This is a long post concerning Bill C-12, which changes the formula for allocating seats for future elections.

Part I - General discussion

Part II - Analysis of the bill

Part III - Estimates of seats after the next redistribution (these are likely to be more accurate than the government's, for reasons explained in bold in Part I)

Part IV - Likely electoral impact

Part I

Here is the text of Bill C-12. There are two changes with respect to the previous Tory proposal, which I analyzed here:

1. The size of districts in ON, BC and AB is no longer be the population of Québec divided by 75. Rather, it is set at 108,000 for the coming redistribution, and increases according to the rate of increase of the 10-province population for subsequent redistributions.

2. The seat numbers for ON, BC and AB (for the coming redistribution, population divided by 108,000) are rounded up, rather than to the closest integer. So 108,000 is the maximum district size.

How many seats would this law give to ON, BC and AB? CBC and most media, citing a government press release, say 124 (+18), 43 (+7) and 33 (+5) respectively (and usually without any acknowledgment of the underlying uncertainty). These estimates are based on the most recent population projections by Statistics Canada. Unfortunately, those projections are outdated (based on July 2005 population estimates), and correct for census undercounting (which we do not want to adjust for in this case, since raw census numbers are used for redistribution). Hence, the numbers above are inaccurate. I believe that those estimates are too high for ON and BC, and too low for Alberta, and outline my calculations in Part III.

Part II

Before going into the nitty-gritty of estimates, let me analyze the broad impacts of this law, as well as compare it to the previous version, and to my proposal:

1. It gives ON, BC and AB fewer seats than the previous Tory proposal, which would have given those three provinces representation in proportion to Québec's. This is because Québec's population in Census 2011 will likely be around 7.8 million, which is lower than 75*108,000 = 8.1 million. Thus, Québec will remain overrepresented with respect to ON, BC and AB.

2. However, it still gives those provinces more seats than under my proposal, which would have given Québec representation in accordance to its demographic weight in Canada. In order for Québec to be proportionately represented with 75 seats, the House size would have to be around 323 seats. Under current law, it is likely to be about 315 after the next redistribution; under C-12, it will likely be around 335. Thus, C-12 makes Québec go from being overrepresented to underrepresented with respect to the rest of Canada.

3. Assuming that Québec grows more slowly than Canada as a whole (not true lately due to the Ontario-concentrated recession, but likely to be true in the long run), the rate of growth of the size of the House is lowest under current law, higher under my proposal, and highest under the old Tory proposal. Under C-12, the rate of growth will be similar to the one under current law. Thus, while C-12 will increase the size of the House significantly in the next redistribution, it will lead to small increases in subsequent ones. This means that C-12 is a one-time patch, and in the long run:

a) AB, BC and ON will resume losing relative representation as fast as they do now if their population growth keeps outstripping the national average;

b) Québec will eventually once again become overrepresented if its growth stays below the Canadian average.

Point 3 is the major factor distinguishing C-12 from old Tory proposals. Point 3 is also why I still favour my own idea: it should be reasonably durable by slowing the rise of representational inequality (unlike current law and C-12), while not resulting in an exploding size of the House (unlike the old Tory proposal).

Part III

Now, let me discuss why I think C-12 would increase the size of the House by about 27 instead of the widely reported figure of 30. First, let's look at the number of seats C-12 implies, based on the most recent population estimates, which are for Jan. 1, 2010:

ON - 122 (121.6)

BC - 42 (41.6)

AB - 35 (34.4) (remember the rounding up rule under C-12)

The intuitive thing to do next would be to add 1-2% to each of these numbers in order to account for the likely population growth between now and the next census, in May 2011. That would bring us to 123-124 for ON, 43 for BC, and 35-36 for AB. However, as explained above, population estimates adjust for census undercounting, while the redistribution of seats does not. Thus, figures above should also be reduced for expected undercounting. By how much? Well, across Canada, the May 2006 census count was 2.7% lower than the April 2006 population estimate. Doing that adjustment brings us to the following numbers:

Projected Seats Under Bill C-12

ON - 120-121 (+14 or +15, 3 or 4 fewer than the government projection)

BC - 42 (+6, 1 fewer)

AB - 34-35 (+6 or +7, 1 or 2 more)

Canada - 334-336 (+26 to +28, 2 to 4 fewer)

The above numbers have a fair degree of uncertainty: the 2.7% undercount in 2006 was actually 4.2% in BC, but just 1.3% in AB. However, regional variations are likely due to inaccurate April 2006 population estimates rather than the census actually missing 3 times more people in BC than in Alberta. That's why I applied a uniform 2.7% rate, since it's anyone's guess in which direction the January 2010 estimates are biased.

Also, I cannot help but notice that it's politically convenient for the government to cite lower gains for Alberta and higher ones for Ontario. While it can defend itself for using 2005 population projections because those are the latest official ones, it certainly knows that the actual calculations will give fewer seats to Ontario and more to Alberta than announced.

By the way, under current law, I get the following:

ON - 108-109 (+2 or +3)

BC - 37-38 (+1 or +2)

AB - 31 (+3)

(The government's estimates are 110, 38 and 29.)

The government projects that Ontario would get 14 more seats under C-12 than under current law, BC 5 and AB 4. My calculations suggest that the actual numbers are about 12, 4-5 and 3-4. So viewed this way, the government is maybe not deliberately using a suboptimal methodology after all.

Just for fun, my proposal would give:

ON - 113-114

BC - 39

AB - 32-33

Part IV

Finally, let's look at the likely electoral effects of Bill C-12, relative to current law.

In a tight election between the Liberals and the Conservatives, the 12 extra Ontario seats would probably go 7L, 4C and 1NDP; the 4-5 extra in BC might go 2C, 1L and 1NDP; the 3-4 in AB would likely all go Tory. On the whole, the 20 seats split roughly 10C, 8L and 2NDP, so the Tories gain a small edge over the Liberals.

However, in an election like 2008 where the Conservatives are strong, and the Liberals weak, the splits of the extra seats would be something like 6C, 4L and 2NDP in ON; 3C, 1-2NDP and 1L in BC. Then you'd get 12-13C, 5L and 3-4NDP in the aggregate. Thus, C-12 facilitates the formation of a Conservative majority government.

What about an election where the Liberals are strong enough to flirt with a majority? The splits might then be 9L, 2C and 1NDP in ON; 2C, 1-2L and 1NDP in BC; 3C and 0-1L in AB. That's 11L, 7C and 2NDP. Thus, C-12 marginally facilitates the formation of a Liberal majority government.

Obviously, the reason why a majority is made easier for both parties is the decreased weight of Québec.

It'll be interesting to see what emerges in the end.

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