Spreadsheets
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Description
The Amalgam Formula used one electoral divisor and two electoral quotients: the divisor for “large provinces” with populations of at least 2,500,000 under the latest census, one quotient for “intermediate provinces” with populations between 1,500,001 and 2,499,999 under the previous census, and another quotient for “small provinces” with populations less than or equal to 1,500,000 under the previous census. The large provinces would obtain their numbers of MPs based on their populations divided by the number of people per MP in Quebec in the current census, as in the Confederation Formula. Quebec would obtain 75 MPs in the 1970s and then 75 plus four times the number of decennial censuses since that of 1971 in subsequent decades: 75+(4×1) in the 1980s for a total of 79, 75+(4×2) in the 1990s for a total of 83, and so on ad infinitum. In contrast, the electoral quotient for the small provinces came from adding up the total population of the small provinces from the previous census and dividing that sum by the total number of MPs which these same small provinces held under the previous representation order. The electoral quotient for the intermediate provinces also came from dividing the sum of the populations of the small provinces under the current census by the sum of the MPs allocated to the small provinces under the current census.
The Amalgam Formula carried over The Alberta Clause of the Flexible Floor Formula, and it also contained the first Grandfather Clause such that a province could never lose MPs from one decade to the next. The number of MPs under the Representation Order, 1976 would therefore have become the new point of reference for the Grandfather Clause until 2022. Oddly enough, despite increasing the size of the House of Commons with reckless abandon, the Amalgam Formula completely rejected fractional remainders and always rounded down a province’s allocation of MPs to the smaller integer. Parliament had to draw the line somewhere.
Rule 3: MPs for the Small Provinces
I have used the only operative and completed readjustment under the Amalgam Formula in sheet 1 (RO, 1976) as the example here. I have not listed the rules in numerical order under section 51(1) because I found starting the spreadsheet with the previous decennial census of 1961 as less confusing than starting with the latest decennial census in 1971. In other words, I privileged time as an x-axis over the numerical order of the rules as written. I also relied more on manual entry for this spreadsheet because I couldn’t be bothered to create a quadruple-compounded if-then function that yields either small, intermediate, Quebec, or large across multiple categories. I sometimes have trouble keeping track of all those brackets and what not, and since we only have 10 provinces, I considered manual entry less onerous than automatic formulas, even if it might also be less rigorous. But this also unintentionally shows the absurdity and complexity of the Amalgam Formula compared to all the others. Alberta even stradled two categories, counting as a small province for the calculations done using the census of 1961 but then becoming an intermediate province for the purposes of its representation in the 1970s.
Rule 3 shows the MPs for the small provinces and takes up columns B, C, D, E, F. I also put the Senatorial Clause in this section in columns G, H, and I simply because it only applies to the small provinces. The Amalgam Formula also does not directly integrate the Senatorial Clause of section 51A into the text of section 51(1), which is why the Senatorial Clause does not fall under Rule 3 or any other rule.
Column B shows the size of a province under the census of 1961. I used an IFS function to classify the provinces as “Small”, “Intermediate”, or “Large” depending upon their populations. (Here Quebec can count as Large provided that the spreadsheet elsewhere assigns it a separate number of MPs).
=IFS(B4<=1500000, “Small”, B4<=2500000, “Intermediate”, B4>2500000, “Large”)
And I entered the number of MPs for the provinces under the Representation Order, 1966 in column D and their populations under the census of 1961 in Column B. I also added rows for the sub-totals of the small provinces (15), intermediate provinces (16 ) and large provinces (17) for the purpose of the calculations. Cell B15 adds up the total population of the small provinces in 1961, and cell D15 takes the corresponding sum of the total number of MPs of the small provinces in 1961:
=SUMIF(C3:C12, “Small”, B3:B12)
=SUMIF(C4:C13, “Small”, D4:D13)
Those latter two sums produce the electoral quotient for the small provinces in column E, rounded down because the Amalgam Formula says to disregard fractional remainders:
=C15/D15
Finally, column F shows the sub-total number of MPs for the small provinces for the 1970s by dividing the populations of the small provinces in 1971 (in column K) by their electoral quotient:
=IF(J4<1500000,ROUNDDOWN((J4/E$15),0),0)
Senatorial Clause
The Senatorial Clause only applied to Prince Edward Island and New Brunswick in the 1970s, as shown in columns G, H, and I. In column G, I entered the number of senators for the small provinces. Column H then shows the number of additional MPs added to Prince Edward Island and New Brunswick:
=IF((F4<G4), (G4-F4), 0)
Column I then displays the total number of MPs for the small provinces in the 1970s:
=F4+H4
Cell I15 adds up the total number of MPs for the small provinces, which enters into the calculation of the electoral quotient for intermediate provinces later:
=SUM(I4:I13)
Rule 1: MPs for Quebec
I entered manually the populations of the provinces under the census of 1971 in column J and then in column K relied on another IFS function to classify the provinces as “Small,” “Intermediate”, or “Large.” Quebec counts as “Large,” but it also obtains its own separate electoral divisor through a separate function.
=IFS(J4<=1500000, “Small”, J4<=2500000, “Intermediate”, J4>2500000, “Large”)
I then used another SUMIF function to tally up the total populations of all the small, intermediate, and large provinces.
=SUMIF(K3:K12, “Small”, J3:J12)
=SUMIF(K3:K12, “Intermediate”, J3:J12)
=SUMIF(K3:K12, “Large”, J3:J12)
In column L, Rule 1 assigns 75 MPs to Quebec in the 1970s, and then four new MPs each decade thereafter, which would make the generic formula 75+(4x), where x equals the number of decennial censuses after that of 1971.
In column M, the electoral quotient for the large provinces simply equals Quebec’s population in 1971 divided by Quebec’s MPs in the 1970s.
=J8/L8
Rule 2: MPs for Large Provinces
In the 1970s, only Ontario qualified as a large province. In column N, Ontario’s number of MPs equals its population in 1971 divided by the quotient from the previous step under either of the two possible if-then functions:
=IF(K9=”Large”,ROUNDDOWN((J9/M$17),0),0)
=IF(J9>2500000,ROUNDDOWN((J9/M$17),0),0)
Rule 4: MPs for the Intermediate Provinces
This quotient requires the most complicated calculations of the entire Amalgam Formula in columns O, P, Q, and R. Column O shows the electoral quotient for the intermediate provinces by dividing the total number of MPs for the small provinces in the 1970s by the total population of the small provinces in the 1970s.
= J15/I15
The initial calculation for the number of MPs for the intermediate provinces in column P applies to Alberta and British Columbia as their populations in 1971 divided by the quotient as either of the following:
=IF(AND(J12>1500001, J12<2500000), J12/O$16,0)
=IF(K12=“Intermediate”, J12/O$16,0)
But the intermediate provinces remain tethered to their seatcounts in the previous decade somehow in an unnecessary and convoluted extra step of finding one-half of the difference of their seatcounts from the current and previous readjustments and then adding that number to the total number of seats under the current readjustment. This calculation reduces the number of MPs for these intermediate provinces in column Q:
=IF(P4>0, ((P4-D4)/2)+D4, 0)
I separated the last step of disregarding any fractional remainders and rounding down because of some finicky thing in Calc in column R:
=ROUNDDOWN(Q4,0)
Grand Total
The total number of MPs for the provinces then equals the sum of the calculations under Rule 1 (Quebec), Rule 2 (Large Provinces), Rule 3 (Small Provinces), and Rule 4 (Intermediate Provinces), which corresponds to L8, N9, I4 through I7 and I10 to I11, and R12 to R13, respectively.
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