Note — After sharing an earlier version of this post with my friend JJ McCullough, he noted that many historical sources on Canadian election data differ considerably: you need to be careful about what sources you pull from. He has produced a wonderful website on Canada (The Canada Guide), which also covers historical elections. You should check it out!

How many parties are there?

The previous post got me thinking: it's clear that the number of political parties has increased over the last century but how can we quantify this? Counting the number of different candidates running is unsatisfactory since that includes all sorts of irrelevant parties (e.g., the Communist Party of Canada). Instead, we can calculate a quick metric known as the "effective number of parties".

To calculate this, sum the squares of the support that each party achieved and then invert the total. In economics, this method is a quick-and-dirty (although very dated) way to look at the competition in a given market: the more “effective firms” (or parties), the more competition. In short, this metric gives an indication for how many political parties people have either voted for or are taking seats in the House of Commons.

The chart below shows two things: the top panel shows the effective number of parties that Canadians voted for, while the bottom panel show how many political parties took seats in the House of Commons. I've calculated this for every election since 1987 (using data from the Library of Parliament):

This plot shows the effective number of parties for each election. The top panel shows the effective number of parties based off the votes, while the bottom panel shows the effective number of parties that show up in the House of Commons. The averag… — This plot shows the effective number of parties for each election. The top panel shows the effective number of parties based off the votes, while the bottom panel shows the effective number of parties that show up in the House of Commons. The average for each era is in the oval.

Eyeballing the data, there appear to be three eras in Canadian politics (also discussed in a previous post). I've coloured these in black, blue, and orange. From 1867 until 1917, Canadians voted for ~2 political parties and ~2 political parties showed up in the House of Commons (2.1 and 1.9 respectively, to be precise).

But from 1920 until 1990 this changed: Canadians voted for roughly 3 political parties and only 2.4 showed up in Ottawa. After 1990, this became more extreme: Canadians voted for 3.7 parties but only 2.8 showed up at Parliament. What's going on?

For every incremental effective political party that Canadians voted for, only ~0.5 effective parties show up in Ottawa. I've shown this in the scatter plot below.

The data shows that, over time, Canadians have voted for more political parties but, although there are now more political parties entering the House of Commons, this is not fully reflected in Parliament's composition. The reason for this is the convexity inherent in our first past the post system: smaller parties are typically under-represented, while larger ones are over-represented.

Each dot in this plot represents an election (they are colour-coded by dated). This plot shows that as Canadians vote for more effective parties, the effective number of parties in Parliament increases, but at a slower rate.

A desirable property of FPTP?

I don't think the above trend (alone) is sufficient to warrant worrying about under-representation — in fact, it shows a desirable (and often forgotten property) of the FPTP system: the incentive to merge political factions into larger parties.

Party mergers and breakups are quite common in many political systems. However, in First Past the Post system, the convexity of the system provides an in-built incentive for similar political factions to resolve their differences and present a united front to the electorate. Two similar parties that each receive 15% of the vote will typically have fewer seats than a single party that achieves 30%. This was the major incentive for the Canadian Alliance and Progressive Conservatives to overcome their differences and form a united Conservative Party in 2003.

This dynamic is often ignored when discussing whether we should adopt a Proportional Representation (PR) system: under PR systems (like in Israel or the Netherlands), factions have little incentive to overcome their differences before an election. Instead, they formally negotiate their differences after an election in order to form government (sometimes this takes a significant amount of time). Had Canada adopted a PR system in the early 2000's, I doubt the Progressive Conservatives and Canadian Alliance would have merged. Further, if we adopted PR today, there is no reason to think the Conservatives (or any of the other parties) would necessarily remain united.

This is not to say that PR is inferior or superior to FPTP; however, the two systems differ in their incentives to create new political parties. PR allows for the existence of small parties, while FPTP incentivizes the creation of “broad churches” from many political factions.

The dynamic process of creating new political parties, destroying old ones, and merging similar ones is akin to creative destruction. Ignoring party formation in analysis of changes to the electoral system is a bit like analyzing a market under the assumption that there will be no more technological improvements or that the current major players will always be on top. It might give some insight into what could happen in the very short run but it won't tell you anything about how the new system will behave.

Mergers and acquisitions

The creation of new parties and the mergers of old ones is a perfectly normal part of the Parliamentary system and one that is sometimes overlooked: in discussions on electoral reform, it's tempting to focus on which party today would benefit from a proposed change (after a quick Google, here is an example). Although these articles can be fun speculation, there is a problem with this sort of analysis: it assumes today's political parties will remain static even after some fundamental change to the voting system.

Over the course of two short posts, I want to show you a longer time series of Canadian elections and a couple quick cuts of the data to show how parties rise and fall. Their emergence (and destruction) is a crucial part of the "first past the post" (FPTP) system — in fact, a crucial part of any democratic political system! Ideological (or other) movements must iron out their difference and coalesce into a well-organized party so as to present the country with a coherent and unified option for Government. These "broad churches" are themselves smaller deliberative bodies, where different factions must compromise.

When factions cannot find reasonable compromise within an existing party, they can start their own. This is what happened when Lucien Bouchard left the PCs to form the Bloc Quebecois or when Preston Manning (and others) founded Reform. The converse is also true: Stephen Harper and Peter MacKay merged the Canadian Alliance and the Progressive Conservatives, which created the Conservative Party in 2003.

Even over the last decade there has been plenty of speculation on whether the Liberals and NDP should merge (here is but one example).

Federal votes and election outcomes

I've pulled the historical Federal election outcomes since Confederation from a variety of sources (although mainly from the Library of Parliament). Below are two plots: the top one shows the distribution of seats from every election since 1867, while the lower one shows the popular vote percentages.

I have ordered the parties (roughly) so that the Conservative / Right-wing parties are near the top of the chart and the Liberals are at the bottom. Since these are the only two parties that have held government, this should show the back-and-forth between them over time (in particular, whenever one crosses the white 50% line).

This first chart (above) shows the distribution of seats in the House of Commons after every Federal vote coloured by political party. It is easy to see the Liberal and Conservative majorities as they cross the white horizontal 50% line.

This second chart (above) shows the distribution of votes coloured by political party). There are few cases where any political party gets over 50% of the vote (these cases are mostly when there were only two major parties from 1867-1917)

A few quick reflections from these charts:

After the 19th century, majority governments have been common but majority popular votes are not: since the rise of >2 major political parties, there has only been 2 elections where a party received the majority of the popular vote
The distribution of seats is more volatile than the distribution votes: this shows the convexity that emerges from our voting system - small changes in the vote proportions lead to large changes in the seats (I have another post on this topic.)
There appear to be two major "fragmentation moments" in Canadian politics over the last 150 years:
- ~1917 (onward): The rise of the Progressives, Social Credit and other parties (CCF, New Democracy)
- ~1990: The fragmentation of the political right and the rise of separatism
Political fragmentations take years to resolve: after the break-up of the Right in the 1980s / 90s, the Liberals achieved four mandates (three majority and one minority) before a Conservative party took government

In a future post, I'll show some more detail on how the the “number” of political parties has increased over time.