I like Canada and I like elections (it’s my largest tag word at the moment, which I should really do something about). Canada had an election a couple of days ago hence I shall discuss.

For a country considered fairly liberal the political system is somewhat backward. The Senate is not elected (and there have been some moves to abolish it) and they use a first-past-the-post voting system. In a country with three main parties on the left and one on the right (at the moment anyway) this is a rather daft way to go about things. I have long maintained that the Canadian electoral system gives the Conservative party more seats (or ridings as they are known) than they deserve.

This election gave me an opportunity to put that theory to the test. At the time I scraped the data off Elections Canada most of the vote had been counted and this was the results:

(A note on parties. BQ is the Bloc Québécois who campaign only in Quebec on a secessionist agenda with left leaning policies otherwise, the Liberals are liberals with a little l and formerly Canada’s primary left leaning party. The NDP are the New Democrat Party, social democrats and the new opposition. The Greens also won their first seat)

This has given the Conservatives a majority government for the first time in a while (they went into the election with a minority government). This is also something a lot of my Canadian friends are unhappy about.

So would preferential voting have made a difference? I spent a couple of nights crunching numbers to find out. I’m going to assume the introduction of the Alternative Vote (AV), a form of preferential voting. There is currently a referendum on this in the UK on which there is excellent Australian coverage.

The alternative vote is also known as optional preferential voting which is used in most Australian states and territories. The BBC explains it well here. It aims to elect the most preferred candidate. Basically it works by allowing voters to express preferences for more than one candidate. You mark 1 on the ballot paper to vote for your most preferred candidate and then you can add as many more numbers as you wish (or just leave it at one).

The papers are counted on the one votes. If a candidate has more than 50% of the vote they are elected. If not then the candidate with the least number of votes is eliminated and their papers redistributed according to preferences (if no further preferences are indicated then those votes ‘exhaust’). If a candidate still doesn’t have 50% of the remaining votes (the exhausted votes are not counted in this total) then then next lowest candidate is excluded and so on.

Most of the time AV will elect the same candidate as FPTP. Where it can have an impact is where votes are split between two similar candidates, as is the case in many ridings in Canada between the NDP and Liberals. Using the data I undertook a simulated distribution of preferences. First I counted up all those ridings where the candidate had won with more than 50% of the vote. In these ridings AV would not make any difference.

For the remaining 163 ridings I distributed preferences on the following assumptions:

1. Roughly 50% of the votes would exhaust (which is the usual rate in Australia)
2. Preferences from the Greens would flow to the NDP
3. Preferences from the Liberals would flow to the NDP and vice versa
4. Preferences from the Conservatives would flow to the Liberals
5. Preferences from the BQ would flow to either the NDP or the Liberals.

For 112 of these ridings the use of AV would not make a difference to the result. However for 51 ridings there could be. The results of my simulated distribution are below:

Under AV the conservatives would only get 129 ridings with a further 12 possible. The Liberals and NDP would have at least 160 between them. 4 ridings could go to either the BQ, Libs or NDP and would be decided on Conservative preferences. 2 ridings were influenced by high polling minor parties or independents making them impossible to predict. The 24 uncertain ridings would depend on the rate preferences are exhausted (particularly in the left vs right contests) and how preferences from the Conservatives or BQ flow to the Liberals and NDP.

Under AV the Conservatives would not have won a majority. They could still have governed from minority, however unlike in the previous parliament the NDP and Liberals would have the numbers to form a coalition. Here’s a list of the ridings I’ve predicted that would be different under AV:

Would this have been the actual result? It’s very hard to predict what would have happened in reality. It’s likely that the rate of exhausted votes would be higher for Conservatives and lower for voters on the left, depending on the how-to-vote campaigns of the parties. The reduction in strategic voting would also have different consequences (the Greens and other minor parties would probably have gotten higher votes) and could have led to an increase in votes for the left as these candidates would have been less concerned about vote splitting.

What does seem to be the case is that the Liberals should have the most interest in AV given the numbers of seats they’d pick up. First Past the Post would seem to be preferred by the Conservatives, while there’s still only one party on the right.

What are the prospects for AV in Canada?

Some of the provinces used it in the period between 1920s-1950s, however none have used it since.  British Columbia tried twice to introduce a complicated form of preferential voting similar to what is used in Tasmania, but the referenda weren’t successful.

There will certainly be some discussion about it after this election but the reformists argument will be split between some form of AV and some form of proportional representation. Just like the vote on the left….