3. The Third “Flexible Floor” Formula (1952-1974)


Spreadsheets

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Description

In 1952, Parliament tacked on one more rule to the end of the Representation Formula. This new rule 5 created the Third Formula and contained two substantive clauses: first, “The 15% Clause” held that no province could lose more than 15% of its MPs in one decennial electoral redistribution, and; second, “The Alberta Clause” said that no province could hold fewer MPs than another province which had a smaller population.

For the purposes of these spreadsheets, I will describe for the Third Formula only the new 15% Clause and the Alberta Clause, because the calculations under rules 1 through 4 remain identical.

Rule 5: The 15% Rule

For the purposes of the 15% Clause, I am using the second sheet in the workbook (RO, 1966) as an example, because this being the second readjustment to use the Third Formula, it properly illustrates the importance of column T. The 15% Clause takes up columns S. T, U, and V. In column S, I manually entered the number of MPs per province not under the previous Representation Act, but instead the number of MPs per province in the 1940s under rules 1 to 4 before the application of rule 5. The rule has to follow this method, or else it would lock in a minimum number of MPs per province from the time of its enactment in 1952; parliament did not decide that provinces could never lose MPs under 1974. These figures therefore come from column S under the first worksheet (RA, 1952).

Column T then calculates 15% of those numbers of MPs, almost of all of which contain fractional remainders:

=S4*0.15

But column U shows the maximum number of MPs which the province could lose in one readjustment as the number in column U rounded down, because the text of Rule 5 says “the number of members for any province should not be reduced by more than fifteen percent below the representation to which such province was entitled under rules one to four of the subsection at the last preceeding readjustment […].” If the province cannot lose more than 15%, and column T gives a fractional remainder, then we have to round down, because rounding normally or rounding up would give a whole number larger than 15%.

=ROUNDDOWN(T4,0)

Consequently, the minimum number of MPs which a province could hold in column V equals the difference between columns S and U: =S4-U4

Rule 5: The “Alberta Clause”

This heading does not appear until the 1990s under the scenario of what would have happened if Parliament had kept the Third Formula instead of repealing it in the 1974. It shows up as Rule 5B in a dark pink or something (I only know the names of perhaps a dozen colours) and in columns W and X.

John Courtney referred to the second half of Rule 5 as the “Alberta Clause” because Parliament originally enacted it in 1952 to avoid a scenario where Alberta would end up with fewer MPs than Saskatchewan because of the 15% Rule despite having a larger population. In reality, this second half of Rule 5 never came into operation at all because Parliament repealed and replaced the Third Formula in 1974, and it would not have applied until two decades later in the 1990s. Furthermore, by the 1990s, the Alberta Clause would not have applied to Alberta at all because that province grew so quickly after the 1970s while Saskatchewan continued to stagnant as it had since the 1930s. By the 1990s, the second half of Rule 5 would have applied to Saskatchewan with respect to New Brunswick; in the 2000s, it would have applied to both Manitoba and Saskatchewan with respect to New Brunswick. The Senatorial Clause guaranteed New Brunswick 10 MPs, even though its population would only have warranted 7 MPs. But since Manitoba and Saskatchewan each only hold 6 Senators instead of New Brunswick’s 10, the Senatorial Clause could not stop Manitoba and Saskatchewan from slipping below 10.

This second half of Rule 5 could therefore more aptly have been described as the New Brunswick-Saskatchewan Clause or the Saskatchewan Clause or something like that. It means that if a province with a larger population than that of New Brunswick ends up with fewer than 10 MPs, then that province must obtain an additional number of MPs to match New Brunswick’s representation in the House of Commons. If not, then the province would get 0 additional MPs under this rule. I expressed this clause with the following compound if-then – AND function in column W:

=IF(AND(B10>B$7,V$7<K$7), K$7-V10, 0)

Column X then shows the sum of the minimum number of MPs under the 15% Clause and the number of additional MPs under the New Brunswick-Saskatchewan Clause:

=V4+W4

The Grand Total

Column W (or column Y in the 1990s onward) tallies the number of MPs per province after taking into account Rule 5 with an if-then function: if the minimum number of MPs that a province must hold the 15% Rule is less than the number of MPs awarded under the application of Rules 1 to 4, then the province must obtain the minimum number of MPs under the 15% Rule instead of the smaller number under Rules 1 to 4; if not, then the province’s number of MPs comes only from the application of Rules 1 to 4:

=IF(V4>R4, V4, R4)

