¹ It is worth pointing out that not all parties expect and/or seek to be included in a government. This is because their strategic position in the party system either makes inclusion unlikely (e.g., the British Liberals), and/or their ideological position precludes participation (e.g., the Irish Sinn Fein).

² See, for example, Riker, William H., The Theory of Political Coalitions (New Haven: Yale University Press, 1962)Google Scholar, Leiserson, Michael A., “Factions and Coalitions in One-Party Japan,” American Political Science Review, 62 (September, 1968), 770–787CrossRefGoogle Scholar, and Gamson, William A., “A Theory of Coalition Formation,” American Sociological Review, 26 (June, 1961), 373–382.CrossRefGoogle Scholar For methodological discussion and empirical illustrations of coalition formation, see also Groennings, Sven, Kelley, E. W., and Leiserson, M. A., eds., The Study of Coalition Behavior: Theoretical Perspectives and Cases From Four Continents (New York: Holt, Rinehart and Winston, 1970).Google Scholar

³ See Riker, especially Chapters 5 and 6 where he discusses the nature of side payments and indicates that smaller players are likely to be more advantaged in the distribution process than “weightier” ones.

⁴ Leiserson, p. 774.

⁵ Leiserson, pp. 777–782.

⁶ Gamson, pp. 375–376.

⁷ Gamson, p. 376.

⁸ Garmson, p. 376.

⁹ Gamson, p. 376.

¹⁰ Leiserson, p. 778. Note: Leiserson's reference to the receipt of “high party posts” is only germane to factional bargaining and should not be considered appropriate in our context.

¹¹ Notice that we have altered Gamson's proposition to postulate that the proportionality must be one-to-one. Naturally, a relationship may be proportional on any basis, 1:1, 2:1, 3:1, etc. It was obviously Gamson's intention that the relationship be 1:1 since any other interpretation is contrary to the logic of his theory.

¹² Regarding each party in each coalition-forming situation as one “case” gives us 358 such cases. However, 32 of these cases in fact represent ministerial distributions made to individuals who served in a nonparty capacity. The proportionality proposition is not relevant to these cases, and they were therefore excluded. Of the remaining 326 cases, two represent parties that received no ministries at all in return for the seats they contributed. These were parties which lent support to a coalition during a period of crisis, while refusing the responsibilities of office. Since it was not the bargaining process that led them to receive no ministries, these are cases where the proportionality proposition is again not relevant; these were again excluded, leaving us with a final universe of 324 cases.

¹³ These techniques are so well known as to require a minimum of documentation. The computing formulae used were taken from Hays, William L., Statistics (New York: Rinehart and Winston, 1963), 490–538.Google Scholar

¹⁴ The values taken on by both variables in fact vary all the way from 1 per cent to 99 per cent.

¹⁵ Readers who are left unimpressed by correlation coefficients and regression equations are invited to apply to Figure 1 what has been named the “interocular trauma test”: a relationship is significant if it hits you between the eyes. See Tufte, Edward, “Improving Data Analysis in Political Science,” World Politics, 21 (July, 1969), 641–654.CrossRefGoogle Scholar

¹⁶ For example, an additional independent variable which might be considered potentially fruitful in explaining additional variance is a partner's relative size or position in the coalition. Regardless of its absolute size, the largest coalition partner might be able to exercise exceptional influence over distributions, relative to his other partners. When relative size was treated as an interval-level variable and correlated against ministerial distribution, controlling for absolute size, it yielded a correlation coefficient of —0.25. Yet, when brought in as an additional term in the basic regression equation already presented, the total of the variance explained rose by only 1 per cent.

¹⁷ In another context, Hubert Blalock has argued that correlation coefficients are affected by factors that may be considered “accidental” to specific populations, so that in stating general laws or comparing populations (both of which we do in this paper) attention should be concentrated rather upon the more stable regression coefficients. Blalock, H. M. Jr., “Causal Inference, Closed Populations, and Measures of Association,” American Political Science Review, 61 (March, 1967), 130–136.CrossRefGoogle Scholar

¹⁸ The relationship is not quite reflexive. The displacement coefficient of —0.01 tells us that the smallest parties in general only contribute about 1 per cent fewer seats than they receive ministries, while the slope coefficient of 1.07 tells us that the very largest parties can expect on average to contribute about 6 per cent more seats (seven per cent more than the smallest parties) than they receive ministries. (See Equation 1.) Because there are many more small parties than there are large ones, however, the difference averages out, and about as many parties gain somewhat from the bias (155) as lose (166).

¹⁹ It is impossible in a footnote to demonstrate the manner in which the major coalition theorists arrive at this conclusion. We may say, however, that in general, large parties appear to suffer under certain limitations which are imposed on them because of their size. See, for example, Caplow, Theodore A., Two Against One: Coalitions in Triads (Engelwood Cliffs, N.J.: Prentice-Hall, 1969)Google Scholar, and Rappoport, Anatol, N-Person Game Theory: Concepts and Applications, (Ann Arbor, Mich.: University of Michigan Press, 1970).Google Scholar

²⁰ In fact, more than 85 per cent of the coalitions in our universe included the largest party represented in parliament.

