Thursday, March 28, 2013

Preferential ballot poll

I had a thought a little while ago, and asked David Coletto at Abacus Data whether he had ever considered running a poll that would mimic a preferential ballot. He thought it was a good idea, so last week he added it to his regular polling. And he provided me with the results.

I wrote about them for The Globe and Mail. I'm going to go over some of the results here, but the main pieces of information gleaned from the poll are presented in the article.

A little bit about the methodology: Abacus asked respondents to rank seven parties from 1 to 7, adding the Christian Heritage, Libertarian, and Pirate parties to the mix to provide a little variety, and to see whether anyone would rank these parties highly if given the chance.

Unfortunately, respondents were not given the option to stop ranking the parties at any point, which is what a preferential ballot does allow. 'Second choice' polling suggests that Conservative supporters are most likely to say that they have no second choice. However, this should have little effect on the seat distributions I calculated with the preferential ballot, as in only 83 of 338 ridings did the Conservative candidate drop-off the ballot before the 50% threshold was reached - and 53 of those were in Quebec, where Conservatives are probably less likely to not have a second choice.

The Globe article has the national breakdown of how supporters of each party would rank their ballots, but since I have unlimited room here let's go through the results region-by-region. Note that, outside of Ontario and Quebec (and even in those two provinces to some extent), the samples for each party are quite small. I have not included the Greens in some of the regional breakdowns below because it was based on 10 or fewer respondents.
We'll start in British Columbia. You can see the strength of the Greens here - they are the consensus second choice for New Democrats and third choice for Liberals, while they garner decent down ballot support across the board. But you also see that the Conservatives do surprisingly well as a second choice for Liberals in B.C., which could potentially back-fire if the party ever co-operates with the New Democrats.
In Alberta and the Prairies (I combined them as the samples were just too small), the Liberals are the consensus second choice for New Democrats, while Liberals are more likely to go to the NDP as their second choice than they are in British Columbia.
Things break down a little more normally in Ontario, with Conservatives choosing the Liberals second, the NDP third, and the Greens fourth. New Democrats choose the Liberals second, the Greens third, and then split their ballot on their fourth choice.

Liberals are a little more mixed, giving the NDP their second choice and the Greens their fourth, but splitting between the three parties on the third ballot.
Quebec has the most interesting result. Conservatives split between the Liberals and NDP, and very few go over to the Bloc. The Liberals split between the NDP and Conservatives, and very few go to the Bloc.

For the New Democrats, though, more than two-thirds list the Bloc Québécois as their second or third choice. Another large portion go over to the Liberals as their second choice and the Greens as their third, but the Bloc only really has room for growth down ballot from NDP supporters. The problem with that is that in most ridings the race is between the NDP and the Bloc.

The Bloc goes over to the NDP in massive numbers. It is interesting to note that only 2% of Bloc voters list the Liberals as their second choice - though that grows considerably for the third and fourth rankings. They are also the party least likely to rank one of the three fringe parties among their top four.
I include Atlantic Canada in order to complete the region-by-region breakdown, but the samples are very small. Nevertheless, their is nothing too unusual in the results despite the small number of respondents.

In terms of seats, I used the first choices to distribute support across ridings as I would do with a normal poll.

In a number of seats, a candidate has majority support right off the bat. In total, the Conservatives win 60 seats before the instant run-off begins (27 in Alberta, 15 on the Prairies, 13 in Ontario, and five in B.C.). The New Democrats have majorities in 23 seats (14 in Ontario, three in B.C., two each in Quebec and Atlantic Canada, and one each in Alberta and the Priaires), while the Liberals have 11 majorities (six in Atlantic Canada, three in Quebec, and one each in B.C. and the Prairies). The Greens also win a majority in Elizabeth May's riding with first choice support.
This chart shows the number of ridings in which each party leads with first choice support only. The Green leads in Atlantic Canada and the North are just a statistical fluke of the poll. You can see that these results are relatively standard, based on what other polls have been showing.

But the results are radically different once the preferential ballots are distributed to give each riding an MP with majority support.
The Conservatives lose one seat in the north, two each in Atlantic Canada and British Columbia, six in the Prairies (all the seats in which they led but did not have a majority), and 16 in Ontario. The Liberals lose one seat in Quebec in which they led on first choice ballots, while the NDP loses two (both in Ontario). The Bloc loses all four, while the Greens lose the one in the north.

