¹ See Duverger, Maurice, Political Parties: Their Organization and Activity in the Modern State (London, 1954), esp. pp. 373–4Google Scholar; and Rae, Douglas W., The Political Consequences of Electoral Laws (New Haven, 1967)Google Scholar.

² Dahl, Robert A., A Preface to Democratic Theory (Chicago, 1956), pp. 148–9Google Scholar. Dahl regresses Democratic share of major-party seats on that party's share of major-party vote.

³ Kendall, M. G. and Stuart, A., “The Law of the Cubic Proportion in Election Results,” British Journal of Sociology, Vol. 1 (1950), 183–96CrossRefGoogle Scholar.

⁴ T. H. Qualter, in a recent study, puts forward a “modified cube law” for the multi-party case and applies it to Canada. Because of differences in intent and method it is difficult to compare Qualter's results with those presented here. See Qualter, T. H., “Seats and Votes: An Application of the Cube Law to the Canadian Electoral System,” Canadian Journal of Political Science, Vol. 1 (1968), 336–344CrossRefGoogle Scholar. It may be noted that both the two-party cube law and Qualter's “modified cube law” are special cases of the “weak proportionality” function proposed by Theil. See Theil, Henri, “The Desired Political Entropy,” this Review, Vol. LXIII (June, 1969), 521–525Google Scholar.

⁵ The inference would be fully justified if the representation function were continuous and monotonic increasing. Obviously this requirement is not met in fact: the addition of a handful of votes to a party's total will not always result in additional seats won. It is sufficient for present purposes to assume that the probability of a party's winning an additional seat with a modest augmentation of its vote is not zero.

⁶ Shown in parentheses below the sample coefficients are the corresponding standard errors; R² is the coefficient of determination corrected for degrees of freedom; S.E.E. is the standard error of estimate. Asterisks raised above the coefficients indicate significance level according to a two-tailed t–test, as follows: **significant at the .01 level; *significant at the .05 level. A useful and relatively non-technical introduction to regression analysis is Ezekiel, Mordecai and Fox, Karl A., Methods of Correlation and Regression Analysis (New York, 3rd ed., 1959)Google Scholar.

⁷ For a succinct discussion of this problem consult Blalock, H. M. Jr., “Correlated Independent Variables: the Problem of Multicollinearity”, Social Forces, Vol. 42 (1963), 233–237CrossRefGoogle Scholar.

⁸ It seems clear that the minor parties have, on the whole, performed better when they were unopposed by one of the major parties, though the results are mixed. In the election of 1921, for example, the Liberal party did not name candidates in 33 constituencies, and in 28 of them minor-party candidates were successful; the Conservative party passed up 27 seats, of which only five were won by minor-party candidates.

⁹ The cube law implies a non-linear relationship between share of seats and share of vote, i.e., the incremental transformation rate is not a constant but rather varies with share of vote. However, James G. March reports that for shares of vote ranging from 40 per cent to 60 per cent the cube law can be approximated closely by a linear equation which fixes the transformation rate at about 2.8. See March, James G., “Party Legislative Representation as a Function of Election Results,” The Public Opinion Quarterly, Vol. XXI (1957/1958), 521–542CrossRefGoogle Scholar. Dahl (op. cit., pp. 148–149) elicited transformation rates for the Democratic party of 2.50 in House of Representatives elections and 3.02 in Senate elections.

¹⁰ The slanted (equal-representation) lines are truncated at N_M = 100 and N_M = 500 to remain well within the range of observed values of the variable in the sample.

¹¹ See Blalock, H. M. Jr., Social Statistics (New York, 1960), p. 345Google Scholar.