A nation-wide public opinion survey released three years ago had a startling finding.

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''For the first time in our polling,'' began an analysis published by EKOS Politics and iPolitics.ca on July 3, 2012, ''the New Democratic Party of Canada now leads in federal vote intention.''

According to the poll, Tom Mulcair and his New Democrats were the first choice for 32.4 per cent of respondents.

Stephen Harper's governing Conservatives were in second-place at 29.3 per cent, followed by the Liberals under Bob Rae in third with 19.2 per cent.

That poll and many to follow showed the governing Conservatives -- winners of a majority government in May 2011 with 39.6 per cent of valid votes -- were in trouble.

And Mulcair's NDP -- the party that drew 30.6 per cent in 2011 under the late Jack Layton -- was rising ever higher.

Yet, on Nov. 26, 2012, three federal byelections turned them on their head.

In the ridings of Durham (in Ontario) and Calgary Centre -- both won by the Conservatives in 2004, 2006, 2008 and 2011, and by margins of up to 20,000 votes -- Tory MPs again were returned.

The New Democrats managed only a distant second in Durham (more than 8,000 ballots behind the Conservative victor), and an anemic fourth in Calgary Centre (with less than 3.9 per cent of the vote).

Oh, well. Much better results were expected in Victoria, won for the third straight time in 2011 by Denise Savoie, the NDP MP who retired for health reasons.

Yet as ballots were counted, a seesaw battle broke out between New Democrat Murray Rankin, a high-profile local lawyer, and Green Donald Galloway, a little known academic.

Few saw it coming, for while Mulcair's New Democrats were flying high in nationwide polls, Elizabeth May's Greens remained mired in single-digits.

Rankin and the NDP in the end prevailed, but by an unexpectedly close margin of 2.9 percentage points. New Democrats in B.C.'s capital city exhaled a nervous sigh of relief.

The question is this: which determinant proved most useful in forecasting the byelection outcomes in Durham, Calgary Centre, and Victoria?

Was it the plethora of public opinion surveys leading up to those contests? Or was it the margins of victory in each riding from the preceding general election?

Remember, polls kept showing considerable slippage for the Conservatives and manifest improvement for the NDP.

A casual observer might have predicted the three byelections would end with the Tories losing one or both of their two seats, and the New Democrats everywhere romping to victory.

Experienced politicos, on the other hand, would note that the Tories went into the Durham and Calgary Centre byelections with comfortable margins of victory -- of 19,500 and 19,800 votes respectively -- from the 2011 general election.

In Victoria, the NDP had a 2011 cushion of 16,400 ballots.

In the end, it was those sizeable victory-margins from the preceding federal general elections that allowed the incumbent parties, Tories and New Democrats, to retain their seats -- however narrowly -- in all three byelections.

Tale told by 15 byelections

This is important to understand today, two months before the Oct. 19 general election, because public opinion polls again have Mulcair's New Democrats leading the country.

But as I noted in a previous article, New Dems (and pundits predicting their victory) should temper any overconfidence by asking themselves: Is it wise to ignore the 2011 general election results in individual ridings -- now redrawn through electoral redistribution -- and focus exclusively on current public opinion polls?

No, and no. To illustrate why, let's broaden our view to look at the results in the 15 byelections held since Stephen Harper and the Conservatives won a majority government four years ago.

Nine of those 15 tilts were in ridings captured in 2011 by the Conservatives.

For much of the time in which those byelections were contested, Harper and his Tory government remained unpopular with a large number of Canadians.

Voter surveys by well-respected firms over the last four years almost always have put the Conservatives in second-place or worse.

Yet, the Harper record in those nine byelections in Tory-held seats is eight wins and one loss.

In addition to their aforementioned victories in Durham and Calgary Centre, the Conservatives also retained Provencher and Brandon-Souris (both in Manitoba) in November 2013; Macleod and Fort McMurray-Athabasca (both in Alberta) in June 2014; and Yellowhead (Alberta) and Whitby-Oshawa (Ontario) in November 2014.

Their sole loss occurred in a riding -- Labrador -- the Tories won in 2011 by a miniscule 79-vote margin (and for just the second time in 62 years). By no measure could it be viewed as a 'safe' Conservative seat.