That means that the NDP comes from behind to win one seat in British Columbia, four on the Prairies, seven in Quebec, and eight in Ontario. The Liberals win one seat each in British Columbia and Quebec, two each on the Prairies, in Atlantic Canada, and the north, and 10 in Ontario in which they trailed on first choice balloting. That is a huge and important difference, and is primarily due to the inability for the Conservatives to grow after the first choice ballots are counted. In many cases, they lose ridings in which 40% to even 42% listed the Tories as their first choice.

Small parties are rarely included in polls, so it is interesting to see what happens when they are added to the pile. It didn't change much, though. Only 1% listed Christian Heritage as their first choice, 0.9% listed the Libertarians, and 0.7% listed the Pirate Party. These parties never run full slates, so even these levels of support would be hard to achieve.

But which fringe party found the most favour with supporters of each of the main parties? Christian Heritage was the most preferred fringe party of Conservatives, with 11% of them ranking the CHP as either their second, third, or fourth choice. The Libertarians were the most popular choice of Liberals, with 7% listing them in the top four (it may have to do with the similarity in their names). The Pirate Party was the favourite of the Bloc (7% listed it in their top four), the NDP (9%), and the Greens (14%).

Overall, 30% of the ranking slots in the top four on Green ballots were occupied by one of the three fringe parties. Conservative supporters reserved 24% of their slots for these parties, while that dropped to 18% among New Democrats, 16% among Liberals, and only 12% for the Bloc. It is perhaps not too surprising that supporters of the Greens, the fringiest of the main parties, are most likely to consider the other parties highly. For the Conservatives, it may have been a proxy "none of the above" response.

An interesting poll to say the least.


  1. Replies
    1. Thanks! I was like a kid on Christmas when I got the poll results.

  2. If we go into the expense and trouble of updating our ancient electoral system, we might as well do it right, in line with the majority of advanced democracies (mixed form of proportional representation), so we don't have to revisit it again in the near future. To me, AV is simply putting a lipstick on a pig. It may change numbers somewhat, but it is still far from true proportionality, and can result in very distorted representation.

    1. What, praytell, is the advantage of "true proportionality"?

    2. The advantage is in getting closer to representing the voices of all citizens - rather than by vague approximation (or worse).

    3. It increases the degree to which government reflects voters' preferences, and decreases the degree to which our parliament is polarized along regional lines.

    4. It also increase the likelihood that one issue parties will get their way on policies that the majority of the population finds reprehensible as long as they care more about those issues than the other parties and are willing to bargain them against other things - see pro-colonies parties in Israel and anti-immigrant parties in several European countries. AV is my favorite voting system and I really hope we wind up with it.

    5. The Instant Run-off Ballot voting system is NOT "lipstick on a pig"! In fact, I think it is the only type of voting reform that has a chance of passing a referendum in this country.

      Consider its benefits:
      -very simple to understand and explain
      -already used by political parties to select their leaders, so it already has a proven track record
      -no need to redraw electoral boundaries
      -no more "wasted votes"; it has many of the benefits of proportional representation without the drawbacks that have been made against it by its local critics

      Ever watched that segment on CBC in which Rex Murphy defended our first-past-the-post system against proposed proportional representation systems? He complained that PR gave fringe parties too much influence, but more importantly in his view, that it would sever the connection of MPs to being accountable to their geographical communities. You have to realize that we have no concept of this in the big cities, but in many parts of the country geography and local representation really is important. An instant run-off ballot is the only type of voting system that keeps our MP system essentially unchanged - the only difference being that WITHIN each riding, the maximum possible amount of people will be happy with the result.
      And that is something worth fighting for. It's a deceptively simple change that I think will cause a huge ripple effect in the way our politics work. People will stop thinking that their votes are wasted. Supporters of smaller parties will not be afraid to show up and vote for them, and bigger parties will reach out to those voters - yet parties which are vociferously opposed by a majority (whether the parties are big or small) will not be able to get seats.

      We will get more honest voting and a more honest final result.

