If Canada adopted a preferential ballot for its federal elections, outcomes could be radically different – at least according to a new poll. And it would be Stephen Harper's Conservatives who would suffer the most.

Preferential balloting, also known as instant run-off voting, alternative voting, or a ranked ballot, is a system used in many jurisdictions around the world. A proposal to adopt this method will be considered by Toronto's city council in the coming months, and it is a system that is supported by Justin Trudeau. It was used in the federal NDP's last leadership race, and will also be employed to select the next Liberal leader.

On a ranked ballot, voters rank candidates according to their preference. If no candidate gets 50 per cent support on the first ballot, the candidate that received the lowest number of first choice ballots is dropped, and his or her votes are then distributed according to second rankings. If majority support is still not achieved, the next candidate is dropped and their votes are distributed according to second choice (and, if need be, the first candidate's votes are then distributed according to third choice), and so on until one candidate gets over 50 per cent of the vote.

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A new poll by Abacus Data, surveying 1,014 members of an online panel between Mar. 19-21, provides details of how a preferential ballot would break down in Canada. The poll asked respondents to rank seven parties from 1 to 7 (they were not given the option to rank less than seven parties, as a preferential ballot would allow). It included a few fringe parties to determine whether this system would encourage Canadians to give them more of a chance (generally, it did not).

The result lays out how supporters of each of the main parties would rank the other parties if they had to on a preferential ballot, and there are a few surprises.

A majority of Conservatives (57 per cent) ranked the Liberals second, while 20 per cent put the New Democrats as their second choice. Supporters of the NDP split between the Liberals (37 per cent) and the Greens (33 per cent) as their second choice, while most Liberals (57 per cent) ranked the NDP second. But a large proportion of Liberals, or 28 per cent, ranked the Tories after their own party. For the Greens, 44 per cent ranked the NDP second while 26 ranked the Liberals as their next choice, and 61 per cent of people who ranked the Bloc Québécois first put the NDP as second.

These results should give some pause to those advocating electoral co-operation. Almost one-third of Liberals ranked the Tories second instead of the NDP, while roughly the same number of NDP and Green voters ranked the Conservatives, Bloc, or another party second.

But second choice preference is something that has often been polled before. Third and fourth rankings, however, are never polled.

The consensus Conservative ballot puts the Liberals second, but after that things get less clear. The NDP was most often ranked as the third choice at 37 per cent, but 24 per cent of Conservatives put another party as their third preference (mostly the Christian Heritage and Libertarian parties). For their fourth preference (and in many ridings this would come into play), the Conservatives opted for the Greens or a smaller party.

There were some important regional variations: Tories were split in Quebec between the Liberals and NDP for their second choice, while the Greens (not the NDP) were the consensus third choice in British Columbia.

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For the New Democrats, no party had a majority of support on any of the ballots. While their supporters were divided between the Liberals and Greens as their second choice, they were similarly divided on their third choice (people who ranked the Liberals second ranked the Greens third, and vice versa). For their fourth preference, a plurality of New Democrats ranked a fringe party. In British Columbia, the Greens were the consensus second choice of NDP voters, while in Quebec the Bloc Québécois received the most support on the second and third ballots.

The Liberal ballot is mixed after the second choice, with the Greens, NDP, and Conservatives jumbled together on the third ballot. On the fourth ballot, however, the Greens were the clear preference. But in British Columbia and Quebec, Liberals split between the Tories and NDP on the second ballot and in Atlantic Canada the Conservatives were the consensus third choice.

Bloc supporters who did not rank the NDP second did so on the third ballot, while most of the others went with the Liberals. On the fourth ballot, the Conservatives were the preferred option. For Greens, the Liberals were the main third choice while fringe parties were most likely to be ranked fourth.

How many seats would they win?

But how would this all play out in terms of seats? When Abacus Data asked respondents who they would support on a standard ballot, the Conservatives and New Democrats were neck-and-neck (32 to 31 per cent, with the Liberals at 24 per cent). With those levels of support, the Conservatives would likely win 139 seats, the New Democrats 115, and the Liberals 82 on the 338-seat electoral map and using ThreeHundredEight.com's seat projection model.

With a preferential ballot, however, the Conservatives would come out further ahead. They would lead in 147 ridings on the first ballot (after distributing the marginal support for the smaller parties), compared to only 108 for the New Democrats, 76 for the Liberals, four for the Bloc Québécois, and three for the Greens (primarily due to an anomalous result in the poll in Atlantic Canada).

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The Conservatives would have majority support in 60 ridings and win those automatically, while the NDP would win 23 seats on the first ballot and the Liberals 11. But that Tory advantage would disappear once the instant run-off was conducted.

The Conservatives would lose their first ballot lead in 30 ridings, and be reduced to only 117. The New Democrats would move ahead in 18 more seats and take 126, while the Liberals would win 17 more ridings and increase their total to 93. The Greens would hold on to two of the three seats in which they led, while the Bloc Québécois would lose all four.

The inability for the Conservatives to grow after the first ballot is particularly marked in Ontario and on the Prairies. In Ontario, the Conservatives would drop 16 of the 49 ridings in which they led but did not have a majority on the first ballot, with those being split between the Liberals and New Democrats. In the Prairies, they would lose all six of the ridings in which they led on the first ballot but did not have majority support.

Tory growth beyond the first ballot is so limited that having even 42 per cent support in some Ontario ridings on the first ballot would not be enough to ensure a victory after the instant run-off is conducted. By comparison, the Liberals and New Democrats would only lose ridings in which they led on the first ballot to each other – never the Conservatives.

The Bloc Québécois is similarly limited. Though the party is the consensus second choice for New Democrats in Quebec, in the majority of ridings the Liberals, Conservatives, and Greens drop off first. The Bloc has little down-ballot support from these parties, and so is often unable to do better than 35 per cent in ridings where their candidate faces-off against the NDP on the final ballot.

This system of voting would make electoral co-operation between the opposition parties unnecessary, as the effect is much the same. But would the conduct of an election be different if the parties were campaigning knowing that a preferential ballot was going to be used?

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Would the Conservatives move towards the centre in order to attract more second- or third-choice ballots? Would the Liberals campaign on the right to get more Conservative support, or would they move towards the left? And how would the Bloc campaign if support from Liberal and Conservative voters was needed?

This need for a wider tent is one of the benefits often cited by proponents of alternative voting. The necessity of second- and third-ballot votes encourages parties not to alienate non-supporters. It also ensures that each riding is represented by an MP that a majority of constituents preferred to the next most popular candidate.

Because of how this method of voting would limit the ability of the Conservatives to win elections, it is unlikely that it will be adopted while they are in power. The New Democrats prefer mixed-member proportional representation. The Trudeau-led Liberals may push for this kind of change. However, all three parties may lose their enthusiasm for any kind of democratic reform of a system that puts them into office. But if it ever is adopted, electoral politics in Canada could be unrecognizably transformed.

Éric Grenier writes about politics and polls at ThreeHundredEight.com .