#Elxn41, under a different electoral system

Okay, so we all survived Election 41.  We have a Harper Conservative majority that got just under 40% of the popular vote.  Everyone’s shocked and horrified.  But this isn’t a surprise. This is how our system, as currently structured, works.  We elect one Member of Parliament (MP) for each of 308 ridings, which are not evenly distributed (for example, the largest riding of Oak Ridges-Markham is 6.43X larger than the smallest of Labrador), and we use a first-past-the-post system.

During the election, I posted a probably far-too-lengthy post on electoral reform.  In it, I suggested a few things that Canada’s could adapt from Australia:

Without extensive poll-by-poll research, or detailed polls of people who didn’t vote, I can’t in any way quantify the first or last things.  But I want to demonstrate the difference in results under the other two suggestions.

First, the upper house, the Senate.  This is currently appointed, and my proposal is to have a Senate elected proportionally, allowing for a certain number of seats per province (to recognise the fact that we are a federation of former colonies, and must come to consensus on issues of national importance).  My proposal is based on Australia, where each state has an equal number of seats – due to Canada’s history and population, this would not work.  I will accept that, say, provinces like PEI should not have as many seats as Ontario.  I’m going to make the simplifying assumption that we’d use the same allocations as are currently in the Senate, just to keep with our constitution.  That would make 6 seats for each of Alberta, BC, Manitoba, Saskatchewan, and Newfoundland and Labrador, 10 for each of New Brunswick and Nova Scotia, 4 for PEI, 24 for each of Ontario and Quebec, and 1 for each of the 3 territories.  Again, keep in mind that these are the currently-agreed-upon seat distributions in our constitution; changing these would require all the provinces to agree.  I’d advocate for a slightly less-disproportional allocation, but let’s just work with what we’ve got for this example.

I’m also making the simplified assumption that preferencing won’t change the result in the provinces, which would likely hold roughly true.  For NWT and Nunavut the wins were in the high-40s so even with preferencing I’ve assumed they would elect the same senator. In the Yukon, the CPC won by < 1% over the LPC, so I’ve applied the same formula discussed below for determining preferences.

This would play out as follows:

Party Seats – Current Senate % of total Seats – Proportional-by-province Senate (1) % of total National popular vote
Bloc Quebecois 0 0.0% 6 5.71% 6.0%
Conservative Party 52 49.5% 42 40.00% 39.6%
Green Party 0 0.0% 2 1.90% 3.9%
Liberal Party 46 43.8% 23 21.9% 18.9%
New Democratic party 0 0.0% 32 30.48% 30.6%
Progressive Conservative 2 1.9% 0 0.0% 0.0%
Independent 2 1.9% 0 0.0% 0.4%
Vacant 3 2.9% 0 0.0% N/A

(1)    Based on election results as at 10AM EDT (Canada), May 3rd, 2011.  At this stage 71,486 of 71,513 polls had reported so I’ll take this as a good approximation.  Calculations are here (opens in Excel)

This calculation is a bit crude, but it illustrates the point.  For most provinces, I simply applied a percentage formula and rounded to the nearest seat.  For certain provinces this didn’t lead to the right amount of seats, so there are a few notes:

  • Based on simple rounding, NB only got 9 of its 10 seats, so I’ve added one to the Conservatives as they were within1.2% of the popular vote of getting that extra seat (the others were not as close)
  • PEI would have had one extra seat basic entirely on basic rounding – so I’ve applied the actual Australian rule of “to win a seat you need (1/(1+number of available seats) = 20% in PEI) of the vote”- which gives the LPC and CPC each 2 seats and the NDP none.
  • I’ve given NWT and Nunavut to the leading parties, as mentioned
  • To demonstrate preferencing, I’ve shown this for the Yukon, which was a simply four-party example.  This gave the seat to the Liberals (where they lost the lower house seat under FPTP).

While this calculation isn’t perfect, and while the results don’t perfectly match the popular vote nationally, we’re a LOT closer than the current system.

Now, on to the house.  This’ll be fun.  My proposal is a simple preferential voting system.  This means that voters can rank the candidates in order from best to worst.  If after the first vote, one candidate has 50%, they win. If not, the lowest candidate is dropped, their votes reallocated, and the process repeats.