    6. "It also increase the likelihood that one issue parties will get their way on policies that the majority of the population finds reprehensible as long as they care more about those issues"

      Diagram - care to point to an example of this actually happening. Because it doesn't. The most recent Dutch election is a good example of why - a minor party made extreme demands and the government told them to stuff it. That minor party got decimated in the election.

      When small parties do play king-maker, they're invariable of the more moderate inclination. A good example is the Swedish People's Party in Finland. They've spend almost all of the last 50 years participating in government. They're a single issue party - all that they ask for is that the Swedish speaking minority in Finland's rights are respected. Hardly the stuff nightmares are made of.

    7. "An instant run-off ballot is the only type of voting system that keeps our MP system essentially unchanged - the only difference being that WITHIN each riding, the maximum possible amount of people will be happy with the result."

      Neither STV nor open-list MMP substantially change our parliamentary system. A 5 member STV riding leaves a minimum of 83% of voters with an MP they voted for. IRV in a single riding leaves that number at 50%. Hardly the maximum. Granted, in large swaths of Canada the population is too low for such ridings. In urban and suburban areas though, there's no reason to not have constituencies with as many as 7 MPs.

      Both open-list MMP and STV leave MPs directly accountable to voters and their geographic constituencies.

      "Supporters of smaller parties will not be afraid to show up and vote for them, and bigger parties will reach out to those voters - yet parties which are vociferously opposed by a majority (whether the parties are big or small) will not be able to get seats."

      The Australian Democrats were a party that took over 10% of the vote nationally yet were unable to win a single seat. IRV doesn't just present barriers to fringe parties - it presents barriers to decent sized moderate parties too. It's only advantageous to the two largest parties, and I'd prefer not to get stuck with the two party system of the US or the two-block system of France and Australia.

      "-no more "wasted votes"; it has many of the benefits of proportional representation without the drawbacks that have been made against it by its local critics"

      Around 55% of votes are wasted under FPTP. IRV leaves that number at closer to 45%. An improvement, but not much of one.

      Meanwhile, the NDP and Liberals are left with no reason to campaign to rural Albertans, and the Conservatives have even fewer reasons to campaign to Quebeckers, as the barriers to electing Conservative MPs are only higher in IRV. Our politics are divided enough along regional parties as is.

  3. Either way, present system or preferential, if BC votes NDP or Liberal (doubtful because of name confusion with the con lieberals out here), and not con, then harper is hooped and the tail will finally have wagged the dog.

  4. Great analysis and an excellent site! That second preference vote for CPC supporters in Quebec really surprises me. I didn't expect to see so much NDP support. Again, great job and I will be visiting this site daily!!!

  5. About rank stopping - in Australia AV implementation for House of Representatives forces voters to select all parties.

    1. Interesting! Thanks. All of the talk I've heard about AV in Canada, though, includes the ability to not rank some of the parties.

    2. So much better not to have to select all parties - that is just wrong in principle.

      Very interesting poll/projection/analysis!

  6. About ranking - Australian AV implementation for lower house forces voters to rank all parties. This could be a case in Canada if AV would be chosen as electoral system.

    1. They also have mandatory voting though. I agree that it's possible, but I don't think it's the most likely case.

    2. Correct me if I'm wrong here Eric, it seems like you didn't account for "exhausted" ballots at the end of the day, right?

      So this would be an overestimate of how seats would flip if that's the case. Have you thought of re-running the analysis with some sort of estimate of how many voters wouldn't rank anyone second? In the EKOS poll 25% of Greens, 21% of Bloc supporters, 17% of NDPers and 16% of Liberals had no second choice. With so many marginal seats, I'm sure that difference would add up. I don't think it would be unreasonable to assume that carries over for further rounds too.

      It might bring things more in line with how AV performed in Manitoba (where it was used for IIRC ~30 years) and Australia. In Manitoba lower preferences flipped seats ~2% of the time. In Australia on average lower preferences flip seats around ~6% of the time.

      Another confounding issue could be how uniform these preferences are when you drill down to the constituency level. Are Liberals more like to rank Conservatives second in Conservative held ridings? Or is it the reverse? How much do strong candidates skew lower preference support? If high second preference support correlates with high first preference support at a riding level, then far fewer seats will flip from preferences than a model that assumes uniformity would suggest.

