down to 18.3% of the vote, would take 44 seats.

Of course, the Liberals could also benefit from the Conservatives dropping much further below 30% than this, but we're working from current polling levels.

Regionally, the majority threshold awards 59% of the vote to the Liberals in Atlantic Canada, 45% in Ontario, 40% in the Prairies, 39% in Quebec, 38% in British Columbia, and 30% in Alberta. Here again, there could be a more efficient way to reach the majority threshold by, say, taking more of the vote in Ontario and a lot less in Alberta and the Prairies.

Finally, the New Democrats. Because of their advantage in Quebec (akin to the Conservatives' advantage in the West), the NDP can reach the plurality threshold with less of the vote than the Liberals, But they need more of it to reach majority territory.

In a tight three-way race, the New Democrats could win the most seats with 33.5% of the vote, pushing the Conservatives down to 29.9% and the Liberals to 26.8%. The Greens also need to be lower than for the Liberals and Conservatives, and the Bloc down to 15% in Quebec. With these numbers, the NDP would take 124 seats to 123 for the Conservatives and 90 for the Liberals.

At the majority threshold, the NDP needs to be at 42.5% of the vote nationwide. The Conservatives would be at 28.1%, but the Liberals need to sink to about the same level of support they had in 2011, with 20.5%. The Greens need to do worse than 2011, while the Bloc vote is cut in half. With these numbers, the NDP takes 172 seats to 100 for the Conservatives and 65 for the Liberals.

The NDP would take 49% of the vote in Quebec, 46% in British Columbia, 41% in the Prairies, 40% in Ontario, 40% in Atlantic Canada, and 34% in Alberta. The NDP's support is more uniform than the other parties, with the six regions differing by no more than 15 points. That range is 29 points for the Liberals and 41 for the Conservatives.

What about the Greens and the Bloc? Their immediate goal should be to achieve official party status, or 12 seats. The Bloc can reach that level quite easily due to vote splits with around 21% support in Quebec, if the NDP drops to 27% and the Liberals to 32%.

For the Greens, it is much more difficult and, to be honest, the model gets a little wonky once we start trying to extrapolate for this party. But the Greens would win their 12 seats with 18% support nationwide, with the Conservatives at 31%, the Liberals at 29%, and the NDP at 16%.

But just how plausible are the thresholds for the major parties? We've seen the Liberals and Conservatives at the plurality level in many polls recently, but the majority threshold has been harder to achieve.

(Note: the numbers above don't add up to the total number of polls because in some cases no party would have reached the minimum thresholds. For instance, if the Liberals were at 34% and the Conservatives at 31%. Obviously, some party would win a plurality in those cases but the numbers above are in terms of the threshold, which can be considered the level of support where winning a plurality/majority would be very likely.)

There have been 175 federal polls conducted since the 2011 election, and 42 in 2014 alone. The Conservatives have hit the plurality threshold in 93 of those polls (53%), but only in nine of them in 2014 (21%). The party reached the majority threshold in 11 polls, but the last time that happened was in January 2012, almost three years ago.

The Liberals have been above the plurality level in 37 polls since 2011 (21%), but 22 of them have been in 2014 (or 52% of those held this year). The majority threshold has only been hit three times, however, and all in polls by Forum Research (the firm that routinely has the party highest). Only once was that majority threshold reached in 2014.

For the New Democrats, the plurality threshold was reached in 19 polls since 2011 (11%), but these were all in the period between March and September 2012. The party never hit the majority threshold in polls conducted since the last election, and perhaps never before that either.

This little exercise does show how difficult it will be for the parties to secure a majority government in 2015. The Conservatives clearly have the easiest path, but it has been a very long time since the party has been that strong in the polls (and that was at a time when the future of the Liberals was still in question and the NDP was leaderless). The Liberals could conceivably reach the majority level if the campaign goes very well for them, but it would be a tall order. A majority for the NDP seems out of the question.

