A series of new polls suggests the three federal parties are locked in a virtual three-way tie. If that holds until election day, it would be a first for Canada and the resulting seat totals would be nearly unpredictable.

Three polls published over the last few days peg the race to be as close as it gets.

EKOS Research, in a poll for iPolitics, put the Conservatives at 30 per cent, the NDP at 29 per cent, and the Liberals at 27 per cent.

A Global News poll by Ipsos Reid, meanwhile, showed the Conservatives and Liberals in a tie at 31 per cent, with the NDP narrowly behind at 30 per cent.

And a poll by Abacus Data placed the Conservatives alone in first at 31 per cent, with the NDP and Liberals tied for second place at 28 per cent.

These are remarkable numbers, and would be unprecedented in Canadian election history if they carried through a campaign. Polls have recorded three-way contests between elections before, but there has never been an election that finished that close.

In fact, the closest three-way race in federal election history was in 2006 — when the gap between the first-place Conservatives and third-place New Democrats was just under 19 points.

There has been a handful of legitimate three-way races at the provincial level. In none of these cases, where the margin between first and third was less than six points, did the winning party secure a majority of seats.

Moreover, finishing third in a three-way race can be very penalizing. In terms of who comes out with the most seats, it is a virtual toss-up between the first and second place finishers. The party finishing in third position, despite being only marginally behind in the vote count, often takes little more than half as many seats as the other two parties.

An electoral butterfly effect

The three recent polls demonstrate how the outcome of the next election could hang on the thinnest of threads.

Working the regional results of each of these three polls into ThreeHundredEight.com's seat projection model, it is clear that the Conservatives are best placed to win the most seats. The party is awarded between 121 and 129 seats depending on which poll is plugged into it.

The New Democrats, meanwhile, take between 105 and 116 seats, and the Liberals between 94 and 107 seats.

The Liberals are in the weakest position in the three-way race as it is presently constituted. The Conservatives have a strong base in Alberta, Saskatchewan, and Manitoba, where they can win more than two-thirds of the seats. They can also take about half of the seats in Ontario. The New Democrats can win two-thirds of the seats in Quebec.

The Liberals, however, only win such a large share of seats in Atlantic Canada. As the region has just 32 seats, it does not help the Liberals as much as the Conservatives' dominance of the Prairies' 62 seats or the NDP's stranglehold on Quebec's 78.

Nevertheless, it is a very close-run thing.

With the numbers from Abacus's poll, the Liberals would narrowly edge out the NDP in the seat count. With Ipsos, it is the NDP that marginally moves ahead of the Liberals. And with EKOS, the NDP ends up closer to the Conservatives than they do the Liberals.

These differences have major implications for the formation of Canada's next government. In all three polls, the Conservatives are in a weak minority position while the NDP and Liberals combine for well over 200 seats. A handful of votes might decide whether it is Justin Trudeau or Thomas Mulcair who gets the second-largest caucus in the House of Commons, and likely the first crack at replacing Stephen Harper as prime minister if his government is defeated.

The electoral math becomes even more complicated if we consider the model's likely ranges, which act as the margin of error. Considering these, the Conservatives could win between 106 and 154 seats, the NDP between 89 and 130 seats, and the Liberals between 70 and 121 seats.

In other words, all three parties could potentially win a plurality of seats based on where the numbers stand today. All that is required to flip dozens of seats in one direction or another is the proverbial flap of a butterfly's wings.

But perhaps three-way races have been so rare in Canada's electoral history for a reason. If voters want the status quo, they finally flock to the incumbent. If they decide they want change, in the end they converge towards the party most likely to provide it.

If voters do not make up their mind by election day, however, they could be in for a surprising result.

The poll by EKOS Research was conducted for iPolitics between May 20 and 26, 2015, interviewing 2,934 Canadians via interactive voice response. The margin of error associated with the survey is +/- 1.8%, 19 times out of 20.

The poll by Ipsos Reid was conducted for Global News between May 27 and 29, 2015, interviewing 1,003 Canadians via the Internet. As the poll was conducted online, a margin of error does not apply.

The poll by Abacus Data was conducted between May 28 and 31, 2015, interviewing 1,500 Canadians via the Internet. As the poll was conducted online, a margin of error does not apply.

ThreeHundredEight.com's seat projection model makes individual projections for all ridings in the country, based on regional shifts in support since the 2011 election and taking into account other factors such as incumbency. The projections are subject to the margins of error of the opinion polls included in the model, as well as the unpredictable nature of politics at the riding level. You can read the full methodology here.