What if Canada had ditched first-past-the-post this election?

Election results can look very different, depending on the system you use to award seats.

That’s another national election done. On Monday, Canadians shuffled to the polls (with nary a sausage sizzle to greet them!) and cast their ballot to determine the next federal parliament.

Based on the initial projections, the House of Commons will look something like this.

Red: Liberal. Dark Blue: Conservative. Light Blue: Bloc Québécois. Orange: New Democratic Party. Green: Green Party. Grey: Independent.

The incumbent Liberal Party is expected to hang on to government, despite losing its majority. The Justin Trudeau-led centre-left party picked up the most seats (157), followed by the Conservatives (121), Bloc Québécois (32), New Democratic Party (24), Green Party (3), and one independent.

Now let’s take a look back at the diagram. This time, however, every seat in which the winning candidate achieved less than 50 per cent of the vote has been blacked out.

That is a lot of black. And that is a consequence of the first-past-the-post voting system Canadians use to determine who forms government.

Under first-past-the-post, you don’t need to get a majority of your electorate to vote for you. You just need to get more votes than any of your opponents. Even if only 30 per cent of electors chose you, you can become their representative, as long as none of your opponents mustered as many votes as you.

Each of the black boxes in that diagram shows a riding in which the majority of voters did not choose the winner, who in some cases picked up even less than 30 per cent of the vote. And because Canada does not have a preferential voting system like Australia’s, we have no idea whether the winning candidate was that majority’s second, third, or even last choice to represent them.

First-past-the-post is fine in a two-horse race, where two parties dominate. But Canada’s two largest parties, the Conservatives and Liberals, accounted for only 67.5 per cent of the vote on Monday night. Three other parties – Bloc Québécois, the NDP and the Greens – made up a collective 30 per cent of the vote.

This table shows the percentage of the vote each party received nationally and in each province, compared with the share of the seats they received.

LPC vote/seatsCPC vote/seatsNDP vote/seatsGRN vote/seatsBQ vote/seatsPPC vote/seats
BC26.1/26.234.1/40.524.4/26.2 12.4/4.80/0 1.7/0
AB13.7/069.2/97.111.5/2.92.8/00/0 2.2/0
SK11.6/064.3/10019.5/02.5/00/0 1.8/0
MB26.3/28.645.4/5020.7/21.45.1/00/0 1.7/0
ON41.5/65.333.2/29.816.8/56.2/00/0 1.6/0
QC34.2/44.916/12.810.7/1.34.4/032.5/41 1.5/0
NB37.6/6032.8/309.4/017/100/0 2.1/0
NS41.3/90.925.7/9.118.9/011/00/0 1.2/0
PE43.6/10027.4/07.6/020.8/00/0 0/0
NL44.7/85.728/023.9/14.33.1/00/0 0.1/0
YU33.4/10033.1/021.8/010.3/00/0 1.4/0
NT40/10025.8/021.8/010.6/00/0 1.8/0
NU31/025.8/041.2/1002.1/00/0 0/0
Canada33.1/46.434.4/35.815.9/7.16.5/0.97.7/9.51.6/0%

As you can see, the NDP and the Greens are the biggest losers from this system. It’s unsurprising, then, that they are among the most vocal supporters of electoral reform.

Monday’s election didn’t need to be conduted using first-past-the-post. In fact, Trudeau and the Liberals had promised reform. “We are committed to ensuring that 2015 is the last election held under first-past-the-post,” the Prime Minister said during the election campaign four years ago.

It did not come to pass. But what if it had?

Proportional representation was touted as one of the systems to replace the current voting method. That takes many forms, but the concept essentially boils down to this: the percentage of votes a party receives more or less reflects the percentage of seats it receives in parliament.

In practice, it means larger, multi-member electorates, often composed of entire countries, districts, states or provinces. So under first-past-the-post (if I could vote here) I would have voted for a single candidate to represent the riding of Ottawa Centre in the House of Commons. Under proportional representation, though, I would vote for, say, candidates to fill the 121 seats in the province of Ontario.

Using the preliminary voting data, I crunched the numbers to see what the House of Commons would look like if a proportional system was used on Monday. In the hypothetical I have used, every province maintains its current number of seats, but the province itself would become a single electorate.

One of the easiest ways to transfer the data is through what is known as the D’Hondt method of proportional representation. To understand this system, imagine it as a bit like first-past-the-post-plus. Say there are four seats in an electorate, and four parties running in that electorate.

D’Hondt collects the total of all votes cast, then awards the first seat to whoever has the most (not the majority of) votes. Counting then begins with the next seat, with one difference: whichever parties already have seats have their vote total divided by the number of seats they have already won, plus one. Counting then continues under this new formula until all seats are filled.