A plurality for any of the parties would be easier to achieve, of course, with the Conservatives having the easiest route. The Liberals could pull more seats out of fewer votes than estimated here if their support proves to be more efficient than expected in places like Quebec. Nevertheless, they likely need to win by a relatively comfortable margin to come out ahead in the seat count. The New Democrats have it within their reach if the Liberals falter on the campaign trail, but it would require virtually all of that lost Liberal support to go their way, rather than towards the Conservatives.

At this rate, I'd bet on no party obtaining a majority in 2015 - but that is about it.


  1. After that exercise perhaps you could answer:

    How many angels can dance on the head of a pin?

    Using EKOS 2nd choice poll ?

    Using polls that are 3 years old to try to display the threshold probability.

    there were no polls of the 22 taken within 2 weeks of the last election that had the CPC exceed the Majority threshold you established and yet there is in fact a majority.

    Over the same time period 5 polls called for a NDP plurality along with a CPC plurality in the same poll.

  2. As you seem to be looking for in-direct applications of polls how would you like to interpret the political impact of the Leger poll that says that only 12% of Canadians are willing to spend $1500/ year.

    This is the cost of proposals of two environmentalist groups, Équiterre and Vivre en ville.

    In terms of environmental impact for the province of Quebec, despite the magnitude of the sums in play, total oil consumption would only be reduced by 20% and GHG emissions would fall by just 12%.


  3. The Conservatives need not a plurality, but a majority in order to govern past the next election. There is no way that the Conservatives will be able to govern without the party having a majority. A lot has changed from the 2006 to 2011 period. Stephen Harper and his circle knows that.

    Last time the Conservatives were polling in majority territory, the government was still in a honeymoon phase after winning a majority and were facing a leaderless NDP and Liberal Party in disarray.

  4. There's a strong rationale for proportional representation here - how can our votes be equal if they're not equally "efficient"?

  5. What's the history on parties winning a plurality without winning the popular vote? It seems like a very large gap needed before the Liberals win a plurality, but I can't think of this ever happening before. And I imagine most Canadians would be up in arms about how undemocratic it is if it did happen.

    Basically, I'm wondering if this high bar to a liberal victory is a result of your model, as opposed to a likely election outcome.

    1. The last time was 1979, when the PCs won 136 seats with 36% of the vote and the Liberals won 114 seats with 40%.

      Prior to that, it happened in 1957, 1926, and 1891.

      The fact of the matter is that very close popular vote results are not all that common, so this aspect of the FPTP system hasn't been tested that much. A gap of five points or less between the two major parties has happened four times since WWII, and two of those were in 1957 and 1979.

    2. Provincially it's happened more recently than 1979. In Quebec, Charest as Liberal leader the first time around became the Leader of the Official Opposition even though he won the popular vote. In fact the PQ got a majority thanks to Quebec (practically) being a 2 party province then, save for Mario Dumont's then-fledgling ADQ. Even more recently who can forgot Al Gore losing the Presidency thanks to Florida, despite winning the popular vote in 2000...and the denied recount which would have almost certainly made him the president instead of the clown the US ended up sure helps having your brother a Governor eh! America and the world would sure be a different place today had Gore won.

    3. Seeing what Gore has become since, I think we can safely agree that Bush was a blessing.

      However, He still won the election as the Democrats were advocating selective recounts in Democratic strongholds.

  6. I believe no party will get a majority..My money is betting large on a Justin Trudeau minority Government.

    The public has seen Stephen Harper`s majority in action, they don`t like it, public it about to take away the car keys from Harper..

    If Stephen Harper manages a whisker thin minority Government.....Harper can`t govern in a minority, his plans get flushed down the toilet..

    Expect a February 2015 snap-election call....Followed by another election in the fall of 2015.


    1. People have also now witnessed young Trudeau's leadership for the better part of two years and he has been unable to provide the Liberals with a solid lead, meaningful policies, plan or reason for governing. Don't expect miracles from an unproven leader, if Justin can't place the Liberals in government territory before an election he's unlikely to boost the Liberals into "governing polling range" during a campaign.

      Aside from Liberal smears that people "don't like Harper" (whatever that means?) Canadians respect the man and appreciate the honest and well governed administration he has provided. Canadians may not love Harper but, they respect his abilities, the same can not be said about Trudeau.