The byelection was called, moreover, because Peter Penashue, the newly elected Conservative MP, resigned after Elections Canada found he had accepted ineligible campaign donations. Penashue sought redemption by contesting the byelection, but fell to the Liberal candidate by nearly 1,900 votes.

Was there a key factor that enabled Harper's Tories to retain their grip on those eight seats?

Clearly it was not incumbency, for in every contest but one the byelections were called because of resignations or death (that of the finance minister, Jim Flaherty, the MP for Whitby-Oshawa). And, as mentioned earlier, Penashue was the sole incumbent in any of these contests and he lost his bid for re-election.

Nor was the determining factor the popularity -- or lack thereof -- of the Prime Minister or his Conservative government. Again, the Tories nearly always were behind in the polls.

Nope. Two simple reasons explain Harper's byelection successes.

First, Tory candidates prevailed in those eight byelections because a sizeable number of voters in each district -- by custom, personal values, or some demographic characteristic -- were Conservative supporters.

The second reason (a corollary of the first) is that a sizeable number of locals -- again, by custom, personal values or some demographic characteristic -- were not attracted to the alternatives as presented by the New Democrats, Liberals or Greens.

Basically, the victory margins recorded in 2011 by Tory candidates in ridings such as Macleod (9,500), Brandon-Souris (13,500 votes), Fort McMurray-Athabasca (17,900), Provencher (20,800), Whitby-Oshawa (23,200) and Yellowhead (26,500), illustrated exceptionally strong and enduring local support for Harper and the Conservatives.

That support proved more than sufficient to help the Tories weather byelection storms, even as they foundered in nation-wide public opinion polls.

Separating safe from unsafe

The indisputable fact is that a sizeable (but unknowable number) of Canada's newly drawn electoral districts are 'safe' for the Harper Conservatives.

Similarly, there also are many safe New Democratic Party strongholds across the country, as well as safe Liberal fortresses.

Jenny Kwan, a 19-year NDP veteran of the B.C. Legislature, ought to have little trouble holding Vancouver East for Mulcair's party. She faces residents who, four years ago, gave the New Democrats 62.8 per cent of the vote in a slightly re-drawn riding.

For the Liberals, a newly drawn Newfoundland and Labrador district called Long Range Mountains may be one of their safest. The Grits took 55.2 per cent of the local vote in 2011, giving them a cushion that should be sufficient to send Gudie Hutchings, a Corner Brook businesswoman and outfitter, to Ottawa.

Still, a scan of past races shows Harper's Conservatives, who won more votes than their rivals in 188 re-drawn electoral districts, have a greater number of safe ridings than do Mulcair's New Democrats (with 109 transposed seats), or Trudeau's Liberals (at 36). And that poses a big challenge for the poll-leading NDP.

This is not a reason for despair for those readers anxious to see the back of Harper and his Conservative government. But it signals how important it will be for opposing parties to identify and wage potent campaigns in those electoral districts the governing Tories captured four years ago by a very small margin of votes. Call them 'unsafe' Harper seats -- or, as they do in the United Kingdom, Conservative 'marginals.'

Consider the northern Ontario riding of Nipissing-Timiskaming. That's a seat Tory newcomer Jay Aspin won four years ago by just 18 votes -- after a judicial recount -- over the Liberal incumbent, Anthony Rota.

Those results now have been flipped through electoral redistribution, and Grit Rota heads into a rematch in the re-drawn riding with a 36-vote advantage over Tory Aspin.

(Readers who complain that Canada's redrawn electoral map is the product of 'gerrymandering' are being very silly.)

It is the election results in seats like Nipissing-Timiskaming that will determine whether Harper is returned as Prime Minister on Oct. 19 -- or not.

The greater the number of Conservative losses in these marginal seats, the greater the likelihood Canada will have a new government after the general election.

And this is the real utility of nation-wide public opinion polls. They reveal that the Harper Tories are in tough to retain the seats they won in 2011 by relatively narrow margins.

Where are those marginal seats, who is most likely to win them, and what scenarios are likely to unfold? On Monday, we provide a Tyee guide.