Creative destruction: The fragmentation and consolidation of Canadian political parties (2/2)

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 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.