Spreadsheets 0, 1, 2, and 3: The Four Main Datapoints
For each iteration of the Federal Electoral Boundaries Commissions and electoral redistribution, I have striven to provide five classes of information, though only the three electoral redistributions from the 21st century show the complete record:
- Proposals
- Preliminary Reports
- Objections from PROC
- Final Reports
- Analyses
At a minimum, my analyses for each federal electoral boundaries readjustment provide four datatables showing the following under the Loosemore-Hanby Index:
0. The Population and Dwelling Counts, which show the population of the ridings established under the previous representation order in the latest decennial census;
1.The Proposals, which show the population of the new ridings that the commission has presented for public comment;
2.The Preliminary Reports, which show the population of the new ridings after the commissions have taken public feedback into account;
3.The Final Reports, which show the population of the new ridings after the commissions have responded to MPs and either accepted or rejected their suggestions.
These datatables contain the names and populations of electoral districts from all iterations of the Federal Electoral Boundaries Commissions from the 1960s to the 2020s and constitute the main record, as well as the calculations done under the Loosemore-Hanby Index to measure the overall proportionality of each electoral map under each report. Columns A and B show the names and populations of the electoral districts, respectively, as printed in the various reports. Column C shows the variance of the population from the electoral quota as a percentage, and Column D converts those percentages into absolute values for the calculation under the Loosemore-Hanby Index.
I hope that future researchers find these datatables useful and can build upon them as the decades go by.
Spreadsheets 0, 1, 2, and 3: The Loosemore-Hanby Index
David Samuels and Richard Snyder, “The Value of a Vote: Malapportionment in Comparative Perspective,” British Journal of Political Science 31: 654-656.
The Loosemore-Hanby Index measures inequality on a scale of 0 to 1, where 0 means perfect equality and 1 signifies abject inequality, and relies on the following mathematical formula: x = (1/2) Σ | si – vi |.
This scale can also therefore measure the malapportionment of MPs per province under the Representation Formula by comparing the percent of MPs assigned to a province and the percent of the total provincial population that a province holds. It can likewise measure the disproportionality of the distribution of electoral districts within a province by comparing the percent of the total provincial population contained in any given electoral district to the percent value of each electoral district within a province. For example, if a province had 100 electoral districts, then each electoral district would equal 1% of the total number of electoral districts and should each therefore contain 1% of the population of the province. The former remains constant, but the latter varies. And that variance is what causes disproportionality. In Microsoft Excel or Libre Office Calc, I created columns listing the percent of seats per electoral district and the percentage of the population that each contains. I then calculated the average of the differences between those two columns while also converting the differences to absolute values, because otherwise the average would simply equal 0. Only converting the differences to absolute values gives a workable number; in other words, negative numbers become positive (like +4 instead of -4) because what matters is the overall deviation from the quota, not whether the deviation goes above or below the quota. I then divided that sum of the differences by two and obtained an answer as a percentage, or a non-integer decimal between 0 and 1.
Spreadsheets 0 and 12: The Ridings The Populations of Which Exceeded +25%
Spreadsheet 0 shows the starting point of each readjustment and the population and dwelling counts under the decennial census of each electoral district established under the previous representation order. In the provinces which gained MPs, I added the number of new MPs to the sum at the bottom of column F, which counts up the total number of MPs, so that the calculation in column C would yield the official and proper electoral quota for that decade. I added an extra column E in this series called “Exceeds Electoral Quota?”, used an if-then function to answer “yes” or “no” whether the absolute value of the variance exceeded 25%, and then used a “count if” function to tally up the number of yeses to an integer. I used the absolute value so that I only needed to add one test in the if-then function instead of an additional or test account for +25% or -25%.
=if((dx>0.25), “Yes”, “No”)
For ease of reference, I also sorted spreadsheets 0 by column C, “Variance from Electoral Quota,” instead of on the name of the riding in column A, and highlighted in light grey all those the populations of which exceed the electoral quota by more than 25%. I also expressed the integer as a percentage of the total number of MPs.
In this series, I skipped the two abandoned electoral readjustments in the early 1970s and the early 1980s because this comparison only pertains to those electoral readjustments completed and implemented under a representation order.