Pickersgill’s Proposed Amendment of 1963

Jack Pickersgill argued before cabinet on 30 July 1963 that Parliament should amend the the Flexible Floor Formula in two ways: first, to increase the electoral divisor from 263 to 286 (even though it was, in fact, 261); and, second, “no province which is not protected by the ‘Senate rule’ and is greater in population than whichever of the provinces protected by the ‘Senate rule’ has the largest population, would have fewer members in proportion to population than the latter province.” The Senatorial Clause only applied to two provinces in the 1960s, Prince Edward Island and New Brunswick, the latter of which had the larger population. New Brunswick would therefore serve as a new point of reference for calculating a new (lower) electoral quotient. The Pickersgill Rule would have rendered the 15% Rule moot. It would also have massively increased the House of Commons from 263 to 311 MPs at once because it would have applied to all provinces except Prince Edward Island and New Brunswick. In addition and apparently unknown to Pickersgill, adding this Rule 6 (probably best called the New Brunswick Clause) would in and of itself have increased the House of Commons to 311 even while preserving the original electoral divisor of 261, which makes increasing the electoral divisor to 284 or 286 redundant and mathematically unnecessary.

This new Rule 6 now takes up columns W, X, and Y in the two worksheets on “1960s (Pickersgill 1).” Column W shows New Brunswick’s Electoral Quotient based on its population divided by its minimum number of 10 MPs guaranteed by the Senatorial Clause. Here I also did not bother with creating an elaborate series of equations to identify New Brunswick automatically as the province with the larger population to which the Senatorial Clause aplies:

=B$7/R$7

Column X shows the number of MPs for each province based on its population divided by New Brunswick’s electoral quota:

=B4/W4

In Column Y, I then rounded up these values:

=ROUNDUP(X4)

Finally, Column Z now lists the Final Tally of MPs per province in light of all six rules in an if-then function to take into account that Prince Edward Island still only obtained two MPs under New Brunswick’s electoral quota instead of the requisite four under the Senatorial Clause:

=IF(Y4>R4, Y4, R4)

Pickersgill later dropped his own proposed amendment and suggested keeping it in reserve unless an MPs in opposition raise the possibility of increasing the size of the House of Commons during the debates on the Electoral Boundaries Readjustment Bill.

Pickersgill’s Plan Approximated More Accurately, 1963

The calculations above make no sense and also do not correspond at all to the figures that Pickersgill later presented to cabinet on 3 August 1963. If Parliament amended the Representation Formula and increased the electoral divisor to 286 versus under the formula from 1952, then, according to Pickersgill, Newfoundland would get 8 instead of 7 MPs; Prince Edward Island and New Brunswick stayed at 4 and 10, respectively; Nova Scotia would go from 11 to 12; Quebec, from 74 to 81; Ontario, from 88 to 96; Manitoba, from 13 to 14; Saskatchewan, from 13 to 14; Alberta, from 19 to 22; and British Columbia, from 23 to 25.[1] However, Pickersgill provided accurate figures only for Prince Edward Island, New Brunswick, Nova Scotia, Manitoba, Saskatchewan, and British Columbia presuming an electoral divisor of 286; Newfoundland and Alberta would still have obtained 7 and 21 MPs, respectively, while Quebec and Ontario would have ended up with 82 and 97, respectively. Increasing the divisor to 286 would still have prevented every province, except Saskatchewan, from losing MPs, but Pickersgill supported this measure primarily because it would have given the FEBCs greater latitude to award new MPs to fast-growing cities and suburbs without forcing them to expand the geographic size of too many rural ridings.[2] Increasing the number of MPs would therefore “sharply reduce the difficulty of redistribution.”[3] Pickersgill concluded that Newfoundland would qualify for one additional MP based on the ratio of New Brunswick’s MPs to population, even though Newfoundland also had a smaller population than New Brunswick.[4]

The worksheet “Pickersgill’s Plan 2, 1960s” shows what happens simply when we increase the electoral divisor to 286 and run through all the calculations the same as before. In reality, the provinces obtained the following number of MPs presuming an electoral divisor of 286 under the decennial census of 1961:

  • Newfoundland, 7
  • Prince Edward Island, 4
  • Nova Scotia, 12
  • New Brunswick, 10
  • Quebec, 82
  • Ontario, 97
  • Manitoba, 14
  • Saskatchewan, 14
  • Alberta, 21
  • British Columbia, 25

Notes

[1] Library and Archives Canada, Cabinet Conclusions, 3 August 1963, RG2 A-5-a, v.6254, ID 2251, at page 5.

[2] Library and Archives Canada, Cabinet Conclusions, 3 August 1963, RG2 A-5-a, v.6254, ID 2251, at page 6.

[3] Library and Archives Canada, Cabinet Conclusions, 3 August 1963, RG2 A-5-a, v.6254, ID 2251, at page 6.

[4] Library and Archives Canada, Cabinet Conclusions, 3 August 1963, RG2 A-5-a, v.6254, ID 2251, at page 6.