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If the New Democrats and Liberals decide to run joint candidates in the next election, they would be swept to power with a larger majority than the Conservatives currently enjoy. Or at least so says a recent poll – but would that actually happen in a real election?

There has been some discussion of late about the idea of the NDP and Liberal party joining together to run single candidates against the Conservatives. It was one of the major planks of Nathan Cullen's NDP leadership run, and according to a survey by Angus-Reid it is a winning idea.

After removing those who said they would not vote or were undecided, fully 50 per cent of Canadians surveyed said they would vote for a joint NDP or Liberal candidate. This is compared to 39 per cent who would vote for the Conservatives and 11 per cent who would cast their ballot for the Greens, Bloc Québécois, an independent or another party. The tandem Liberals and NDP would capture a majority of the vote in every part of the country except Alberta, Saskatchewan, and Manitoba.

With a disparity of only a few points, the results of the Angus-Reid poll are remarkably close to the combined totals of ballots cast in favour of the NDP and Liberals in the 2011 general election, indicating that if the parties decided to co-operate they would lose very few votes.

If the two parties were able to garner as much support as Angus-Reid attributes to them they would win a large majority of seats in the House of Commons. Using ThreeHundredEight.com's seat projection model, the results of the poll would deliver a total of 185 seats to the two parties (118 to the NDP and 67 to the Liberals, assuming that the party that had the better performance in the last election in each riding is the one that gets to field the joint candidate). The Conservatives would win only 122 seats, while the Greens would still manage to elect Elizabeth May.

Though the Tories would still win the majority of seats in Alberta, Saskatchewan, and Manitoba, the Liberal-NDP partnership would capture 20 seats in British Columbia, 26 in Atlantic Canada, 61 in Ontario, and 69 in Quebec, extinguishing the Bloc in the process. There is little wonder, then, why some say the split of the "progressive" vote gave the Conservatives their victory last year.

This sort of split on one side of the political spectrum has been credited for Jean Chrétien's Liberal majority governments after the 1993, 1997, and 2000 general elections. There is some truth to this, as the combination of Reform/Canadian Alliance and Progressive Conservative votes would have changed things dramatically.

In 1993, the Liberals would have been kept to only 134 seats and a minority instead of 177, while the right-wing parties would have won 101 seats instead of 54. In 1997, the combined PC and Reform votes would have handed the two parties 122 seats and the Liberals only 117. In reality, the Liberals eked out a majority with 155 seats, while Reform took 60 and the Tories 20. And in 2000, the Liberals would have been handed another minority with 138 seats with the Canadian Alliance and PCs winning 114, instead of the split of 172 for the Liberals and 78 for the two right-wing parties that actually occurred.

But when the right was finally united, things were not as simple as adding their votes together. The Canadian Alliance and Progressive Conservatives together captured almost 38 per cent of the vote in 2000, only for the newly merged Conservatives to drop to less than 30 per cent in 2004.

If this sort of vote bleeding had occurred in 1993, 1997, and 2000 with a united right, the Liberals would have likely still won a majority in 1993 and 2000, though their share of seats would have been reduced. The 1997 election would have likely delivered the Liberals a strong minority government.

If the Liberals and New Democrats were to lose votes in the same way that the Conservatives did in 2004, rather than managing to keep them all as Angus-Reid says they could, would the "united left" still be able to defeat the Conservatives?

By reducing the combined Liberal and NDP vote by the same proportion that the Conservatives lost in their first election as a single party, the Tories manage to take the plurality of votes in Atlantic Canada and the majority everywhere else, except Quebec.

As a result, the Conservatives would likely win 174 seats and be returned to power with a majority government. The New Democrats would win 88 seats and the Liberals 38, giving them a combined total of 126 seats. The Bloc Québécois would manage seven seats and the Greens would still win their one.

It is extremely unlikely that the Liberals and NDP would lose votes in exactly the same way as the Tories did in 2004. A number of factors were at play that influenced the results of the 2004 election, and voters on the left may react much more differently than did voters on the right. But even if the Liberals and NDP presented joint candidates to take on the Conservatives, the margin for error would be very slim. Though they have the potential to defeat the Tories if they work together, the result of a Liberal-NDP co-operative effort might equal less than the sum of its parts.

Éric Grenier writes about politics and polls at ThreeHundredEight.com

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