      Now, estimating how much that correlation affects things... that's tougher. Perhaps a logistic regression to see how second preferences correlate with first preferences regionally?

      Also, do you have a regional breakdown of these seat totals Eric?

      The biggest concern I have with AV/IRV is that often makes legislatures more polarized along regional lines. I'd be interested to know that compares under your analysis. Under AV, would the Conservative caucus be more concentrated in the West? Would the Liberal caucus be more concentrated in Toronto, Montreal and Atlantic Canada? Would the NDP caucus be more concentrated in Quebec? Would AV increase or decrease the likelihood of a Liberal majority government with no seats in the West (or no seats in Alberta, or in BC, or in Saskatchewan, individually or together)? Would AV increase or decrease the likelihood of a Conservative majority with no seats in Quebec? Or no seats in multiple Atlantic provinces?

      Not easy questions to answer I know. It would probably take a pretty sophisticated sensitivity analysis to know for sure. If there's a rough idea from what you have though, I'd love to know.

    3. And that wasn't meant to be a reply. Oops.

    4. There are regional breakdowns in the post above. As to "exhausted" ballots, as mentioned the poll did not give people the option so I didn't take it into account. I assumed mandatory ranking for all parties.

    5. Oops. Missed those breakdowns.

      Yah, on exhausted ballots, my question was more how much of a difference would that make if you assume they are exhausted at the rate described in the EKOS poll.

  7. Have to wonder if these results would hold if the voter was actually confronted with a preferential ballot.

  8. I said before that I'd kill for this data. Hopefully no one holds me to that. :/

    1. Are you like the guy in Game of Thrones? I have three names for you.

    2. Is one of the names my own?

  9. Does your analysis account for third preferences?
    For example, if the NDP were eliminated in any particular riding it's second preferences would largely split between the Greens and the Liberals. But the Greens are likely to be eliminated before the NDP so would not gain NDP second preferences.
    Intuitively NDP/Green votes would favor the Liberals as their third preference.
    Have you (or can you) calculate for third preferences?

    1. Yes, it accounts for third and even fourth preferences. Based on the poll's data, I calculated how the ballots would be distributed each time a candidate dropped off.

  10. Ranked ballots, this is so exciting!

    Can you look at who the winner would be under a Condorcet voting system (Simpson-Kramer, for example)?

    1. I agree totally, It would be interesting to see if this would play out the same as the 2009 Burlington mayoral election, where the Plurality, IRV, and pair wise condorcet winners were three different people.

  11. What would be the Atlantic Green riding even thought it was probably a fluke?

    Great article by the way

  12. Awesome work. This is probably the most interesting analysis of voter preference and alternate voting schemes I've read. Big thanks to Abacus for providing you the data.

  13. I find this so ironic as I was just talking about this exact topic yesterday, trying to make sense of what a STV would look like across the country. Brilliant!

    1. This is only for single member ridings though. Traditionally in STV you'd have 2 to 6 member ridings.

    2. I'd love to know how that would effect Green representation. Generally speaking I am inclined to suggest STV is best served at the municipal level.

  14. By the way Eric, I noticed that former BC Liberal MLA Judi Tyabji is missing from Joyce Murray's list of endorsers. I can't find a formal announcement of her support, but a quick Google of "Judi Tyabji Joyce Murray" makes things pretty clear.

  15. Could you reanalyze this data, to predict a winner using one of the many variants of Condorcet (Pair-wise)?

    It uses identical ballots to IRV so it should possible to perform the calculation again assuming you have the preferences for individual respondents.

    The calculations are more complex, but can easily be accomplished with any spreadsheet program.

    I would suspect you might find a third winner if you calculated results using that method...:)

    But you might also like to see how many ridings would not have any clear pairwise winner, and thus would have to go to one of the many "tie breakers".
    Presumably >95 ridings would have a pairwise winner.


  16. This is very fascinating. I'm a proponent of proportional representation, but lately I have been giving IRV a second look. Great analysis.

  17. If there were a STV system I would expect the second preferences to be more one-sided than this poll suggests.

    Such a system would encourage alliances between parties like in Australia where preferences are routinely recommended. There,for example, the Green party is able to deliver the great majority of its second preferences to Labor.

