The May 2011 Canadian election under AV

(Note: If you are looking for statistical data re: the 2 May 2011 Canadian federal election, please visit Elections Canada or the Pundits’ Guide to Canadian Federal Elections [which uses Elections Canada data].)

I came across a couple of blog posts written by people in the UK looking at what transpired in Monday’s general election and arguing that had said election taken place under the Alternative Vote rather than FPTP, the Conservative party would not have emerged with a majority government.

In a previous post, I wrote that my initial impression was that even under AV, the Conservatives would still have emerged with a majority. I hadn’t had a chance to examine riding by riding results, but given how AV has worked in Australia, in most instances, the candidate that emerges in first place after the first count, but short of a majority of votes cast, retains the seat even after preferences are factored in.

I have since had a chance to look at the preliminary results from the May 2 election in some detail.

(Note: what follows is based on preliminary results from the Elections Canada website, not certified final results. Consequently, some of these number might change in the coming weeks. Two seats will undergo mandated recounts due to the closeness of the results.)

Based on the preliminary results available on the Elections Canada website, there were 163 seats (53%) that were won with less than 50% of the vote (out of 308). This is a slight improvement over the 2008 election, I should point out. In 2008, 61% of the seats were won with less than a majority of the vote.

Of those 163 seats, I quickly determined that 136 would have yielded the same outcome under AV. The main reason for this was because in a majority of these ridings, the candidate who finished first was very close to the 50% mark, and so would have required few votes transferred on preferences to achieve a majority. In other instances, the winning candidate was further from the 50% goal, but had a significant lead over the second-place candidate. With such a large gap between first and second, the odds of the candidate in second-place after the first count moving ahead of the first place candidate were at best remote.

This left me with 27 seats that might have had a different outcome under AV.

I decided to try to guesstimate how many of these likely would have changed hands under AV. Please note that my methodology is, to be blunt, deeply flawed. There were no mock AV polls conducted in Canada as occurred in the UK in 2010. I got the impression that some of the UK bloggers I referenced above may have been working on the assumption that, for example, all NDP voters would have indicated Liberals as their second choice, and vice versa, and that few, if any votes would have transferred to Conservative candidates. Others may simply have added up all the votes cast in a given riding for the non-Conservative candidates and found that total to exceed the total votes won by the Conservative, and concluded that under AV, obviously, a non-Conservative would have won. While my methodology is far from scientific, anyone doing what I’ve just described is using an even more flawed methodology.

The closest thing I had that indicated potential second-preference voting trends was an EKOS poll conducted just before the election (April 26-28 2011) which asked voters about their second choice (click on the gallery images and scroll through to find the second choice chart – I can’t link to it directly). EKOS asks this question to try to determine how committed supporters are to their party of choice, not to guess at how they might vote if they could rank candidates. They don’t ask about 3rd or 4th preferences.

The poll indicates two important facts to keep in mind. First, a significant number of those polled (30.6%) stated they had no second choice. This is important because, as we know, not everyone would indicate a second preference on an AV ballot. Of course, they weren’t being asked about second preferences under AV voting, but the fact that many voters are very committed to one party and have next to no interest in other parties matters. Among party supporters, Conservative voters are the least likely to indicate a second preference – 47.4% said they had no second choice. They were followed by Green party supporters (27.4%), BQ supporters (21.7%), NDP voters (17.4%) and Liberals (17.1).

Next, it’s a mistake to assume that NDP, Liberal and Green supporters wouldn’t indicate a Conservative as their second choice. While the Conservatives were the party least likely to be chosen as anyone’s second choice (not counting the BQ since most Canadians can’t vote for BQ candidates), 13.5% of NDP voters, 12.6% of Liberal supporters, 11% of Green supporters and 7% of BQ supporters indicated that the Conservatives were their second choice. That is why it is a huge mistake to conclude that all “progressive” voters would favour another “progressive” party as their second choice.

Conservative supporters’ second choices were: NDP 21%, Liberal 16%, Green 11% and Bloc 0.5%; NDP supporters opted for the Liberals 37.7%, Greens 19%, Conservatives 13.5% and BQ 11%; Liberal supporters said their second choices were: NDP 54%, Conservatives 12.6%, Greens 12.0% and BQ 3.3%, while Green supporters favoured the NDP 40%, Liberals 17%, Conservatives 11% and BQ 2.6%. Finally, BQ voters’ second choices were the NDP 48%, Liberals 13%, Greens 8% and Conservatives 7%.

Using this poll as a guide, to simulate voting under AV using preliminary results from Elections Canada, I first reduced the number of transferable votes for each eliminated party by the percentage of those who indicated they had no second choice. Meaning, if the Green candidate was the first eliminated, I reduced the total number of votes cast for the Greens by 27% since that is how many Green supporters indicated they had no second choices. Before anyone jumps in to criticize this methodology, I know full well that this wouldn’t necessarily hold up if we were actually using AV rather than FPTP, nor would they apply across every riding. For example, I would think that Conservative supporters in provinces outside Alberta would be more likely to rank other candidates, and Conservatives in Alberta even less likely to rank candidates (but since only one seat in Alberta was won with less than 50% of the vote, this is a rather moot point). Still, I preferred to be rather conservative in this exercise and thought it made more sense than simply blindly transferring all the votes cast for a given party.

After I had eliminated those with no second choice, I then redistributed the remaining votes based on the numbers listed above. So of my remaining Green votes, 11% went to the Conservative candidate, 40% to the NDP candidate, etc. I repeated this process, eliminating one candidate then the next, until someone had a majority of the vote.