      The other Liberal myth that Harper can not govern with a minority is absolute nonsense-never mind the fact Harper was prime minister through two minority parliaments! Harper as prime minister will remain as prime minister until defeated on a confidence motion, at which point the Crown will either appoint a new PM or call an election. If the numbers remain where they stand today Tories; 133, Grits 128, NDP 74 I don't see much incentive for either the Liberals or NDP to prop up the other in government. For the NDP it would mean returning to third party status and for the Liberals it would mean abdicating their traditional governing party status and giving the NDP governing party legitimacy. Then of course is the question of whether Trudeau can govern without senators? How can the Crown appoint a man who does not believe in party senators? How will Trudeau introduce legislation without the willingness to appoint government senators? The Crown may very well wish to avoid the impending constitutional crisis constructed by young Trudeau and appoint a PM with a clear plan; either Mulcair who favours abolition or Harper who has senators and favours reform.

  7. And this is why I like FPTP - it's vastly more likely to produce majority governments.

    For examples of oddity, I'd point to the 1921 Alberta provincial election. There, the Liberals won the popular vote 34-29 over the UFA, but the UFA won a majority.

    1. Majority governments are undemocratic.

    2. This comment has been removed by the author.

    3. Is that a good thing Ira? Lol.

      PR produces majority governments more often than FPTP has for Canada though. They're majority coalitions. The phrase you're looking for is a single party majority government.

    4. People who think majority governments are not democratic are not democrats themselves.

      The fact of the matter is there needs to be a mechanism for society to decide questions and majority rule is the best and most logical way to do so. In parliamentary systems with PR parliamentary votes are still decided by majority vote. If questions were note decided by majority nothing would ever be resolved

  8. From Eric's work it would seem in 2014 it is to be a Liberal majority !!

    1. unfortunately for you, the election will be in 2015, not this year... ;~)

    2. Peter,

      As per Eric's analysis above only 1 poll gave the Liberals a majority, 22 gave Liberals a plurality a 9 gave the Tories a plurality therefore, 1/32 polls predicted a Liberal majority. I would suggest revising your statement above as it is incorrect.

    3. Pick many nits chimurenga ???

  9. Interesting article, but what about a study in all those close ridings discribing the probabilities of winning for each party?

  10. Interesting to see. I'd also wonder how the UK's three-way swingometer model would work in Canada?

  11. Excellent analysis. But once again, I must point out that the seat threshold for a majority (50%+1) in the new 338-seat parliament is 170 seats, not 169.

    1. With a Speaker from one of the opposition parties, you could have a majority government with 169 MPs.

    2. Eric and Nicholas,

      In theory an evenly divided House with the Speaker from the opposition would provide a 1 seat majority for the Government, however, I suspect an opposition M.P. in such a scenario would be prevented from running by his party and cross the floor providing the Government with a two seat majority. This is a good time to remind everyone that in the case of an evenly divided House the Speaker votes in the affirmative to continue debate but against the final enactment of bills (3rd reading).

    3. The opposition parties are unlikely to go along with that for that very reason though.

    4. That's true and in the event of a tie, "parliamentary tradition" dictates that the speaker votes with governing party, even if they're a member of the opposition. Didn't Milliken (a Liberal) side with the then-minority Conservatives on a tie vote of confidence?

    5. Yowzaa,

      Convention does not dictate the Speaker vote with the governing party. Speaker Denison's rule which governs the behaviour of the Speaker in the case of a tie stipulates the Speaker votes in the affirmative to carry on debate but, against implementation of bills (3rd reading) and confidence motions.

    6. addendum:

      Speaker Denison's rule means that the Speaker votes in favour of opposition motions at first and second reading. Therefore, one can not say the Speaker "votes with the governing party".

  12. The trouble for Harper is its majority or bust. So long as Liberal+NDP+FeD+Green>Conservatve+Bloc, the Conservatives will lose their throne speech, and the Liberals+NDP+FeD+Greens will send letters to the Governor General saying they have the numbers to form a government with the confidence of parliament. The best the Conservatives can do at that point is prolong the inevitable by proroguing.