Here it is in action:

Seat 1Seat 2Seat 3Seat 4
Party A100 (Win)50 (100/2)50 (Win)33.3 (100/3)
Party B5656 (Win)28 (56/2)28
Party C44444444 (Win)

So Party A, with 50 per cent of the vote, receives 50 per cent of the seats. Parties B and C, on roughly a quarter of the vote each, receive a quarter of the seats.

The more seats there are, the more acccurate the method will be. Many national parliaments in Europe, Asia, South America and Africa use this system.

Now, back to our hypothetical.

This system does not work in the sole ridings of each of the territories, so I maintained first-past-the-post in those three seats.

Using this system, if everybody voted exactly the way they did on Monday, the House of Commons would look a little like this:

Same colours as before, but with the addition of Purple: People’s Party.
LPCCPCNDPGRNBQPPCTotal
BC11151150042
AB425410034
SK110300014
MB47300014
ON514121701121
QC28138325178
NB43120010
NS53210011
PE2101004
NL3220007
YT1000001
NT1000001
NU0010001
Total1151205620252338

Quite a bit more of a colour mix there. As you can see, the Liberals have had their seats slashed. The biggest relative winners under this system are the Greens, soaring from three seats to 20, and the NDP, which more than doubled its caucus. The Conservatives lost a single seat.

Let’s have a look at the percentage table again, this time comparing parties’ vote share to their seat share under this new system:

LPC vote/seatsCPC vote/seatsNDP vote/seatsGRN vote/seatsBQ vote/seatsPPC vote/seats
BC26.1/26.2 34.1/35.7 24.4/26.2 12.4/11.90/0 1.7/0
AB13.7/11.869.2/73.5 11.5/11.8 2.8/2.90/0 2.2/0
SK11.6/7.164.3/71.4 19.5/21.42.5/00/0 1.8/0
MB26.3/28.645.4/5020.7/21.45.1/00/0 1.7/0
ON41.5/42.133.2/33.916.8/17.46.2/5.80/0 1.6/0.8
QC34.2/35.916/16.610.7/10.34.4/3.932.5/32.1 1.5/1.3
NB37.6/4032.8/309.4/1017/100/0 2.1/0
NS41.3/36.425.7/27.318.9/18.211/00/0 1.2/0
PE43.6/5027.4/257.6/020.8/250/0 0/0
NL44.7/42.928/28.823.9/14.33.1/00/0 0.1/0
YU33.4/10033.1/021.8/010.3/00/0 1.4/0
NT40/10025.8/021.8/010.6/00/0 1.8/0
NU31/025.8/041.2/1002.1/00/0 0/0
Canada33.1/3434.4/35.515.9/16.56.5/5.97.7/7.41.6/0.6

Much, much closer to the actual percentage of votes received. But, of course, the metric I have used is flawed.

The major parties’ numbers are still slightly inflated. D’Hondt rounds up votes to ensure every seat is filled. If a quota system, like that in the Australian Senate, was used, parties would only be entitled to those seats they achieved enough votes for. When dealing in hypotheticals, however, D’Hondt was easier; I tried the quota system and came up with about 15 blank seats that no party mustered a quota for. Without some sort of preferential system in place, it’s very difficult to determine a result.

Another flaw is in the voting data itself. There is no way that the party share of the votes would be exactly the same under both first-past-the-post and preferential voting. First past the post has required progressive voters, in particular, to vote “strategically”.

Say you align most with the NDP politically. You disagree with the Liberals on a lot of policies, but you live in a riding which will be won either by the Liberals or the Conservatives. You want the Conservatives to win even less than you do the Liberals, but if you vote NDP, you risk splitting the vote between left-wing parties and the Conservative could push through to win the seat.

Under a proportional system, that would not be an issue. You could vote for the party that best represents you, safe in the knowledge that they have a better chance of gaining a seat. It also sends a clearer message to the major parties about your voting intentions and where your interests lie.

So even though the major parties lost seats in the above diagram, under an MMP system they probably would have lost even more.

Is MMP the best system for a lower house? Not necessarily – it can shut out independents, could result in a concentration of candidates from a single geographic area, often creates less stable governments, and formalises the party system. And the one I’ve created isn’t the only version, either; there’s nothing stopping electorates from being split into intra-provincial divsions, or from the adoption of a mix of single member electorates and party list proportional representation like New Zealand.

But judging by Canadians’ vote on Monday, no one party has been singled out as representing the country at large. Reforming the system from first past the post to another method could be what voters are crying out for.

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