Keeping the same ridings, and the results of the election that just passed, I’ve applied the following assumptions:

  • In the event of needing to reallocate votes for the CPC, NDP, LPC, GP, or BQ, votes have been allocated proportionally based on the last Ekos poll in which voters were asked for their second choice (page .  It is assumed that voters’ third choice is the second choice of people who would’ve voted for their second choice.  This is obviously a simplifying assumption but without better data it’ll have to do.  In non-Quebec provinces I’ve pro-rated the distribution to reflect peoples’ choices without the BQ.
  • In the event of needing to reallocate the other parties, I’m making broad assumptions here about voters’ preferences, as follows:
    • Animal Alliance/Environment Voters – Green
    • CAP (Canadian Action party) – NDP (they’re somewhere between NDP and Green, based on their website, I’m throwing this to NDP based on relative popularity)
    • CHP Canada (Christian Heritage party) – Conservative
    • Communist – NDP
    • FPNP – Green
    • Independent and No Affiliation (these mean the same thing) – based on the “Other” Second Choice distribution in the Ekos Poll since there’s not enough information to allocate these votes
    • Libertarian – Conservative
    • Marxist-Leninist – NDP
    • PC Party – Conservative
    • Pirate Party – NDP
    • Radical Marijuana – Green
    • Rhinoceros – since this is a joke party, in Quebec I’m allocating them to the BQ, in BC I’m dropping their votes altogether on the assumption anyone voting for them wouldn’t actually want to vote for the others (and thus wouldn’t preference)
    • United Party – Green (their policies page says “fiscally responsible, socially progressive, environmental sustainable” which are the exact words Green Party leader Elizabeth May uses all the time)
    • WBP (Western Block Party) – Conservative
    • Where parties receive a trivial portion of the vote (1% or less in the riding), unless the result is really close, I’m simplifying by eliminating them all at once (i.e., if there are 8 candidates, I’m eliminating the bottom 4 at once instead of in sequence which is how the votes would normally be allocated).
    • For the second choice allocations from the Ekos poll, second choice of “other” is being disregarded, on the assumption that these would eventually make their way to the same allocation as if they hadn’t selected “other.”   The only exception to this is ridings where there was an independent – in these cases the independent was allocated the “other” votes if they survived the first round.

I’ve plugged this all into a giant spreadsheet, using Elections Canada’s “Preliminary” data because not all ridings have “validated” data – and the differences on the ones that do are generally not material.  This took FAR too much time as I pretty well had to do it manually by riding.  I’m sure there was a more efficient way of doing this but it’s too late now J

After all of this insanity (it’s seriously 4:30 AM here but the nerd in me couldn’t put it away!), these are the results if we have preferential / instant-runoff voting:

Party Seats – Current House % of total Seats – using preferential voting % of total National popular vote
Bloc Quebecois 4 1.3% 1 0.32% 6.0%
Conservative Party 167 54.2% 144 46.75% 39.6%
Green Party 1 0.3% 1 0.32% 3.9%
Liberal Party 34 11.0% 46 14.94% 18.9%
New Democratic party 102 33.1% 116 37.66% 30.6%

Interestingly, I set out to prove that this would work out a little bit more proportional – it turns out it’s closer to proportional than the existing system, but not by much.  The bigger advantage, though, is that the MPs elected better represent the communities that elect them, so people get their second or third preferred choice.

The detailed riding data, along with the poll data I used to calculate this, showed that a lot of our conceptions about strategic voting are flawed – people try to convince people to vote strategically on the grounds that if all supporters of one party would support another, that other party would win.  We can see that not all supporters of any party are willing to support another across the board – while taking people’s second choices does change some of the seats (and prevents a majority government elected by 40% of the population, here), it doesn’t swing drastically (except in the case of the NDP… everyone’s second choice!)

I’m sure I’ll have more insight on this when I’m more awake… feel free to play with the data!


7 responses to this post.

  1. Props to Greg for beating me to publishing the Senate proposal (great minds think alike!) http://www.gregburrell.ca/archives/1311

    And also to Dave Meslin for always being an advocate for improvements! http://meslin.wordpress.com/2011/05/02/beyond_band-aids/


  2. Posted by Charles in Vancouver on 2011/05/05 at 4:51 am

    Thanks as always for your delightful ability to geek out on numbers and reach useful conclusions! Looking forward to seeing you in East Van where a true majority elected our MP 🙂


  3. […] opinions than I expected. At the same time, fellow accountant/blogger Neal Jennings was writing his own post on Senate reform. Although we worked independently and used different methods, we came up with exactly the same […]


  4. […] electoral and legislative systems.  I then took it a step further after the election and calculated the allocation of seats if we had used an Australian-style system (and keeping the allocation of provincial Senate seats in […]


  5. […] election, despite being many time zones away!  There was even one almost-sleepless night writing this blog entry that no one read.  I also got to catch up with the Canadian Australian Club again, as well as […]


  6. […] because we’re spread out, the various failures in our voting system that allow people to get elected with far less than 50% of the vote in a constituency mean our votes consistently don’t matter […]


  7. Posted by Louis B on 2017/07/18 at 11:57 pm

    Would your model allow for the Leader of the party to nominate the Senators to the allocated spots elected or have a list from voters to choose?
    I think if parties wanted greater political involvement, they could entice future members to join in the chance of becoming or selecting a Senator. That is the Liberal Party is allocated 50 Senate spots, each provincial branch would then nominate, respective of the seats assigned, the candidates they wish to fill the vacancies from a pool of nominees.


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