I also compiled the results from each province into a sheet entitled “All Provinces (Exceeds by 25%”), which tracks the province, its total number of MPs – crucially, under the new representation order, which means that some do not match the number of MPs in the sheet for each province – the total number of ridings the populations of which exceeded plus or minus 25%, and then that same figure as a percentage. Only the percentage of ridings the populations of which exceed the electoral quota by plus or minus 25% can serve as a valid comparison across the decades because the number of MPs per province can change each decade. I then created spreadsheet 12 in my compilation of datatables across the decades and created a sheet for each decade (2020s, 2010s, 2000s, 1990s, 1980s, 1970s, and 1960s). This compilation lists only each province individually, the sum total of the ten provinces, and then the percentage of ridings the populations of which exceeded the electoral quota by plus or minus 25% for each decade. Finally, I turned that datatable into a bargraph which illustrates the data by province and decade.
The aggregate data “All Provinces” shows a clear downward trend from the 1960s to the 1990s, a flatline from the 1990s to the 2010s (inclusive), followed by another sharp drop off in the 2020s. Upon the first electoral redistribution under EBRA in 1966, the populations of 52% of the ridings of the 10 provinces exceeded the various provincial electoral quotas by more than plus or minus 25%. This demonstrates that the Representation Act, 1952 did not establish electoral districts with regard to equal population at all. That proportion decreased by about 20% to just over 33% upon the second completed electoral readjustment in 1976, which shows that the first iteration of the FEBCs created a much more proportional electoral map than Parliament did in 1952. That proportion decreased yet further to 22% in 1987 and then held steady at 16% to 17% in 1996, 2003, and 2013. Finally, in 2023, the proportion decreased significantly again to a mere 7%.
Ultimately, this series of spreadsheets 0 and the compilation shreatsheet 12 measure or allude to three main variables: the evenness (or not) of population growth from the previous electoral readjustment to the next decennial census, the efficacy of the Representation Formula itself in allocating MPs to each of the provinces, as well as the proportionality of the electoral maps established under the previous representation order. The average scores on the Loosemore-Hanby Index of the ten provinces at the end of electoral redistribution from the 1960s to the 2020s (in table x of the manuscript) and the average proportion of ridings the populations of which exceeded the electoral quotas by plus or minus 25% at the beginning of each electoral redistribution from the 1960s to the 2020s mirror each other very closely. They both show gradual reductions each decade from the 1960s to the 1990s and then hold steady in the 1990s, 2000s, and 2010s. For instance, the proportion of ridings the populations of which started out at greater than plus or minus 25% of the electoral quotas held steady in the 1990s, 2000s, and 2010s at 16% to 17%, which mirrors the consistency and stasis of the Loosemore-Hanby Indices on the representation orders of the 1990s, 2000s, and 2010s. This suggests a combination of even population growth over the previous decade as well as a good proportionality of the final electoral map under the previous representation order. This trend culminated under the Representation Order, 2013 and the decennial census of 2021 because the new Representation Formula gave Ontario, Alberta, and British Columbia significantly more MPs in one full swoop in the same decade that the FEBCs generally established proportional ridings under the Loosemore-Hanby Index. This confluence built slack into the system.
But they differ on the 2020s: the Loosemore-Hanby Index on the representation orders increased slightly in 2023 compared to 2013, but the proportion of ridings the populations of which exceeded the electoral quota by more than plus or minus 25% decreased sharply in 2021 compared to 2011. I would therefore expect that the combination of the highest sustained population growth in the 2020s since the 1950s coupled with the higher average disproportionality under the Representation Orders, 2023 will mean that the proportion of ridings the populations of which exceed the maximum variance under the electoral quotas will increase significantly in 2031, probably to somewhere between 15% and 20%.
