Mr. Chair, members of the committee, thank you for the time and energy you are investing in the health of our democracy. You are investigating important issues related to how Canadians express their will as we elect our leaders. I very much appreciate the work you are doing.
I also appreciate this opportunity to address you regarding my own work. I teach computer science at the University of Waterloo, where I've been a faculty member for 25 years. I've also been interested in electoral reform for the last decade.
Over the summer and into the fall, I combined my expertise in computer science with my interest in electoral reform to model many of the systems that have been proposed for Canada. “Model” is a critical word to understand in this context. This is the definition I would like to use: the application of electoral system rules to data, producing results that assist in understanding the behaviour of the system.
I want to emphasize the last phrase. I'm trying to understand the overall behaviour of electoral systems. My goal is not to predict who wins and who loses under a different system. That goal has many difficulties, including voters changing how they vote when the system changes. Instead, I'm attempting to use past elections to see if the system is well behaved. If it has been well behaved in many such elections, we could expect it to be well behaved in future elections, even if voters change how they vote.
What does it mean for a system to be well behaved? I think this committee's own mandate provides a helpful definition that I'm sure you'll recognize. A well-behaved system “reduces distortion and strengthens the link between voter intention and the election of representatives”. Distortion is introduced when representation in government is significantly different from the level of popular support expressed in the election.
A well-behaved system should not be arbitrary or erratic. First past the post, for example, will award a party earning 40% of the vote anywhere from zero to 338 seats in the House of Commons. With a well-behaved electoral system, a small change in the votes cast should result in only a small change in the MPs elected. Another way to say that is that in a well-behaved system, the number of MPs awarded is proportional to the number of votes earned.
With that preamble, let's dig into the meat of my results.
Graphs like this are essential to my methodology for understanding whether a system is well behaved. It shows the proportionality of an electoral system across seven sets of data.
This graph is for first past the post and shows what a misbehaving system looks like. In contrast, here is the graph of the rural-urban system. It is well behaved. Notice how each pair of coloured lines track each other closely.
Let's take a few moments to understand these graphs. The centre, at 0%, represents the data from an actual election. In this case, it is first past the post 2015. The heavy points are the percentage of the popular vote for a particular party. The Liberals earned almost 40% of the votes, the Conservatives 32%, and so on for the other parties. The lighter points reflect how the parties were rewarded with MPs in the House. The Liberals' 39% vote share turned into 54% of the MPs at the expense of the other parties, which received fewer MPs than they deserved.
In 2015, first past the post was a misbehaving electoral system. But this is old news. We knew this on election night. What value have I added?
Remember that we want to see how each electoral system behaves in many different but realistic elections, not just in 2015. We can simulate a different election by taking the 2015 results and shifting 10% of each Conservative candidate's vote to the local Liberal candidate. That might reflect an election in which late-breaking good news for the Liberals swings voters to their camp. Applying the first-past-the-post voting rules to that set of data gives the Liberals 64% of the MPs, with only 43% of the vote.
If we swing 30% of the Conservative votes to the Liberals, they get 81% of the seats but still don't have a majority of the votes. Meanwhile, the effect on the Conservatives is devastating, with 7% of the seats in spite of earning 22% of the votes.
Of course, we can also simulate the movement of Liberal voters to the Conservatives. That is shown on the left side of the graph. Other graphs can simulate votes shifting between other combinations of parties.
First-past-the-post misbehaviour plays out in previous elections as well. These four graphs represent four real elections and 24 simulated elections. First past the post did not give a proportional result in any of them.
Let's move on to take a brief look at some of the other electoral systems.
The rural-urban proportional system is very well behaved. Here is the graph applying those rules to the 2015 election data and simulating related elections where votes swing between Conservatives and Liberals. Recall that the heavy lines represent the popular vote, while the lighter lines indicate the number of MPs. The important thing to note is how the two lines track each other very closely.
Here are the graphs based on earlier elections. In each case, the system is well behaved. I like the rural-urban proportional system, as proposed by Fair Vote Canada, because it addresses our huge disparity in riding sizes. It keeps our already huge ridings at about the same size by electing a single MP in those ridings. It gains proportionality by using multi-member ridings where higher population densities make that feasible.
Finally, a small layer of top-up seats, like the ones used in MMP, offsets the disproportionality of the single-member seats. That top-up layer is important. Rural-urban proportional is inspired by Kingsley's proposal, but it is not the same. Kingsley's proposal leaves off the top-up layer. When we model that, the result is surprisingly good, but not as good as rural-urban.
I've also modelled STV, single transferable vote, with both small ridings averaging 4.1 MPs and larger ridings averaging nearly 11 MPs. Both are well behaved, but predictably, the system with the larger ridings does better.
Modelling mixed member proportional, or MMP, with two sizes of top-up regions shows that it is also well behaved.
Alternative vote has the distinction of being the only system I modelled that misbehaved more than first past the post. Using data from four real elections and 72 simulated elections, alternative vote did not produce a single proportional result.
Another alternative that might seem attractive is to keep exactly the same riding boundaries we have now but enlarge the House with 10% more MPs, making them top-up seats similar to MMP. We might call this MMP-light if we elected MPs in the local ridings using first past the post, or we could call it AV-plus if we elected MPs using the alternative vote.
While both of these systems would be a step toward proportionality, my modelling shows that it would be a very small step, even with the best-case scenario of calculating top-up seats over each province, rather than smaller regions, as is common with MMP. A 10% top-up simply is not enough to overcome the disproportionalities of all those single-member ridings. But if we use exactly the same constraints with the rural-urban system, that is, 32 extra MPs assigned to top-up seats and calculated at the provincial level, we get a well-behaved system.
Thank you for your attention thus far. I've gone over some very detailed and technical material. You may feel at this point like my brother, who said, “That makes my head hurt.” Nevertheless, I believe it is important information for your decisions.
Let me summarize. First past the post frequently misbehaves. Alternative vote is worse than first past the post. STV, MMP, and rural-urban are all well behaved across many different simulations. Last, half-hearted attempts such as MMP-light and AV-plus are only slightly better than what we have now. Rural-urban, under exactly the same constraints, is excellent.
The program I've written and the input data are available for anyone to download, run, or modify. The results I've shown here are readily available on the web at election-modelling.ca.
Thank you again for your attention and for the incredible service you are performing for Canada. I look forward to your questions on my comments here, as well as my earlier submission to the committee.