²¹ We do not wish to advance this explanation as definitive since it is inferred from our data rather than being tested by them. Instead, we offer it as a tentative explanation which awaits further testing.

²² Leiserson makes much the same point when he adds to his theory of coalition formation a “bargaining proposition” which states that in the universe of minimal winning coalitions, smaller rather than larger ones will form regardless of which is closer to the decision point, since bargaining difficulties among large numbers of partners are dysfunctional to the viability of the coalition.

²³ In three-party coalitions in our universe, there happens to be a much greater polarization in party sizes than in two-party coalitions, and, as can be seen from Table II, the loss to large parties amounts to an astronomical 20 per cent: fully a fifth of the ministries to which they might otherwise have been entitled, or five ministries in our hypothetical example. The figures are arrived at by subtracting the displacement coefficient from the slope coefficient for large parties, and taking the displacement coefficient itself for small parties. This procedure yields hypothetical values for parties which hold 100 per cent and 0 per cent of seats, respectively, and provides fairly accurate estimates for the largest and smallest parties in our universe.

²⁴ For those who insist that party ideology is an important, if not the crucial, variable associated with coalition behavior, these results will be discouraging. Clearly, ideology can have little effect upon the quantitative distribution of government ministries. However, since it may be of more than passing interest for some scholars to know the extent to which particular ideological types of parties fare in ministerial distributions, the following table summarizes the experience of those parties which were not more or less equitably treated. The table depicts those parties which formed a sufficiently large concentration within an advantaged or disadvantaged situation as to affect noticeably the position of their ideological type taken as a whole. The numerals before the party labels indicate the number of parties concerned, and the percentage these constitute within their ideological type. Numerals following the labels indicate the average index of overpayment (proportional excess of ministries received over seats contributed) to the ideological type taken as a whole (not just for the individual parties depicted).

Socialist and Communist parties do not figure in the table. Their distribution into different size categories was so even as to preclude any significant gain or loss to their ideological type taken as a whole. The Conservative, Religious, and Agrarian parties all had a disproportionate number of large parties in small coalitions, and this, it has been demonstrated, accompanies heavy ministerial loss. It should be clear that the only ideological type to profit in the distribution is the Radical/Liberal. This type is the only one which contains a large concentration of parties in the strategic position that characterizes small parties in small coalitions (i.e., they benefit most from the relative weakness effect). Their gains are substantial. Radical/Liberal parties, on average, provide five per cent fewer seats than they receive ministries. This represents about one ministry in twenty as a bonus in return for nothing more than their presence as coalition partners. Moreover, it is important to remember that these figures are averages and that a number of parties do even better (or worse) than they might suggest.

²⁵ Since larger parties are more likely to receive ministries of all types than are small parties, it is necessary to standardize the data by dividing the number of ministries of each types received by the total number of ministries of all types received by that party. This calculation yields the proportion share of each ministerial type that each party receives.

²⁶ Essentially this is because (as explained earlier) we are seeking to gain the maximum descriptive power from the analysis rather than to maximize the variance explained. Descriptive power is gained from simple bivariate relationships, while most variance is explained in complex multivariate relationships. We have chosen to take account of the fact that larger parties are more likely to receive a ministry of any type by dividing M (the number of any particular ministerial type received) by N (the number of all ministries of any type received). We would have done better, from the point of view of explaining variance, to take out N as a separate term in a multiple regression equation of the form

M = a + b₁N + b₂I + b₃NI + e,

where M and N are as described above, I is the index of overpayment, and NI is the interaction term for the joint effect of size and overpayment. Such an analysis in fact explains between 3 per cent and 43 per cent of the variance in the distribution of different ministerial types; with a low multiple correlation of 0.176 for specialized portfolios, and a high multiple correlation of 0.660 for prime ministerships. The relationship we are interested in, however, then becomes some function of b₂ and b₃ which is relatively hard to describe.

²⁷ It should be borne in mind that because we are dealing with a universe rather than with a sample, there is no question of whether our coefficients are statistically significant. Even the smallest r describes a real relationship.

²⁸ It should be borne in mind that ministries have been assigned to types on the grounds of their area of concern, not their value in any ordinal sense. When several portfolios have the same area of concern, all were assigned to the same category, though only one of them would normally be honored with the title of the category concerned. This is particularly important in the case of the Foreign Affairs ministerial type, which often contains a number of portfolios other than that actually called the Ministry of Foreign Affairs. If these additional portfolios are excluded from the analysis, this ministerial type correlates negatively with the index of overpayment, though not strongly enough to take it out of group two.

²⁹ Schelling, Thomas C., The Strategy of Conflict (New York: Oxford University Press, 1963)Google Scholar, especially Chap. 3.

³⁰ See Browne, Eric C., “Testing Theories of Coalition Formation in the European Context,” Comparative Political Studies, 3 (January, 1971), 391–410.CrossRefGoogle Scholar Here, we are concerned with determining the extent to which the theories of Gamson, Riker, and Leiserson are able to predict coalition formation outcomes in our universe of thirteen European democracies. Gamson's theory (and Riker's) only had about two chances in a hundred of predicting correctly the formation of an actual winning from sets including ail possible winning coalitions. Leiserson's theory, while somewhat better a predictor than the others, also performed poorly.