Spreadsheets
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Description
Canadian political scientist Andrew Sancton argued that the Representation Commissioner had miscalculated the number of MPs per province under the decennial census of 1971. Castonguay assigned 91 MPs to Ontario instead of 92 because he only applied rules 1 and 2 once when he should have applied them twice in two distinct rounds in between applying rules 3 and 4. Whether Nova Scotia obtained 10 MPs under rules 1 and 2 versus under rules 3 and 4 changed whether Ontario obtained 91 MPs or 92 MPs in general.[1] The Fixed and Flexible Floor Formulas necessitated redistributing the remainders under rule 2 twice, both before and after applying the Senatorial Clause under rules 3 and 4, as Sancton showed, but only in the 1970s did Castonguay’s erroneous method produce different outcomes.[2] Consequently, the FEBC for Ontario issued a proposal, held public hearings, and published a preliminary report in 1973 based on Castonguay’s false calculation that deprived the province of one riding. However, Parliament ultimately rendered Castonguay’s miscalculation moot by halting the electoral redistribution in 1973 and then replacing the Representation Formula altogether in 1974.[3] This once more shows the perils of deliberately entrenching malapportionment and that pure representation by population not only helps secure good government but also requires the simplest arithmetic and lowers the risk of miscalculating the number of MPs per province. Sancton’s article did not appear in the Canadian Journal of Political Science until the spring of 1973, and he had not acknowledged therein the Trudeau government’s attempts to amend the Flexible Floor Formula in 1971 and 1972.
The Trudeau government introduced identical bills in 1971 and 1972 which would have amended the Flexible Floor Formula in precisely such a way that would have made Castonguay’s miscalculation impossible: decoupling the Senatorial Clause from the electoral divisor and eliminating the second round of calculations under rules 1 and 2 altogether. The Senatorial Clause would then have awarded additional MPs over and above the electoral divisor in the same way that the 15% Clause did; consequently, Prince Edward Island and New Brunswick would no longer have taken MPs away from the more populous provinces.[4] This proposed simplified calculation all but confirms that Nelson Castonguay had misinterpreted the more complicated rules in the 1950s and 1960s, as had his father Jules Castonguay before him in 1946.
Simplifying Rule 2 and Decoupling the Senatorial Clause from the Electoral Divisor
This example follows worksheet 2, “Bill C-2, 1972.” Rule 1 calculates the electoral quotient and the raw number of MPs per province, relies on the same electoral divisor of 261, and carries over from the Second and Third Formulas. These steps appear in light green in columns B, C, D, and E using the same arithmetic as in the spreadsheet for the operative Third Formula.
But crucially, MacEachen’s Modification only runs Rule 2 once. These steps appear in light blue in columns F, G, and H using the same arithmetic as in the spreadsheet for the operative Third Formula.
Under MacEachen’s Modification, the Senatorial Clause has become Rule 3 and also appears in light red in columns I, J, and K with the same arithmetic as in the spreadsheet for the operative Third Formula.
The 15% Clause would then have become Rule 4 under this simplified and modified Flexible Floor Formula; it relies on the same calculations as under the spreadsheet for the operative Third Formula but now appears in light yellow in columns L, M, N, and O instead.
Overall, MacEachen’s Modification would have increase the House of Commons from 262 provincial MPs to 267: Quebec would have obtained 73 instead of 72; Ontario, 93 instead of 91 under Castonguay’s erroneous calculation; Alberta, 20 instead of 19; and British Columbia, 27 instead of 26 – all because the fast-growing provinces would no longer have sacrificed their representation for the sake of the Senatorial Clause.
[1] Andrew Sancton, “The Application of the ‘Senatorial Floor’ Rules to the Latest Redistribution of the House of Commons: The Peculiar Case of Nova Scotia,” Canadian Journal of Political Science 6, no. 1 (March 1973): 60. I had actually made exactly the same mistake as Castonguay in my original reconstructions of the Fixed Floor and Flexible Floor Formulas; only in the 1970s did the different methodologies produce different outcomes. Thankfully, Sancton’s article allowed me to go back and correct my spreadsheets.
[2] Sancton, “The Peculiar Case of Nova Scotia,” 60-61.
[3] Andrew Sancton, “Comment: The Representation Act, 1974,” Canadian Journal of Political Science 8, no. 3 (September 1975): 468. Sancton could only lament in 1975 that no one had followed up on his article from two years before. No one did until fifty years later in 2025.
[4] Allan J. MacEachen (President of the Privy Council), Bill C-257, An Act to amend the British North America Acts, 1867 to 1965, with respect to the readjustment of representation in the House of Commons, 28th Parliament, 3rd session, 19-20 Elizabeth II, 1970-1971, First Reading, 30 June 1867; Allan J. MacEachen (President of the Privy Council), Bill C-3, An Act to amend the British North America Acts, 1867 to 1965, with respect to the readjustment of representation in the House of Commons, 28th Parliament, 4th Session, 21 Elizabeth II, 1972, First Reading, 21 February 1972.
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