    The other parties cannot support a Conservative government at this point. The well has be poisoned too many times, and if Trudeau or Mulcair tried to prop up Harper, they'd be lynched by their own supporters.

    1. I think the CPC knows they need another majority, or a badly weakened opposition party (some serious scandal befalling the Libs or NDP to prevent the other from publicly cooperating) in order to win.

      I'm sure a majorty is the goal, as it was last time.

      And CPC support appears to be rising. They're consistently polling now at about 33, a level they haven't seen consistently since 2012.

    2. Ryan,

      Government formation does not work the way your comment implies. It would be inappropriate for opposition leaders to offer unsolicited advice to the Crown and it would be unconstitutional for the Crown to act on that unsolicited advice! As the two previous attempts at unsolicited advice demonstrate the Crown rightly ignores such letters and advice. If the Government is defeated on the Throne speech the GG will either invite another party leader to form government or dissolve the House. Since, Trudeau foolishly dismissed his senators the GG may recognise Trudeau can not guarantee supply and call an election.

    3. The majority or bust theory is risible. Never mind that Harper is Canada's longest serving minority parliament PM! Harper more than any PM in recent history has demonstrated he can work with other parties to get his agenda passed while governing on behalf of all Canadians.

      Fundamentally the majority or bust theory rests on a strange presumption: it is in the best interest of the NDP to prop up a Liberal minority and vice versa. Why would the NDP whose main competition is the Liberal party wish to strengthen their opponents hand? If the NDP is to repeat the success of Labour in the UK (this has been the main goal of the NDP for most of their history) they know Liberal instability is their best bet. The Liberals will not be reduced to a minor party in the course of a single election, but, like in the UK through successive elections close together. The NDP will want to keep the Liberals off balance so they don't have time to regroup or prepare for the next election.Propping up a Liberal minority would give Justin Trudeau and Liberal major party status by default and revert the NDP to third party status.

      Why would the NDP or Liberals wish to be a junior partner? The UK experience is less than optimistic for the junior partner. More importantly why would the Liberal party give "government legitimacy" to the NDP? To do so would create two left-of-centre governing parties. A split centre-left vote is a recipe for continued Tory government. To enter into coalition would be to admit the Liberal party is no longer a majority government or national party.

      The biggest obstacle to the majority or bust theory are the Liberal party and the NDP.

  13. Your Conservative majority scenario has them at 169 seats, and against 164 for the Liberals + NDP. I'd like to see the numbers that generate 163 Conservatives and 170 Liberals + NDP, since that's the threshold to boot Harper out of office.

  14. Wilf

    163 Cons 100 NDP and 70 Liberals means a Cons minority Government..... or the end of the Liberal Party of Canada and the other party have to worry about extinction.

    If a vote for the Liberals actually mean a vote for Mulcair to be PM.

    The Ontario NDP and Liberals .... with basically a NDP budget couldn't hold together a coalition.

    For Trudeau or Mulcair to become PM one of their parties would have to come at least within 10 of the Cons in the number of seats.

  15. this exercise is just mathematically wrong--

    The Cons level for plurality is 31% the NDP is 33%

    so based on the last election results with the Cons at 39.6% and the NDP at 30.6 %

    so if the NDP gets an extra 3 % from say the Liberals... the Cons could have a majority in this model but the NDP would be over the % that they would have a plurality.

    1. The model assumes that whatever party one is looking at has a plurality ergo, 31% produces a Conservative minority if the Liberals receive no more than 35.2% and the NDP no more than 21.6% of the popular vote.

      I don't think the exercise is mathematically wrong but, it is based on assumptions. For instance Eric; "uniformly lowered or raised each party's support in each region of the country". So, if the Tories garnered 80% of the Alberta vote that 31% number would be unlikely to give them a plurality. The exercise is not mathematically wrong but, it does have certain limitations. What is does show is the approximate popular vote needed for a plurality of majority government by party.


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