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The Liberal Party has signed up as many as 294,000 Canadians to vote on its next leader. More than half have pledged to support Justin Trudeau.

Simple math suggests that the race is over. If every Liberal member and supporter who has promised to vote for Mr. Trudeau actually does, then he should win easily on the first ballot, before any second-place votes are reallocated among the lesser candidates.

But what if some of those promises go un-kept? If enough of Trudeau's 150,000 supporters leave him at the altar, then the computer program that counts the votes could be in for a ride.

Let's be extremely generous, and assume that overall voter attrition between now and next month's balloting will be in the neighbourhood of 20 per cent. (Even in an internal party election, 80 per cent turnout would be astronomical; as of Monday evening, less than a third of all Liberal members and supporters had registered to vote, and the deadline is Thursday.)

If this assumption holds, then just under 59,000 of the Liberals' 294,000 members and supporters will drop out of the process between now and April 14. They may fail to sign up to receive a ballot, or they might lose interest in the process, or they could just simply forget to vote.

Now, let's assume that this 20 per cent voter attrition is spread evenly among the leadership candidates. If that happens, then the first ballot results will be the same, percentage-wise. Mr. Trudeau wins.

But what if Mr. Trudeau has more trouble than his rivals in getting out the vote? He has attracted far more media attention than his competitors combined, and so his supporter tally may include undecided voters, or supporters of other candidates for whom his website was simply the first port of call. He is the undisputed frontrunner, and so some of his supporters may not bother to vote – or may not rank him first – on the assumption that a Trudeau victory is assured. According to Mr. Trudeau's campaign, more than 100,000 of his supporters signed up without providing an e-mail address. Their voter registrations could simply get lost in the mail.

There may also be some Liberals who signed up for Mr. Trudeau but have simply changed their minds, swayed by David Suzuki's endorsement of Joyce Murray, or Martha Hall Findlay's economic liberalism, or Martin Cauchon's cabinet experience, or Marc Garneau's keenness for policy.

To be sure, some of these possibilities apply to other candidates as well. But assume just for a moment that Mr. Trudeau's turnout ends up being lower than his rivals'. If we stick with 20 per cent attrition for the party as a whole, then our total universe of voters shrinks to 235,200. In this scenario, a simple majority would require 117,601 votes. If at least 21.6 per cent of Justin Trudeau's 150,000 supporters don't vote, or don't rank him as their first choice, then he will fall short of the 117,601 first-place votes that he needs to win on the first tally. Second-place votes will suddenly start to matter. That's when Justin Trudeau could lose. The further he is from 50 per cent on the first count, the more likely it is – though, to be sure, this is still very unlikely – that another candidate will pick up enough second- and third- and fourth-place votes to beat him.

For the next and final month of the leadership race, then, every campaign's most important task is to convince as many Liberals as possible that their candidate is the next best thing. This will be harder for some than for others.

Mr. Trudeau has plenty of charisma and, polls suggest, popular appeal, but frontrunners can be polarizing; in various ways, the other candidates have all campaigned as not-Justin, and so their supporters may prove difficult to persuade. The happy few who have resisted the juggernaut's gravitational pull throughout the leadership campaign may be all the more reluctant to board the bandwagon in its final moments.

Marc Garneau has been portrayed as Mr. Trudeau's chief rival, and rightly so; he is brilliant and likeable, has considerable political chops, and is a bona fide Canadian hero. Yet Mr. Garneau may have done irreparable damage to his second-place prospects on Feb. 25, when he challenged Mr. Trudeau – and only Mr. Trudeau – to a one-on-one debate. A candidate who tries to turn a campaign into a binary choice between A and B invariably alienates voters who support C, D, and E. Liberals have learned this lesson the hard way: when Michael Ignatieff challenged Stephen Harper to a one-on-one debate during the 2011 election, Jack Layton won.

Joyce Murray has drawn plaudits from pundits for promising to co-operate with other "progressive" political parties to "defeat Stephen Harper." Sure, the NDP has categorically ruled out such an arrangement, and yes, the scheme smacks of defeatism, but Ms. Murray's real problem is that her plan to unite progressives is, ironically, deeply divisive; Liberals who agree with her will have already pledged their support, and those who haven't almost certainly won't. To rank Ms. Murray second on a preferential ballot would require a blend of logical gymnastics and profound pessimism: a Liberal voter would need to believe that, unless his or her first-choice candidate wins, the party never will.

Martha Hall Findlay has offered a refreshing readiness to slay sacred cows, with a boldness that befits a party in need of defibrillation. But when Liberals mark their ballots, many will instead remember her for her too-personal, too-pointed swipe at Justin Trudeau during last month's leadership debate in Mississauga. Nothing scares off second-ballot support more swiftly than the scent of malice.

Martin Cauchon's laudable record as a cabinet minister might have made him a safe second choice, but he has never seemed quite excited enough about his own campaign to excite anyone else. Mr. Cauchon – like Karen McCrimmon, Deborah Coyne, and David Bertschi – will matter less to the race's outcome than their supporters will; preferential balloting means that the sooner a voter's first choice is eliminated from contention, the sooner their second-place votes will start to count.

Not all second-place votes are created equal, either. The rules of the race require that votes be weighted by riding, all 308 of which will receive 100 points to be allocated proportionally among the candidates after each tally, and reallocated as bottom-ranked candidates are eliminated and ballots are recounted. To win, a candidate can win every vote in one more than half of the ridings, or one more than half of the votes in all 308 ridings, or something in between. The crucial implication is that the smaller the number of Liberals in any particular riding, the greater the weight each of their votes will carry. If you're a Liberal in northern Saskatchewan, Marc Garneau's campaign wants to buy you a beer.

And yet, if Justin Trudeau can convince the lion's share of his supporters to vote – and, first, to register to vote before Thursday's deadline – and unless all of them happen to live in a tiny number of ridings, then he will win the leadership before any second-place votes are counted. Until that happens, however, expect every candidate – including him – to spend the next month running for second.

Adam Goldenberg is a Kirby Simon Human Rights Fellow at Yale Law School and a contributor to CBC News: The National. He was a Liberal staffer on Parliament Hill and at Queen's Park.