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A Formal Analysis of the Amending Formula of Canada's Constitution Act, 1982

Published online by Cambridge University Press:  10 November 2009

D. Marc Kilgour
D. Marc Kilgour
Affiliation:
Wilfrid Laurier University
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Abstract

A formal analysis of the amending formula of Canada's Constitution Act, 1982 is presented. It is shown that larger provinces have greater voices in determining constitutional amendments, except that there are two groupings of provinces within which power with respect to constitutional amendments is exactly equal. Further, it is argued that differences in power among the provinces are disproportionately small in comparison to differences in population, so that the amending formula systematically directs greater influence to the individual citizens of smaller provinces.

Résumé

Ce texte présente une analyse formelle de la formule d'amendement de l'Acte constitutionnel de 1982. On y soutient que les grandes provinces sont plus puissantes pour orienter les amendements, sauf qu'il y a deux groupes de provinces qui, d'après les amendements constitutionnels, ont un pouvoir égal. Ensuite, les différences de pouvoir entre les provinces varient peu en comparaison des différences de population, faisant en sorte que la formule d'amendement donne systématiquement plus d'influence aux individus des petites provinces.

Type
Notes
Information
Canadian Journal of Political Science/Revue canadienne de science politique , Volume 16 , Issue 4 , December 1983 , pp. 771 - 777
Copyright
Copyright © Canadian Political Science Association (l'Association canadienne de science politique) and/et la Société québécoise de science politique 1983

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References

1 The population percentages shown in Table 1, and all calculations using populations, are based on the 1981 Census (Statistics Canada, 1982).

2 For a discussion in a different context of the congruence of the “power to pass” and the “power to block passage,” see Brams, S. J., Game Theory and Politics (New York: Free Press, 1975), 163–64.Google Scholar

3 Introduced in Banzhaf, J. F. III, “Weighted Voting Doesn't Work: A Mathematical Analysis,” Rutgers Law Review 19 (1965), 317–43.Google Scholar

4 The main competing measure is the Shapley-Shubik index, introduced in Shapley, L. S. and Shubik, Martin, “A Method of Evaluating the Distribution of Power in a Committee System,” American Political Science Review 48 (1954), 787–92.CrossRefGoogle Scholar The two indices are discussed and compared in Brams, Game Theory and Politics, 157–97,Google Scholar and in Lucas, W. F., “Measuring Power in Weighted Voting Systems,” in Case Studies in Applied Mathematics (Washington: Mathematical Association of America, 1976), 42–106.Google Scholar A good case favouring the use of the Banzhaf index in such situations as this is presented in JrStraffin, Philip D., “Homogeneity, Independence, and Power Indices,” Public Choice 30 (1977), 107–18.CrossRefGoogle Scholar While values of the Shapley-Shubik index will not be reported below, it should be noted that they are in fact quite close to the corresponding values of the Banzhaf index, thus lending additional support to the conclusions drawn from the values of the Banzhaf index.

5 Introduced in Owen, Guillermo, “Multilinear Extensions and the Banzhaf Value,” Naval Research Logistics Quarterly 22 (1975), 741–50.CrossRefGoogle Scholar Relative values of the individual Banzhaf index are very closely approximated by dividing each province'sBanzhaf index value by the square root of its population percentage. An analogous individual Shapley-Shubik index was proposed in Shapley, L. S., “Political Science,” in H. A. Selby, Notes of Lectures in Mathematics in the Behavioral Sciences (Washington: Mathematical Association of America, 1973), 83–85.Google Scholar An earlier, and less justified, procedure placed the population percentage, rather than its square root, in the denominator. It was used in the application of the Shapley-Shubik index to the Victoria Formula by Miller, D. R. in “A Shapley Value Analysis of the Proposed Canadian Constitutional Amendment Scheme,” this JOURNAL 4 (1973), 140–43.Google Scholar It should be added that the individual Shapley-Shubik index, or versions of the individual indices as used by Miller, would lend at least equal support to the conclusions presented below.

6 The procedure described in footnote 5 has been used. Technically, it has also been assumed that each province has the same proportion of voters. Since the calculation yields only relative values of the individual power index, the data in Table 1 have been normalized so that the least index value is unity.

7 For comparison, any (hypothetical) amending formula in which the powers of the provinces were exactly equal would accord to the most influential voters about 8.5 times the individual power of the least influential voter. Again, the difference is by a factor of about one-third.

8 This assertion is again based on the 1981 Census, as are the calculations to follow.