Math-challenged Transposition of Population not up to usual Elections Canada standards
February 4th, 2014
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It's probably the last thing Chief Electoral Officer Marc Mayrand needs to hear right now, but the Transposition of Population his office released last Friday as part of the 2013 Redistribution does not add up.
Election data geeks – officially known as "psephologists" – have been exchanging emails, comparing notes on the reliability of the data, and wondering if it can be fixed.
But approaches to Elections Canada so far have proved fruitless.
At issue is the population being transferred from each of the old ridings to each of the new ridings. The population counts add up by new riding, but not by old riding. So for example 102.9% of the old riding of Avalon's population is allocated to new ridings, while only 98.1% of the old Brampton-Springdale's population is accounted for.
The errors are all within plus or minus 5%, but previous transpositions have always added up in both directions. This is not just academic – political parties need to have those percentages accurately, so that EDAs from out-going ridings can transfer their assets in the proper proportions to the new ridings. But, here, the outgoing Avalon EDAs would have to come up with extra money or extra surplus sign stakes, while the outgoing Brampton-Springdale EDAs would have money left over. The ratios are also used by psephologists and political scientists more generally to project results backwards and forwards.
The agency, in conjunction with a contact at Statistics Canada, decided to reproject population counts from old ridings to new ridings using ratios derived from the redistribution of elector counts from old to new. The first problem is: they used the wrong ratios. Viz: if a part of your old riding makes up 50% of my new riding, it does not necessarily follow that I am inheriting 50% of your old riding. I might be getting 75% of your riding, and 25% of another one, even though both chunks represent 50% each of my new one.
However, even using the correct ratios, the old riding populations add up but now the new ones are off. Meaning that populations don't redistribute between ridings in the same proportions as electors, and so the entire assumption behind this Transposition is not exactly iron-clad. This makes sense when we consider that different ridings have differing numbers of non-elector residents (i.e., people who are not yet citizens, or have not yet attained voting age).
By contrast, an exercise that calculated riding population transfers based on summing the population of the 2011 Census Dissemination Blocks contained within them – which must have been the previous methodology used by Elections Canada – was far more precise. I do not know why it wasn't used this time, but I fear budget cuts and/or the reduced timelines resulting from last year's amendments to the Electoral Boundaries Readjustment Act may be the culprit. The populations counts generated in earlier transpositions were always accurate in both directions, but now they are merely estimates. It is as though the Transposition of Population has gone the way of the long-form census.
[click image to open full-sized PDF version]
I give a demonstration of the errors using Brampton ridings here, but for those who are interested in greater detail, I've also reproduced the exchange I had with Elections Canada to try and point out the problem and/or get clarification on why the numbers were off.
Here's what I wrote to my contact at the agency's media relations service:
–> Look at the old Avalon (2003-10001), which is split up between:
* the new Avalon (2013-10001)
* the new Bonavista-Burin-Trinity (2013-10002), and
* the new St. John's South-Mount Pearl (2013-10007) ridings
and therefore those 3 riding files.
The old population of Avalon is correctly listed in all three files as 78,908, but gets allocated between the 3 new ridings as follows:
* 61,048 to 2013-10001
* 17,123 to 2013-10002
* 2,521 to 2013-10007
This adds up to 80,692 – a difference in allocated population of 1,784 (or 2.9%) !!! I cannot believe that such a magnitude of over-allocation is a mere rounding error.
There are numerous other examples of either over- or under-allocations of the old riding's population to its descendant ridings:
* old Brossard-La Prairie (2003-24011) is under-allocated by 2,432
* old Hull-Aylmer is under-allocated by 2,924
* old Mississauga-Brampton South (2003-35047) is over-allocated by 5,137, while Mississauga-East Cooksville (2003-35048) is under-allocated by 6,988
… And it continues in much the same manner right across the country.
Now, these mis-allocations of population all zero out across the country, but the errors are bigger than I've ever seen in your earlier Transpositions (± 5%).
And – note – the only major errors I see are for the transpositions of Population. The transpositions of Electors and Valid Ballots are all within ±2 at worst (not 2%, but 2 voters), and most are bang on. The transpositions of votes also add up to within tolerable tiny errors.
Which is what makes this truly weird, because your Methodology section says that the transposed population percentages were calculated using the same ratio as transposed electors. Yet the electors match, while the populations don't.
And here's the answer my contact received from the subject matter experts in the agency:
As described in section 3.7 of the document, the population counts for the old FEDs [ed. FED=Federal Electoral District] were published by Statistics Canada. The population counts for the new FEDs were derived by independent commissions in consultation with Statistics Canada and are based on the 2011 Census of Population. These are official counts that require no calculation. These old and new FED's population counts are used to derive the population transferred to the new FED or population taken from the old FED.