    If Liberal voters knew that their party was in an alliance with the NDP we can expect that they would be more comfortable giving their second votes to the NDP and vice versa.

    1. That's the danger if it's in single member ridings though. The Liberals and NDP cozy up to each other, and pretty soon we have a two-party system like in Australia.

  18. I think your Quebec seat projections are wrong. You project NDP 58, Lib 12, Con 6 and BQ 4.I assume this is on the new boundaries, which Pollmaps calculates , using the 2011 election results, as N 60, L 8, C 6 , B 4.
    It seems impossible that STV would reduce the NDP total given the Forum second preferences in every case gives the NDP has higher numbers than the other parties except the Conservative vote would split evenly with the Liberals. The Liberals break 54 N 40 C and 7 B. The Cons break 40 N 40 L and 10 B. And the Bloq breaks N 61 (!) L 2 and C 14.
    You don't give figures for the Green preferences but intuitively they would also be heavily NDP.
    Without doing precise calculations it seems to me that STV would greatly benefit the NDP in Quebec.
    They would gain all four of the Bloq seats (Richilieu, Gaspesie, Avignon-Matane and Richmond-Arthabaca. They would gain Levis- Lotbiniere and Montmagny from the Conservatives and likely Bellechasse-Levis and Lac St Jean. The NDP would gain Ahuntsic, Bourassa and Papineau from the Liberals and maybe NDG-Westmount.
    The Quebec totals would then be: NDP 69 to 72, Liberals 4 to 5, Conservatives 2 to 4.
    Perhaps you can share your detailed riding projections for Quebec with us in odrer to clear this up.

    1. I did not use 2011 as the basis from which to assign second choice, but the first choice results of the poll. In Quebec, the NDP had less than 43% first choice support in the poll, which means they lost seats.

  19. Alternate Voting can be as bad or worse than First-past-the-post at reflecting voter intention. For examply:

    Round 1:
    - Pro-dog party gets 44%
    - Moderate anti-dog party gets 20%
    - Extreme anti-dog party gets 36%

    Under this scenario, Moderate Anti-dog has to drop out. 3/4 of Moderate Anti-dog's voter 2nd choices are for Extreme Anti-dog, so:

    Round 2:
    Pro-Dog: 49%
    Extreme Anti-Dog: 51%

    Note, however, that nearly all Pro-dog supporters have Moderate Anti-dog as second choice, as they can't stand Extreme Anti-dog.

    In a run-off between Moderate and Extreme Anti-dog, Moderate Anti-dog would win easily (65%-35%). But AV never considers this possibility and elects Extreme Anti-Dog, which is neither the most popular 1st choice nor the most popular 2nd choice.

  20. I am starting to consider your website is paying paid by the conservative..... A new poll this weekend suggest the Liberal are in advance and a huge drop for the conservatives. But you are not talking about it. The only polls you show are the one good for the conservatives. Why is that?

  21. I am late to the party on this article, but, thanks to Google, time is no object!, though one wonders whether this late in the game if I might be speaking to a vanished audience.

    In any case...

    This is indeed an interesting analysis. But it errs in taking the notion of a "Preferential Ballot" strictly in terms of an Alternative Vote (AV), aka Instant Runoff Vote (IRV) ballot. There are many forms of preferential ballot.

    While AV / IRV, despite that it retains some of the flaws of first past the post, and fails to take account of all preferences, it is still better than first past the post (FPTP). If that's the best we can achieve, let's have at it.

    But we can easily do better, without resorting to MR or PR solutions, which typically arise at this point in the conversation.

    I have done some work in this area, and have prepared a proposal (specifically referring to BC in terms of election data and pro-forma legislation, but the approach is fully applicable to other provinces, and indeed for federal elections as well).

    This method is called ”Ranked Pairs” — There is a summary here:,

    … as well as links to a pdf that portrays the approach in additional detail, and a link to a Java (jar) that implements a ”workbench” with which people can submit their own sets of balltot data and compare the Ranked-Pairs outcomes vs IRV and FPTP.

    I believe this should be on the table in any discussion about electoral reform, and would appreciate any feedback, whether here or on the FB page associated with this proposal.

  22. Is any similar data available at the provincial level for Ontario?


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