Deviation from Proportionality in the 2011 Election

So once again Canada finds itself with a majoirty government elected by a distincly non-majority number of voters. We`ve been here before, of course, but being here again merely serves to remind us of the degree to which our electoral system produces disproportionality.

The simplest way to calculate deviation from proportionality is to take, for each party, the difference between total percent of votes and total percent of seats. Then you add the differences together and divide by two.

For 2011, this gives us a number of 0.17. This compares unfavourably with 0.14 for 2008, 0.13 for 2006 and 0.14 for 2004, and matched the 0.17 of 2000 exactly, suggesting of course that a minority government is likely to be more proportional than a majority. But let's face it - these numbers are pretty similar.

And pretty deceptive, too, as it turns out. 2011 is unique not only in being the first federal election perhaps ever where the NDP have actually gotten a higher percentage of seats than votes but also being the first election in which the BQ didn't, and the first in as far back as I care to look when the Liberals didn't. Seeing the Liberals on the losing end of FPTP disproportionality is a real shock.

The thing is, though, that this not-bad 0.17 number is largely a question of luck. When the same quotient is calculated for each province, it turns out that the federal total is more proportional than the results for every province except two. How is that even possible? Well, it's largely an accidental balance of disproportionalities: the NDP get a disproportionately high number of seats in Québec and the Conservatives a disproportionately low number, but these values are inverted for most of the rest of the country, so there's a kind of correction happening. Said differently, the 30.6% of the vote that went NDP and the 33.4% of the seats that did may seem quite similar, but they're located in very different parts of the country.

Party-by-party, the disproportionality looks like this:

• The Conservatives got 14.3% more seats than votes.
• The NDP got 2.8% more seats than votes.
• The Liberals got 7.9% fewer seats than votes.
• The BQ got 4.7% fewer seats than votes.
• The Green Party got 3.6% fewer seats than votes.

 I realise I haven't really worded that properly: the difference in percentage points between the percent of votes that the Conservatives got nationwide and the percentage of seats that they got nationwide is 14.3. For the BQ in particular, that masks the overall difference, since they didn't run in what is effectively the vast majority of ridings. For that, we need to look at the results by province, from best to worst:

