With the results coming in for the 2020 American elections, I thought it was an opportune time to do some quick analyses on Canadian election data.

In October 2019, despite a pledge from the Liberals to adopt a more representative electoral system, Canadians went to the polls to elect a new Parliament using the First Past the Post system (FPTP). Although they lost the popular vote, the Liberal Party retained a strong Minority Government, benefitting structurally from their broken promise to remake the electoral system.

The two clear losers in the election were the Liberals (who admittedly held on to power) and New Democrats. Versus their 2015 results, both parties lost seats, absolute vote (despite an increased voter base), and share of vote. Conversely, the Conservatives and Bloc Quebecois improved on all of these dimensions. The Conservatives picked up support, primarily in the West, but were unable to break through in Ontario. In spite of their gains, the perception in the media was that the Conservatives had under-performed and Andrew Scheer resigned soon after the election amid in-party squabbles.

Living as a Canadian expat in San Francisco, many Americans I meet assume that Justin Trudeau must be remarkably popular in Canada. This is not a terrible assumption given his government was re-elected; however, the numbers show that he is not universally supported. Trudeau’s Liberals won only 33% of the popular vote and he had similarly low approval numbers. Many of my American friends are surprised to learn that Trudeau’s approval in Canada at the time of the election (mid-30s) was lower than Trump’s approval in the US (mid-40s).

And yet, despite losing the popular vote to the Conservatives, Trudeau remained the Prime Minister. This is because the FPTP system is similar to the electoral college: by design, different regions are represented disproportionately.

A disproportionate outcome: Liberals lose the popular vote

Like in American Presidential elections, the overall popular vote in Canadian Parliamentary elections is meaningless. The Americans select their President by electing 538 “electors” in 51 separate elections. In Canada, we conduct 338 separate elections across the country to choose Members of Parliament, with districts varying substantially in population. The party with the most MPs forms government, effectively controlling both the legislature and the executive. Due to this regional electoral structure, the national popular vote often differs substantially from the seats in the House of Commons. The 2019 Canadian General Election, however, is the most unrepresentative minority government since WWII.

The Gallagher index, a measure of how unrepresentative an outcome is, for this election was 12.18. By contrast, the US House of Representatives has an index that ranges from 2 to 5. Compared to the US Presidential Electoral College, this Parliament is less representative than any US Electoral College outcome since 1996. As an aside, the below chart shows how the Gallagher index can be misleading: the knife-edge elections (e.g., Bush v. Gore) appear more “representative” than blow-outs (e.g., Reagan v. Mondale). This is because knife-edge outcomes result in a narrowly split Electoral College, while blow-outs result in one candidate carrying nearly all the Electoral College votes (despite only winning by a few percentage points nationally).

Further, even accounting for the convexity of the FPTP system, the Liberal party was able to outperform what would be expected given their national vote. This is because their vote was structurally more efficient than other parties. In particular, incremental Conservative support was “wasted”, being clustered in Western Canada by winning ridings in Alberta with “Saddam Hussein-style” margins. To translate this to the American context, it is much like Democratic support in California: running up the number of Democratic votes in California has no impact on the Presidential election once the state has already been won.

Another way to see the efficiency of the Liberal vote is to look at the seats won per 10K votes cast. Although this metric is somewhat tautological — winners do better — it shows the Liberals have outperformed the other parties in the last 2 elections by capturing seats with fewer votes.

I should stress: high Gallagher indices and unrepresentative outcomes are not decisive evidence against an electoral system. Electoral systems are designed with more than simple majoritarianism in mind, sometimes intentionally giving disproportionate representation to certain regions. There is, however, an irony in the results of the 2019 election: the party that committed to ending FPTP (due to it being unrepresentative) was only able to retain power as a result of a historically unrepresentative election.

Vote splitting: an irrelevance?

Another consideration in the 2019 election was the emergence of a new right-wing party: Maxime Bernier, a disaffected Conservative MP, launched the populist People’s Party of Canada. Historically, a divided Right allowed the Liberal party to govern Canada with little threat of electoral defeat. Although vote splitting with the PPC was a worry for the Conservative party, it does not appear to have had a material effect on the outcome.

Some “back of the envelope” math shows the PPC, at most, directly cost the Conservatives 7 seats. Obviously, this sort of crude arithmetical analysis neglects how the election “narrative” was impacted by this new party but it does show that vote splitting on the right does not explain the success of the Liberals. At the time, I shared this analysis with my friend (and award winning Youtuber) J.J. McCullough who tweeted out:

Had at least 80% of the PPC vote shifted to the Conservatives, the Conservatives would have captured 7 more ridings: 6 from the Liberals and 1 from the NDP. Assuming these gains, the Conservatives would still have been in opposition and Justin Trudeau would still be Prime Minister.

Sensitivity analysis: uniform vote shifting

Historically, only the Liberals and Conservatives have been able to form government under the FPTP system. In order to win a Minority, the Conservatives would have needed 6% of the Liberal base to defect to the Conservatives (roughly 360K votes). To capture a Majority, the Conservatives would have required ~16% of the Liberal voter base to defect, roughly 1 million votes. This implies that, under this distribution of votes, the Conservatives would need ~40% of the national vote to achieve a Majority, while the Liberals could get a Majority with only only slightly more than their 33%.

This asymmetry between the Liberals and Conservatives is partly caused by the weakness of the NDP, a contributing factor to the Liberal victory. In general, it is difficult for the Conservative party to win an election without a strong showing from the NDP and Jagmeet Singh proved a weak leader. Versus 2015, the NDP lost over half a million votes and 20 MPs due to a collapse in Quebec. Had 11% of the Liberal vote switched to the NDP (roughly 600K votes), this would have delivered the Conservatives a Minority government.

The Liberals were the major beneficiary of the FPTP system in 2019. Historically, they have performed well under the FPTP system, which is why it is unsurprising they abandoned their promise to reform it. Given these results, some small-c conservative Canadians might start to consider whether their agenda could be more successfully advanced under an alternative voting system.

Full disclosure: In the Summer of 2007, I interned for Hamish Marshall, the 2019 Conservative campaign manager, in the Prime Minister’s Office and remain close friends with him and his (L)awesome wife. Also, I am friends with Nicholas Insley, who was the candidate for the Conservatives in Coquitlam-Port Coquitlam, one of the seats that the PPC ostensibly cost the Conservatives.