The population transferred to the new FED or population taken from the FED is derived using the ratio calculated from transposed electors on lists. This ratio is then multiplied by the population count of the new FED to obtain the population transferred to the new FED or population taken from the old FED.
In the case of Avalon (new FED), the calculations were as follow:
1) Electors on lists from section 4.3 tables
a. 48192 electors are transposed from old Avalon
b. 16176 electors are transposed from old St. John's East
a. Ratio for old Avalon=48192/(48192+16176)=0.748671
b. Ratio for old St. John's East=16176/(48192+16176)=0.251329
3) New FED's Population for Avalon: 81540
a. For old Avalon=0.748671*81540=61048
b. For old St. John's East=0.251329*81540=20492
If you were going to use ratios of electors from old to new ridings, here's how those calculations should have been done in my view, in order to faithfully represent what a transposition is supposed to do.
1) Electors on lists from section 4.3 tables
a. 48192 electors are transposed from old Avalon to new Avalon
c. 14200 electors are transposed from old Avalon to new Bonavista–Burin–Trinity
d. 2032 electors are transposed from old Avalon to new St. John’s South–Mount Pearl
b. 16176 electors are transposed from old St. John's East to new Avalon
e. 60248 electors are transposed from old St. John's East to new St. John's East
a. Ratio for old Avalon=48192/(48192+14200+2032)=0.748044
b. Ratio for old St. John's East=16176/(16176+60248)=0.211661
3) New FED's Population for Avalon: 81540 || old FED population for Avalon: 78908, for St. John's East: 100,559
a. For old Avalon=0.748044*78908=59027
b. For old St. John's East=0.211661*100559=21284
But, even there, that only adds up to 80,311, which is 1,229 short of the 81,540 census population calculated for Avalon by the Boundary Commission. So, now we know that population doesn't move between old and new ridings in the same proportion as electors. Hence, the Census Dissemination Block population method should have been used.
Using 2011 Census Dissemination Block populations, that we sum using GIS software and best guesses where the Dissemination Blocks crossed riding boundaries, we get the following counts:
* 59591 in population from old Avalon to new Avalon
* 16855 in population from old Avalon to new Bonavista–Burin–Trinity
* 2462 in population from old Avalon to new St. John’s South–Mount Pearl
(for an accurate old Avalon total population of 78,908)
* 21992 in population from old St. John's East to new Avalon
* 78567 in population from old St. John's East to new St. John's East
(for an accurate old St. John's East total population of 100,559)
* 5 in population from old St. John’s South–Mount Pearl to new Avalon
* 3519 in population from old St. John’s South–Mount Pearl to new St. John's East
* 79327 in population from old St. John’s South–Mount Pearl to new St. John’s South–Mount Pearl
(for an accurate old St. John’s South–Mount Pearl total population of 82,851)
All of which also add up to:
* new Avalon population of 81,583 (should be 81,540) +43
* new St. John's East population of 82,086 (should be 81,936) +150
* new St. John’s South–Mount Pearl population of 81,789 (should be 81,944) -155
And with the layers and lower-level Block-Face 2011 Census population information available from Statistics Canada, those totals could have been made perfectly accurate.
I'm currently working on getting the Transposed results into the Pundits' Guide database, but that work ground to a halt when things stopped adding up. The section of a riding profile page that shows Redistribution Info for a riding (what percent of each riding it came from, and what percent of its own population went to what other subsequent riding) has always been calculated on the fly using an accurately cross-referenced table of transposed populations from old to new. Now those won't add up to the proper riding populations anymore for the new Representation Order.
Other psephologists have pointed out to me that the documentation of which polling divisions were transferred from old ridings to new ridings was not correct either, inasmuch as they show a minimum and maximum poll number for each section, regardless of whether the section includes polls that belong with a different riding, or overlaps a subsequent section. One of them (known as Krago at the US Election Atlas) provided me with this fictitious example to demonstrate:
Let's say the old riding of Ottawa-Duffy is split between the new ridings of Ottawa-Harb and Ottawa-Wallin as follows:
* Polls 1-50: Ottawa-Wallin
* Polls 51-100: Ottawa-Harb
* Polls 101-150: Ottawa-Wallin
* Polls 151-200: Ottawa-Harb
It would show on the Transposition of Votes as follows:
* Ottawa-Wallin: 100% Start: 1 End: 150 Polls 100 Votes …
* Ottawa-Harb: 100% Start: 51 End: 200 Polls 100 Votes …
It is frickin' useless to check if it is actually correct.
Something does not seem right when the bigger our data, and the better our software, the worse our public datasets are for accuracy. I really wish Elections Canada and Statistics Canada would go back to the drawing board and produce an accurate dataset for the Transposition of Votes and Population for this Representation Order.