What does the country look like under proportional representation? Here's the math.

I created an algorithm and recalculated every election in Canada under proportional representation. It would be cool having a democracy that represented everyone!

Please note that these interactive charts work best on the computer.

In 2015 Justin Trudeau said he would reform the electoral system. He did not. It is a huge black mark against his time in office, and although he did much good, it could be he is remembered more for this one broken promise than almost anything else. Canada uses a First Past the Post System. It doesn’t work. How would Canada look if we had proportional representation?

The only party who would lose out in the case of proportional representation is the Liberals. I built an algorithm to test what the country would look like under proportional representation.

I have modelled the 2021 and 2025 federal elections, as well as every single province. I have used the Irish system as a model. List-based proportional representation doesn’t work. It is what they use in Israel and the Netherlands. The two best systems available, in my view, are Mixed Member Proportional, which has local and federal representatives, or a Single Transferable Vote (STV). I have modelled the algorithm on STV.

First some clarifications:

1. Proportional representation is not a 1:1 in most countries. Israel and the Netherlands do a 1:1 system, where they offer a list, and based on the amount of votes they get they pull from the list. This is bad. That means that 32 per cent of the vote will not be exactly 32 per cent of seats, it will be a bit more complex.

2. I have modelled this off of the Irish STV (Single transferable Vote), and it is not likely the calculations that elections Canada would use. It is useful as an experiment to explain how the system could work. We can’t think that I, one moron making math, would have a better system than engineers and mathematicians.

3. The other problem is that if we had a truly proportional representation, especially an STV, we would have more people voting for a diverse selection of parties. This is not accounted for in the model. Less people would vote liberal or conservative or NDP, because they would feel more comfortable voting for, say, a communist party, or the revolution party. I can’t account for this type of hypothetical. These numbers that I present are based on our parties that are available, and the numbers I have access to. It is most likely that this system would drastically change if the electoral system changed, since more parties would be able to run. It is probably that there could be ten or fifteen parties in the house.

4. Ranked ballots are hard to account for. The NDP might gain way more seats than we realize because of ranked ballots. The PPC might gain seats. I don’t know. Imperfect model, based only on numbers available. I have weighted different regions based on historical voting patterns (Vancouver and Hamilton/Windsor voting NDP, Quebec voting Bloc, Alberta Voting Conservative)

5. This is a simulation, and would likely work differently in practice. It is a thought experiment, and should not be misunderstood as scientific fact.

I have built an algorithm in order to properly weight the results of an election. We are actively developing it. In the future, we would like to release the numbers before and after elections in every part of the country.

If you’re a data analyst or a prof, or a programmer, here’s my algorithm. It might not be this anymore, I kept tweaking it to find better maths as I recalculated. Sometimes there were 40 seat swings and so I’d adjust it, but I don’t recall if I printed it here. Anyways, it needs more variables in population regions and provinces. It’s not specific enough.

If you’re a freak who’d rather look at a spreadsheet, here you go.

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The 2021 election is a perfect example of why First Past the Post doesn’t work.

In 2021 the Conservatives won the popular vote. A highly efficient vote from the Liberals means that they won 160 seats, 47 per cent of seats available, with 32 per cent of the vote. Under an STV system, they are the opposition, and coalitions would be necessary to form government. The conservatives would still have the largest party, but a coalition could form since the Liberals have 30.7 per cent of the vote, and the NDP walk away with 21 per cent of the vote.

How does this change Poilievre’s rise to prominence? How does this transform the electoral future of Canada? Does the far right exist if this is the house in 2021? Maybe not. Let’s look at 2025.

Using the exact numbers we saw in this election, the Liberals & Conservatives lose a negligible amount of seats each. The NDP reaches official party status, and the Bloc remains similar. This was a hard election to map, and I had to adjust the algorithm several times to compensate for strategic voting. It is likely that this would have been even more different than you see, since strategic voting may not have been necessary at all. In that spirit, I compensated by removing strategic voting from the algorithm. Please note that this is using *historical* data, as opposed to actual, available data and is not even remotely scientific. It is a thought experiment, and should be understood as such. There is no scientific way to determine the attitudes of voters in 2025 under an STV system.

The Conservatives win in that case, but the NDP walks away with 70 seats under proportional representation. There’s a good chance that the Conservatives and Bloc form a coalition in this government. The experiment is imperfect, since we only have hypothetical numbers to work with, but I used the averages from 2021 to change the map, and updated the numbers to match Carney instead of Trudeau. Regardless, STV makes both situations much better for Canadians, better representing the country, although I think the Liberal’s numbers are still too inflated.

Let’s look at Ontario and Quebec next, since their previous elections were undemocratic in their representation, to a degree that should anger anyone who believes in democracy.

The Ontario Election is shocking. 43 per cent of the vote became 63 per cent of seats. It’s not a democratic outcome. Doug Ford should have easily won, he has strong support and many Ontarians voted for him and like him. However, under an STV system he walks away with 45 per cent of the vote, a bit above what he earned, but a good representation. Meanwhile, the Liberals crushed the NDP in the election, having 11 per cent more votes than them, yet they came out in third place. Under STV, the NDP somehow still wind up with a higher vote efficiency, which is tough to compensate for in this type of system, but they wind up third with the Liberals as official opposition, properly representing the will of the voters. The only ones who lose out would be the greens, but once again we are coming up against the limits of my algorithm, since I can’t account for the NDP voters who might vote green if they felt they had the choice.