1. Nova Scotia, with a DV score of 0.07. This is surprising, in that the party that came third in votes tied for first in seats: not a shining example of proportionality, really. But individual errors fail to hide the fact that Nova Scotia remains a roughly even three-way split, reflected both in their seat tallies and their overall votes, this time out.
2. British Columbia, with a DV of 0.13. It's not just that BC is the only place where the Greens got any seats at all - after all, the Greens' individual DV for BC was second-worst of all the provinces (since they got a higher overall share of votes). The NDP were remarkable here, with 33.3% of seats for 32.5% of the vote. The remaining deviation, as we'll see elsewhere, was the Conservatives getting seats at the Liberals' expense.
3. Newfoundland & Labrador, with a DV of 0.19. Already we're above the national average, but we ain't seen nothin' yet. Newfoundland bucked the national trend, giving the Liberals 37.9% of their vote and 57.1% of their seats. This is more or less the national trend inverted, as the Liberals benefit from the disproportionality to the Conservatives' expense. Though I doubt they're complaining about that too much.
4. Ontario, with a DV of 0.24. How quickly things are getting bad now: The seat count is 24.5% up on its overall vote, and the Liberals' is short by 14.9%. The NDP came closest to the mark than they tend to do in Ontario, but still this is an embarrassment. And it's still 'better than average'.
5. Manitoba, with a DV of 0.25. Similar to Ontario overall, but with a ten percent boost in both columns for the Conservatives: over half of the vote, over three-quarters of the seats. That difference of 25% was taken from the other three parties, each in rather painful amounts.
6. Alberta, with a DV of 0.29. It's a strange country where fully four provinces could do worse on proportionality than Alberta, where the Conservatives got 96.4% of the seats. That came from 66.8% of the vote, a number much lower than the first one but still amazingly high. The other one-third of the vote got a single seat out of the bargain.
7. Prince Edward Island, with a DV of 0.34. This should be the benchmark for disproportionality: the party that got 75% of the seats didn't even win the overall vote, getting fewer votes than the party that got the other 25% of seats. But its very size, and the fact that the whole province is merely four ridings, means its disproportionality tends to get overlooked. Plus, there are three provinces worse.
8. Québec, with a DV of 0.35, shows the phenomenon of the 'winner's bonus' in a FPTP system. Well, it pretty much always has: down the years, the party that 'wins' Québec wins big. After this paragraph is a list of the 'winner's bonus' given in Québec down the years to one of four different parties since 1980. This time, of course, it's the NDP who threw the numbers completely out of whack, with a seat count 35.8% higher than their vote percentage. All other parties suffered at the NDP's hands in Québec, worst of all the BQ, who walked away with a measly 5.3% of seats from 23.4% of the vote.
1. 1980: The Liberals win 98.7% of the seats with 68.2% of the vote.
2. 1984: The PCs win 77.3% of the seats with 50.2% of the vote.
3. 1988: The PCs win 84.0% of the seats with 52.7% of the vote.
4. 1993: The BQ win 72.0% of the seats with 49.3% of the vote.
5. 1997: The BQ win 58.7% of the seats with 37.9% of the vote (just 1.2% higher than the Liberals).
6. 2000 is the exception: the Liberals got 48.0% of the seats, fewer than the BQ, with 44.2% of the vote: indicating that the 'winner's bonus' decreases if the race is close.
7. 2004: The BQ win 72.0% of the seats with 48.9% of the vote.
8. 2006: The BQ win 68.0% of the seats with 42.1% of the vote.
9. 2008: The BQ win 65.3% of the seats with 38.1% of the vote.
10. 2011: The NDP win 78.7% of the seats with 42.9% of the vote.
9. New Brunswick, with a DV of 0.36. The phenomenon is similar in New Brunswick, where all but two ridings went to a party that got a mere 43.9% of the vote. The NDP and the Liberals polled at about their national average, but got a single seat apiece for their troubles.
10. Saskatchewan, with a DV of 0.37. Ah, Saskatchewan. I've written before about the ridings in Saskatchewan, which are set out in a strange fashion such that there is not a single 'urban riding' in the whole province: both Regina and Saskatoon are divided into four and stuck onto otherwise-rural ridings. What this means is that the NDP polled 32.3% in the province - effectively in a three-way tie with BC and Newfoundland for highest NDP vote outside of Québec - without managing a single seat - with a similar vote, the NDP carried a third of BC's seats. The Liberals got barely a quarter of the NDP's vote but walked away with a seat, while the Conservatives got 92.9% of the seats with 56.3% of the vote. Strange indeed.

The phenomenon effected each party differently, and while I haven't included the Greens and couldn't include the Bloc, I've put together three graphs to show how each party was effected. This graph shows the difference in percent - plus or minus - between number of seats and percentage of votes.A positive number means they were rewarded with more seats than their votes justified (looking at strict proportionality) and a negative number means they were punished with fewer. Let's look:

This is how the Conservatives won their majority. West of the Ottawa River, it's winner's bonus all the way down. BC does okay by comparison, but in the other provinces - and New Brunswick too - the Conservatives got seats well in excess of what their overall vote justified. Québec and Newfoundland, the only two provinces that voted for another party in larger numbers than they did for the Tories, balance the numbers a bit, and PEI is just an outlier here.

The Liberals have reaped the benefits of the winning-side of the FPTP system on many occasions in the past, but here the numbers hurt them in every province not an island or a peninsula. Only in Newfoundland, in PEI and to a smaller degree in Nova Scotia do the numbers look good for them.

Lastly, the NDP. Down the years the NDP has certainly suffered at the hands of FPTP, regularly getting fewer seats than they deserve. While this is the first time in perhaps ever that they've come away with a higher seat percentage than a vote percentage, we can see that that's all Québec's fault. A significant majority of the NDP's current MPs are from Québec, but this doesn't mean a majority of their voters are. In every province except Québec and BC, the NDP remain punished by FPTP - it just so happens that in one province this time out they were greatly rewarded by the same system. One does wonder what being on this side of the proportionality gap will do for the NDP's long-term commitment to electoral reform. We'll have to wait and see, I suppose.