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Federal Liberal Party leadership candidates Justin Trudeau, left, and Joyce Murray take part in the final leadership debate in Montreal on March 23, 2013. Both leadership candidates butted heads over the question of co-operating with other parties in strategic voting.CHRISTINNE MUSCHI/Reuters

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The Greens will not run a candidate in the Labrador by-election, whenever it is called, because Leader Elizabeth May wants the Liberals to take the riding from the Conservatives. Suddenly, the issue of progressive party co-operation has become the talk of the Liberal leadership race.

Word of Ms. May's decision circulated as the candidates met Saturday in Montreal for their last leadership debate. Joyce Murray, who is the only candidate advocating co-operation with the NDP and Greens, seized on the news, castigating front-runner Justin Trudeau for refusing to work with other parties to defeat the Conservatives.

But Mr. Trudeau predicted in his response: "It leads to [NDP Leader] Thomas Mulcair as prime minister of this country."

Though the real winner could be Stephen Harper.

Ms. Murray, a B.C. MP and former provincial environment minister, has become the most formidable also-ran chasing Mr. Trudeau as the Liberals prepare to choose their new leader April 14.

She believes that in the next election, the Liberals, NDP and Greens should hold runoff contests among their nominees in ridings where the Conservatives previously took less than 50 per cent of the vote. Members of all three parties would be eligible to vote in the runoff.

Whoever won that runoff would face the Conservatives, representing his or her party.

If the Liberals or NDP formed a government, they would pass legislation replacing the current first-past-the-post system of electing MPs with a form of proportional representation, in which parties are elected to the House of Commons based on their share of the popular vote.

At the subsequent election, the Liberals would run entirely under their own banner.

Ms. Murray rejects utterly the suggestion that working with the NDP would simply hand the Official Opposition victory.

"I'm optimistic that we can reach out and rebuild support and re-engineer our party," she said Sunday in an interview.

But co-operating with the NDP in close contests – she points to 57 ridings in the past election where the Conservatives failed to win 50 per cent of the vote – would be "an insurance policy on behalf of Canada."

An early, if incomplete, test of co-operation could come in the Labrador by-election, which Prime Minister Stephen Harper is expected to call within a matter of weeks.

In the past election, Conservative candidate Peter Penashue won the riding by a mere 79 votes.

Earlier this month, Mr. Penashue resigned his seat, dogged by allegations of improper campaign financing. He hopes to win it back in the by-election, whenever Mr. Harper calls it.

Ms. May hopes that by not fielding a candidate, the 139 votes the Greens received in 2011 will transfer to the Liberal candidate, ensuring Mr. Penashue's defeat.

This is the sort of progressive co-operation that Ms. Murray has been calling for all along. But the NDP, which got about half as many Labrador votes as the Liberals or Conservatives in the past election, has rejected Ms. May's call to also stand down.

Under Ms. Murray's plan – should her party and the NDP have a Damascene conversion and adopt it – the Bloc Québécois would not be invited to co-operate. There might or might not be a referendum on moving to proportional representation. (Numerous provincial referendums on similar proposals have all resulted in No.)

In the event the Conservatives won the most seats but were shy of a majority, it's "certainly a possibility" that the NDP and Liberals would combine in a coalition government to unseat the Tories and get the PR bill passed, Ms. Murray acknowledged.

Her proposal is unlikely to succeed. Mr. Trudeau, who is virtually certain to win the leadership, completely opposes it, fearing it would benefit the NDP more than the Liberals.

Mr. Mulcair, who thinks he can best both Mr. Trudeau and Mr. Harper, wants nothing to do with it.

In the past election, Stephen Harper won a majority government by warning that anything less would lead to an unholy coalition of the left. Ms. Murray's proposal, if adopted, would validate that claim, driving some voters over to the Tories.

But the fact remains that as long as the left is divided, the Conservatives are favoured to win any given election.

So when casting their ballots for leader, Liberal members and supporters might ask themselves two questions on ending the divisions of the left:

If not now, when? If not this way, how?

John Ibbitson is The Globe and Mail's chief political writer in Ottawa.