Spreadsheets 5 and 6: Measuring the Exact Differences Between the Proposals and Preliminary Reports, and the Preliminary Reports and the Final Reports
In spreadsheets 5 and 6, I tried to derive the number of electoral districts the boundaries and names of which the commissions changed between the proposals and the preliminary reports after the public hearings, and again between the preliminary and final reports after PROC’s studies. I listed the names and populations of each riding in the preliminary report and then identified the corresponding riding in the proposal. This proved straightforward in most cases, though sometimes the commissions completely re-organised the electoral maps between the proposals and preliminary reports and took away an entire riding from one region and put it in another with a higher population. This occasionally created orphan ridings which did not correspond neatly from proposal to preliminary report; however, they did not change the answers given under the formulas under the headings “Boundaries Changed from Proposal” and “Name Changed from Proposal.” I used a simple if-then function in Excel to measure where the boundaries of a riding changed from the proposal to the preliminary report on the presumption that a change in population necessarily means a change in boundaries:
- =IF(Bx=Fx, “No,” “Yes”)
This formula means that if the population of a riding under the preliminary report (in column B) equals the population of a riding under the proposal (in column F), then “No,” the riding did not change boundaries. Alternatively, if the two cells did not equal one another, then “Yes,” the riding did change in population and therefore boundaries. The cell at the end of the column then relies on a simple formula to count up the number “Yes” responses into an integer, from which the spreadsheet can then calculate the percentage of ridings the boundaries of which changed. Similarly, I ran the same basic if-then and count-if formulas to determine whether the name of the riding changed from the proposal to the preliminary report and to tally up the total number of ridings the names of which the commission changed. I then derived the percentage as well.
Where the aforesaid formula tracks the number of ridings the boundaries of which changed based on a simple yes-no binary, the column “Change in Population (Absolute Value) tallies up precisely the number of people who switched ridings from the proposal to the preliminary report. Only the ridings which already show up as “yes” under the column “Boundaries Changed from Proposal” could possibly yield an integer here other than 0. This column uses the follow formula:
- =ABS(Bx-Fx)
This column finds the absolute value difference between the populations listed under the preliminary report and the proposal. I needed to add the absolute value, or else the sum at the end of the column would merely add up to 0. Furthermore, I also have to divide the sum total of the column “Change in Population (Absolute Value)” by two so that the sum only counts each person once. If I did not divide the sum in half, then I would double-count every person as leaving one riding and joining another. This formula in the spreadsheet works on the reasonable presumption that one person can only travel between two ridings. I then divided that half-sum of the total number of people who switched ridings by the number of ridings to derive the percentage of the population which switched ridings. I further derived an average of the number of people who switched ridings by dividing the total number of such people by the number of ridings the boundaries of which changed obtained in the aforementioned “count if” function, and as well as a percentage of the average population which switched ridings.
Spreadsheet 6 for each readjustment performs the same calculations using the same formulas in Excel but from the preliminary to the final reports.
Compilation of Spreadsheets 5 and 6 Across All Readjustments
For each readjustment, I then created a main datatable tabulating the name of the province, its total number of ridings, the total number and percentage of ridings the boundaries of which changed, and the total number and percentage of ridings the names of which changed. I then added up the total number of ridings the boundaries of which changed across the ten provinces and divided that sum by the total number of ridings of the ten provinces to derive the percentage of ridings the boundaries of which changed across the country. I did the same for the names.
I then took these percentages for the ridings the boundaries and names of which changed across the ten provinces for each readjustment and put them in a main table comparing them all. I also plotted these percentages out on bargraphs to show the trends over time. These graphs rely on the percentage rather than the number of ridings across the ten provinces because the number of ridings changed each decade and would therefore not have provided a legitimate comparison.
Finally, for each readjustment between the 1960s and 2020s, I also included the precise number of people who switched ridings and the percentage of the total provincial population who switched ridings and plotted out the percentages on a similar chart to compare trends over the decades.
Spreadsheet 7 on the Length of the Names of Ridings
Spreadsheet 7 measures the length of the names of ridings simply using the =LEN function in Excel, which counts all the characters in a cell, including spaces and en-dashes. I then derived the average and median length of the names of electoral districts in each report for each province in every readjustment from the 1960s to the 2020s. I then copied the results into tables showing the averages of the proposals, preliminary reports, and final reports of all ten provinces for each readjustment, and another compiling the data for the three reports from each provinces across all the readjustments.
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