These preference transfers are problematic on another front. Just as EKOS poll only hints at how voters might have ranked a second preference, there is no way to know how they might have ranked third or fourth preferences. In this exercise, I am treating transferred votes from one party as votes for that party and further tranferring to the next party based on the second party’s overall preferences. Meaning, If I transfer 400 votes from a Green candidate to an NDP candidate in one riding, and the NDP candidate is the next one to be eliminated, I am treating the transferred Green votes as NDP votes and redistributing them as per the EKOS poll results for the NDP (so most would go to the Liberals, then the Conservatives). I have no way of knowing if this is how most Green voters would have ranked candidates on an actual AV ballot. It probably isn’t, which is why this entire exercise is completely hypothetical and should not be held up as any sort of gospel truth.

With all of these caveats in place, my non-statistician calculations lead me to revise my initial assessment.

Had the 2 May 2011 election occurred under the Alternative Vote, it is possible that the Conservatives would not have won a majority government.

Of the 27 seats that I thought might potentially change under AV, 24 of them did, using my horribly flawed methodology described above. Three seats remained the same. Using my new results, the standings in the House of Commons would look like this:

Conservatives 148 (down 19)
NDP 122 (up 10)
Liberals 48 (up 12)
BQ 1 (down 3)
Greens 1 (no change)

The Conservatives lost five seats to the NDP and 14 to the Liberals (mostly in Ontario where the NDP surge caused a horrible spoiler effect, leading to Liberals being defeated by Conservatives. Michael Ignatieff would still have lost his seat in my scenario, however.). The Liberals lose two seats to the NDP, but gain 14 from the Conservatives, for a net gain of 12. The Bloc loses three seats to the NDP.

More interesting to many, is that the NDP and Liberals together would command a majority of 170 seats.

So there you go. As I’ve stressed, repeatedly, my methodology is very imperfect. But it’s the best I have to go on. Perhaps when Elections Canada makes available its raw data, someone else will take a crack at this exercise and end up with different results. I was mostly just having a bit of fun.


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Radical Centrist

  • Melissa Williams

    Thanks so much for doing this analysis. It’s the best (okay, so far the only) analysis I’ve seen of the question – given the data constraints, your method seems very sensible. I think it’s an important analysis to share with our British friends!

    • Thank you for the encouraging feedback. I was despairing at the tedium of it all, but the final results were surprising enough to justify the effort!

      • Melissa Williams

        I think you should send it into one of the major newspapers. It’s very timely, and important. You might also want to send it (ASAP!) to OpenDemocracy and other UK venues, flagged as important so that they can disseminate it before everyone goes to the polls tomorrow.

        • I’d be hesitant to do that because technically, I’m not even supposed to blog about politics due to the work I do, which is why I blog mostly about the UK – figure that would be less problematic. I wouldn’t want to be drawn into any sort of spotlight. However, if someone else wants to plug this elsewhere, I certainly can’t stop them…

  • Dowen

    Fascinating, thanks for this.

    • Thank you for taking the time to comment. It’s appreciated.

  • Anonymous

    I don’t think your methodology is flawed, it’s a very reasonable way to do the estimates with the given data. If I’m understanding it’s exactly what I used when I did a similar analysis of the 2008 election.

    • I like to emphasize that it’s got a lot of caveats so no one accuses me of definitively proving anything!

  • betaz

    That is really well done, and it actually helped me understand the AV system much more clearly. Thanks!

  • Anonymous

    You’ve probably made a small mistake with the vote for Le Bloc. One should make general preferential vote assessments against parties with a highly regionalised vote. You would probably have to go through the marginal Quebec ridings one-by-one to determine what would happen there.

    And thanks for the analysis, just what I was looking for.

    • I did go through each marginal riding one by one, doing calculations. I have probably made several mistakes given that the data I had to work with was imperfect – I did try to make that very clear in the post. In the UK, on voting day in May 2010, an actual mock AV survey was done outside pollling stations asking people who’d just voted how they would vote if they could rank candidates. Nothing of the sort has ever been done here, so the EKOS poll was really the only hint at 2nd choice preferences I had.

  • Anonymous

    I ran the script I used for the 2008 simulation on the 2011 numbers and got similar numbers, the conservatives lost a few more when I ran the number:

  • Tim Roll-Pickering

    One factor that could throw the data further is whether the opinion polls are showing people’s preferred party in general or their voting intention, as tactical voting can distort predictions.

    If they’re showing general party preferences then it’s probable that if tactical voting happens, the votes left for parties in 3rd and below will often be “purer” voters, committed to the cause and less likely to transfer at all, whilst the ones with second preferences are more likely to have moved anyway. However I’ve no idea how to accurately factor in such views.

  • Alternatevote

    Unfortunately you are not as smart as you think.  There are many instances when people who are “far” below would come to win.  40% conservative, 23% liberal, 19% ndp, 8% green… who do you think is going to win?  I can safely say that 90% of those liberals, ndp, and green, will list any of the three before Harper… Especially if we demanded an election NOW under AV.  We would have a conservative minority at worst. 

    • No there aren’t, going by Australia’s experience, which is really the only country which uses AV at all. According to Anthony Green, who is an elections expert, of the 1,500 electorates contested under AV in NSW and Queensland since 1981, there has been one case of a candidate in third place after the first count ending up the winner. It was the NSW Electorate of Murrumbidgee in 1984. The reality with AV is that whoever is in first place usually ends up winning, and sometimes, the 2nd place candidate moves ahead, but only if they are very close to begin with. The greater the margin between 1st and 2nd, the greater the odds the first place candidate will win. In your example above, if the Tory candidate ended up with 40% on the first count, I’d place my money on that candidate ending up with the seat. It’s simple math – the Conservative needs a much smaller number of vote transfers to win – much easier for him/her to get the number needed than it would be for candidate in second.

  • Alternatevote

    But otherwise, very good analysis with the data that is available.  Thank you!

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