Each of the major parties in the House of Commons has a different idea of how Canada's electoral system should work.

The NDP, for example, are presenting a motion for debate Wednesday calling for the adoption of mixed-member proportional representation, "to ensure 2015 will be the last in the era of unfair elections," as they said in a press release.

The Liberals want to study a preferential ballot system for federal elections, while the Conservatives are fine with the current system.

Perhaps not coincidentally, each party supports a system that would be beneficial to them.

How might the political landscape in Canada look if these changes to the system were implemented?

1st past the post

In the current system, often called "first past the post" (FPTP), Canadians cast a ballot for a candidate to represent their riding. The candidate with the most votes wins.

If an election were held today, based on where the polls currently stand and using ThreeHundredEight.com's seat projection methodology, the Conservatives and Liberals would come out almost even in the seat count, despite the Liberals holding a lead of about four points in national voting intentions. The Conservatives would win about 136 seats, with the Liberals capturing 132. The New Democrats would take 67 seats, the Greens could win two and the Bloc Québécois could be reduced to one seat.

First past the post can reward regional strength, with the Conservatives able to squeak out a plurality of seats thanks to their advantage in the West and outside of Toronto in Ontario. Meanwhile, the Liberals are penalized in Quebec for trailing the NDP among francophones, despite being ahead provincewide.

But it tends to be most beneficial to the leading party. The Conservatives took 46 per cent of seats in 2008 with just 38 per cent of the vote, while they captured 54 per cent of the seats with 40 per cent of the vote in 2011. When the Liberals were in power they were the ones who benefited, taking 44 per cent of the seats in 2004 with 37 per cent of the vote, and majorities from 1993 to 2000, while falling well short of 50 per cent support.

In other words, there is little incentive for the party in power to change the system that got it there.

Mixed-member proportional

In the New Democrats' favoured system, known as MMP, voters cast a ballot both for a local candidate and for a party. MPs are elected to represent ridings but the party votes are used to top up representation in the legislature so it is proportional to each party's overall support. There are different methods for determining how these extra MPs are distributed, but the overall outcome would be that a party's strength in the Commons would be proportional to its share of the vote.

To simplify things, let's distribute proportionally the 338 seats that will be up for grabs in next year's election, according to each party's regional polling levels (and dropping support for "Others").

With MMP, the Liberals would come out ahead with 123 seats, followed by the Conservatives at 106 seats and the New Democrats at 71 seats. The biggest change would be for the smaller parties, as the Greens would be awarded 25 seats and the Bloc Québécois would win 13. Note the Greens also support proportional representation.

The NDP would see its share of seats increase slightly, so a shift to MMP would be only marginally better for the party at current support levels.

But historically, MMP would have been much more beneficial to the New Democrats. In the 2004, 2006 and 2008 federal elections, the party averaged 17 per cent of the vote but won, on average, just nine per cent of the seats.

Preferential ballot

With preferential voting, also known as instant run-off voting, voters are asked to rank candidates. If no candidate gets a majority of first-ranked ballots, the candidate with the lowest first-rank support is dropped and those votes are distributed to voters' second-choice candidates. This continues until a candidate receives a majority.

How this would play out in an election is harder to work out. To get a reasonable estimate, I started with a standard seat projection based on current polling levels. I then dropped candidates off the virtual ballot and distributed their support according to the most recent second-choice polling from EKOS Research. While hardly a perfect method, the results were intuitive.

Seat estimates according to current polling levels and proposed electoral systems. (Éric Grenier)

In that scenario, the Liberals could take 160 seats, falling just nine short of a majority. The New Democrats would finish second with 95 seats, while the Conservatives would fall to third with 81. The Greens could still win two seats, while the Bloc would be shut out.

These are drastically different results, considering the Conservatives are currently 10 points up on the NDP for second place but would drop to third with a preferential vote. This is because Liberal and NDP supporters tend to list the other as their second choice. The Conservatives are the second choice of very few voters, meaning the Tories would need to take nearly a majority of ballots in the first round to secure any seat.

The Liberals, on the other hand, are able to win almost two-thirds of the seats in Ontario with this method, compared to less than half with FPTP and less than two-fifths with MMP.

In Quebec the Liberals struggle, as the NDP tends to be the preferred second choice of Bloc supporters. Though trailing the Liberals in the province overall, the NDP could nevertheless win more than 70 per cent of the seats with a preferential ballot.

Voting change would change politics

The discrepancies suggest a new system would require a different style of politics. FPTP rewards parties for micro-targeting regions, constituencies and demographics. MMP, on the other hand, would penalize any party that writes off a region of the country. A preferential ballot would require parties to reach across the political spectrum, as alienating supporters of another party or parties would be a recipe for disaster — but unlike MMP or even FPTP, a preferential ballot makes it more difficult for smaller parties to get into the House.

Will any of these changes come to pass? As only one party stands to benefit most from each of these systems, it would seem only a majority Liberal or NDP government would be able to get such a change through Parliament.

But if they manage it, the scales may be tipped in their favour enough to ensure no other change could ever occur.

ThreeHundredEight.com's vote projection model aggregates all publicly released polls, weighing them by sample size, date, and the polling firm's accuracy record. The seat projection model makes individual projections for all ridings in the country, based on the provincial and regional shifts in support since the 2011 election. 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.