The Quebec election in 2022 is the perfect election to prove why FPTP is a broken system that should be done away with. The Coalition Avenir Québec walked away with a mere 41 per cent of the vote, and won 72 per cent of the seats. An unbelievable majority that mocks the idea of representation. 72 per cent of seats in completely insane by any metric, and considering the CAQ being accused of authoritarian overreach by experts and unions, we see why the FPTP system is so undemocratic. Meanwhile, the other four parties virtually tied, but they came away with tiny percentages of their voting shares, with the Conservative Party of Quebec not getting a single seat, despite being within the margin of error to the other three losing parties. If current numbers are to be trusted, the PQ could wind up with a similar win in 2026. Today, they have 39 per cent of voter intention. With that percentage of votes, they could wind up with 80 seats.

I have run the simulation for every other province as well. Suffice to say that even with a basic algorithm like this, Canadians would be better represented and have a real democratic system if we had STV, and this is using available numbers. If the system was changed, not only would it better represent Canada under our system’s electoral makeup, it would also be likely to radically transform the voting culture in the country, and the electoral maps wouldn’t be remotely similar.

Here is every single other province simulated under my STV algorithm. Sorry Territories, I didn’t simulate your elections because I don’t know anything about you.

It doesn’t really work in provinces that only have two parties, but if there are 3 or more, it works fantastically.

Opinions (I gave you the math, you don’t have to read my opinions if you only came for the math. Don’t complain if you don’t like my opinions, you didn’t have to read this part!)

One of the arguments against Proportional representation is that it allows extremist parties in. Well, right now one of our two biggest parties is playing with the idea of being an extremist party, and they could well win a super majority in the future.

If Pierre Poilievre leaves, by the way, will they go further right? They very well could. Just saying, it can always get worse.

Right now, the Republicans in the USA are a white-supremacist party, and they hold 100 per cent of the power in the whole US government. Arguments against prop representation that revolve around “preventing extremism by creating big tent parties” are null and void. The Liberals and Conservatives won’t implement the system because they hold out hope for majorities, where they can effectively do anything they want. But let’s be clear, I’m completely unconvinced that a ruling NDP or Green government would do any differently, though I’d be happy to be proven wrong.

In Austria, the Neo-Nazi party won the most seats in their house, but because they have proportional representation, the other parties formed a coalition between three ideologically opposed parties in order to run the country. Yes, it gives extremist a regular spot in the house, but it means that extremists can’t have majorities, or at least are unlikely to. No one ever thinks about what it means when someone like the CAQ gets power and starts implementing authoritarian measures.

It also means socialists can’t get a majority, which is the great fear of the right. The conservatives, under this system, would have won the past three elections.

Why isn’t the tiny little NDP we have pushing the conservatives to vote for a new electoral system? I’m not sure they could convince them, but there could be reasonable people who might be convinced by the stats. The conservatives stand only to gain under proportional representation, unless they enjoy the Liberals ruling at a 2:1 ratio compared to them.

The only party in Canada who benefits from the FPTP system are the Liberals.

Every party should be pushing for this. Canadians want this.

I hope that some conservatives are reading this— folks, you would have won the past three elections under a prop representation system. Right now you’re the party who lost an election where you had a 20% lead in the polls. This is because of strategic voting. Do you understand how badly the system is failing you and your voters?

Trudeau’s greatest failure is that he failed to change our electoral system. It’s because when push came to shove, he realized he would lose under that system. Many NDP insiders (who I speak with often) wish Singh had made their supply-and-confidence with the liberals hinged on proportional representation. The NDP did not have the political will to throw away their recent successes in order to get what’s best for the country. The dental care plan is great, but it was inevitable. Proportional representation is not.

The NDP would have had to be willing to throw the country into an election for proportional representation. It would probably have ruined the deal between them and the Liberals. It would have resulted in the end of the stable government we had. It might have resulted in a conservative government.

Are the NDP willing to risk losing in order for what’s best for Canada? The calculation, in my opinion would have been better for them. “We want you to be better represented, the conservatives and liberals don’t.” Canadians want people with backbones.

Nonetheless, I don’t believe the NDP would do it, even if they were in power. Every time the NDP govern across the country, they turn to austerity measures and they look like the federal Liberals. BC and Manitoba are perfect examples of this. Those provinces are continuing neo-liberal policy-making, and they still haven’t raised taxes on the ultra rich. Tom Mulcair and Jack Layton were the closest leaders to ever forming government as NDP federally— they campaigned less left wing than Justin Trudeau’s Liberals (I just enraged a lot of NDP readers, sorry crew.) Mulcair was literally a Quebec Liberal before he was part of the NDP. The differences between the parties are less than one would hope.

I’m left wondering:

Will the future leader of the NDP have the political will to change the system? Are they willing to stake their future on it? Are they willing to throw away stability for what’s right? Canadians are afraid of any change or instability, but there’s a lot of people who would love to see a party fight and demonstrate a real backbone.

Many questions remain that are unanswerable in the case of proportional representation, and a few points need to be stated. First, my system, based on the Irish Single Transfer Vote system isn’t the only one. There are other effective proportional systems that all work well. Even the worst proportional system, in my opinion, would be better, even a list based system. This would allow people to vote ideologically instead of pragmatically. Enough of brokerage politics and patronage! Let’s see some ideas in this house!

We also must consider the First Nations. They should be reserved 20 per cent of the seats in Canada. They should have a permanent 20% control of the country. Or more! They are the founders and the backbone of the country. A guaranteed Indigenous vote is mandatory for true representation in the country. This would be the most effective way to show true reconciliation, in this journalist’s opinion. Give the indigenous power over our lives.

Give em 50% of the seats, it would be a hell of a lot better than Chretien, or Harper, or Carney, or Poilievre.

The political party to implement it would be guaranteeing that they themselves will never have a majority government again. So I am cynical that this will ever occur. We are long past the days of the great politicians and leaders of the mid 20th century.

I suppose the future is unwritten. But I’m skeptical.