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Coalition governments, where members of different parties are appointed to cabinet, are rare.CHRIS WATTIE/Reuters

With the Liberals and Conservatives close in the polls, a minority government is becoming a more likely prospect. New Democrat Leader Jagmeet Singh even floated the idea of entering into a coalition with the Liberals before shying away from the idea a day later.

So what would happen if none of the parties manage to clinch a majority – at least 170 of the 338 seats in the House of Commons?

The day after the election, Justin Trudeau would still be the prime minister and would remain in power. “The Governor-General’s first duty is to ensure there is always a prime minister. We are never without a head of government or an executive,” said Carleton University political scientist Philippe Lagassé.

Mr. Trudeau is not bound to step down unless Parliament is recalled and he faces a vote on a budget bill, on the Speech from the Throne or on a motion expressly saying the House doesn’t have confidence in him.

“The threshold for determining whether or not you resign is not necessarily who won the election. ... The question that needs to be asked is who is going to be able to maintain the confidence of the House," said Erin Crandall, a political scientist at Acadia University.

Since he remains prime minister the next day, could Mr. Trudeau get the first shot at trying to form a government even if his party should come in second in number of seats?

It is an uncommon scenario but not unprecedented. In 1925, William Lyon Mackenzie King’s Liberals won 99 seats, while Arthur Meighen’s Conservatives had 116 members elected. But King declined to step down and kept governing in alliance with another party.

More recently, New Brunswick Premier Brian Gallant’s Liberals placed second in the 2018 provincial election. Rather than yield his office, he remained in power for five weeks until he lost a non-confidence vote.

If Mr. Trudeau doesn’t get a plurality of seats, the Conservatives would wish he followed the example of Paul Martin, who stepped down as prime minister in 2006 after his Liberals won 103 seats, allowing Stephen Harper to form a Conservative minority government with 124.

But should Mr. Trudeau advise Governor-General Julie Payette that he has enough support to test the confidence of the House, "by convention she would have no grounds to dismiss him," Prof. Lagassé said.

So can the Crown’s representative ever turn down a first minister?

The King–Byng affair in 1926 is the most famous case. Despite having seven fewer seats than Meighen’s Conservatives, King remained in power for nine months. Then King faced a non-confidence vote. He asked the governor-general of the time, Lord Byng, to dissolve Parliament. Instead, Lord Byng called on Meighen to form a government without an election.

A similar scenario unfolded in British Columbia in 2017 when Christy Clark’s minority Liberal government lost a vote of non-confidence. Ms. Clark advised B.C. Lieutenant-Governor Judith Guichon to dissolve the legislature, hoping to trigger another election. However, Ms. Guichon invited NDP Leader John Horgan to form a government.

Does Canada have coalition governments?

Coalition governments, where members of different parties are appointed to cabinet, are rare. Federally, it previously happened during the First World War, when Sir Robert Borden’s Conservatives governed with some Liberal and independent MPs. Provincially, Saskatchewan premier Roy Romanow’s New Democrats formed a coalition with the Liberals in 1999.

Today, the prospect of a coalition in the federal parliament is complicated by the presence of the Bloc Québécois. "To be a sovereigntist party and be in government would be contradictory," Prof. Crandall said. "It does make it interesting."

In 2008, federal Liberal Leader Stéphane Dion faced a backlash when he forged a deal with the NDP and the Bloc, which Mr. Harper thwarted by proroguing Parliament. Current Bloc Leader Yves-François Blanchet has ruled out joining any coalition.

Instead of coalitions, Canadian minority governments have either relied on ad hoc support from the opposition, or in some cases have entered into agreements with other parties. “Certain conditions are laid down and certain policies are identified between two parties, where they determine when they will be supported, when they can disagree on,” Prof. Lagassé said.

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