If Justin Trudeau were to resign as Prime Minister of Canada?.....

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Deputy Liberal Leader, I guess.

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It's not a case from Canada, but since Austrialia operates under a similar parliamentary system:

When Prime Minister Harold Holt disappeared at sea in 1966 and was subsequently declared dead, the Governor General summoned John McEwen, leader of the allied Country Party, to serve as caretaker Prime Minister until Liberals could choose the new leader (and new permanent PM). McEwen served for less than a month before Liberals elected John Gorton.

Another Australian example of a very short tenure would be Deputy PM Frank Forde, appointed in 1945 after John Curtin's death in office. He served just eight days before losing his bid to be selected as Labor's permanent leader.

So I imagine if Trudeau suddenly leaves office the same principle will apply here.

[MASHED POTATOES. VOTE!]

If he were to die, historical precedent would be to select someone from the Senate. Might not work considering all Liberal Senators are officially "independent". And, a prime minister hasn't died in office in over 100 years, so historical precedent may mean nothing.

It should be noted though that before they elected Harper, the Conservative leader was also selected from the Senate after the merger.

If I recall correctly, Turner wasn't even member of either house when appointed PM, but at least he was already elected Liberal Leader. Also, wasn't Mackenzie King appointed PM one time after actually losing his seat in GE?

It doesn't apply here, since both were official party leaders, but theoretically speaking, having a non-MP to head a brief caretaker ministry doesn't sound that far-fetched.