¹ See, for example, Leiserson, M., ‘Coalitions in Politics’ (doctoral dissertation, Yale University, 1966)Google Scholar; and Leiserson, M., ‘Factions and Coalitions in One Party Japan: An Interpretation Based on the Theory of Games’, American Political Science Review, LXII (1968), 770–87CrossRefGoogle Scholar; Dodd, L. C., ‘Party Coalitions in Multiparty Parliaments: A Game Theoretic Analysis’, American Political Science Review, LXVIII (1974), 1083–117Google Scholar; and also Dodd, L. C., Coalitions in Parliamentary Governments (Princeton, N.J.: Princeton University Press, 1976).Google Scholar

² de Swaan, A., ‘An Empirical Model of Coalition Formation as an N-Person Game of Policy Minimization’, in Groennings, G., Kelley, E. W. and Leiserson, M., eds., The Study of Coalition Behavior (New York: Holt, Rinehart, 1970)Google Scholar; and de Swaan, A., Coalition Theories and Cabinet Formations (Amsterdam: Elsevier, 1973)Google Scholar; also Axelrod, R., Conflict of Interest (Chicago: Markham, 1970).Google Scholar A minimal connected winning coalition is one that is winning (i.e., has a parliamentary majority) and connected (all parties in the coalition have adjacent preferred policy positions) and may lose no party yet preserve these properties.

³ Browne, E. C. and Feste, K. A., ‘Qualitative Dimensions of Coalition Payoffs: Evidence from European Governments, 1945–70’, American Behavioral Scientist, XVIII (1975), 530–56.CrossRefGoogle Scholar

⁴ Grofman, B., ‘Applications of a Dynamic Model of Protocoalition Formation to European Cabinet Coalitions in Three Countries’Google Scholar (mimeograph, University of California at Irvine, 1981); and Grofman, B., ‘A Dynamic Model of Protocoalition Formation in Ideological N-Space’, Behavioral Science, XXVII (1982), 77–90.CrossRefGoogle Scholar

⁵ Winer, M., ‘Cabinet Coalition Formation: A Game Theoretic Analysis’ in Brams, S., Schotter, A. and Schwodiauer, S., eds, Applied Came Theory (Wurzburg: Physica Verlag, 1979)Google Scholar; Ordeshook, P. C. and Winer, M., ‘Coalitions and Spatial Policy Outcomes in Parliamentary Systems: Some Experimental Results’, American Journal of Political Science, XXIV (1980), 730–52.CrossRefGoogle Scholar

⁶ Schofield, N.. ‘Instability of Simple Dynamic Games’, Review of Economic Studies, XLV (1978), 575–94CrossRefGoogle Scholar; and Schofield, N., ‘Generic Properties of Simple Bergson-Samuelson Welfare Functions’, Journal of Mathematical Economics, VII (1980), 175–92CrossRefGoogle Scholar; and Schofield, N., ‘Generic Instability of Majority Rule’, Review of Economic Studies, L (1983), 695–705.CrossRefGoogle Scholar

⁷ Riker, W. H., The Theory of Political Coalitions (New Haven: Yale University Press, 1962).Google Scholar

⁸ See, for example, Browne, E. C., ‘Testing Theories of Coalition Formation in the European Context’, Comparative Political Studies, III (1971), 391–411CrossRefGoogle Scholar; and Taylor, M. and Laver, M., ‘Government Coalitions in Western Europe’, European Journal of Political Research, 1 (1973), 205–48.CrossRefGoogle Scholar

⁹ Gamson, W. A., ‘A Theory of Coalition Formation’, American Sociological Review, XXVI (1961), 373–82.CrossRefGoogle Scholar

¹⁰ Browne, E. C. and Franklin, M. N., ‘Aspects of Coalition Payoffs in European Parliamentary Democracies’, American Political Science Review, LXVII (1973), 453–69.CrossRefGoogle Scholar

¹¹ In a later analysis of the data Browne and Frendeis verified that this phenomenon was not purely an artefact of the lumpiness of the data. See Browne, E. C. and Frendeis, J. P., ‘An Assessment of the Evidence from Cabinet Coalition Situations’, American Journal of Political Science, XXIV (1980), 753–68.CrossRefGoogle Scholar

¹² Schofield, N., ‘The Kernel and Payoffs in European Government Coalitions’, Public Choice, XXVI (1976), 29–49.CrossRefGoogle Scholar

¹³ For a fuller discussion of these bargaining notions, see Schofield, N., ‘Generalised Bargaining Sets for Cooperative Games’, International Journal of Game Theory, VII (1978), 183–99.CrossRefGoogle Scholar

¹⁴ See Schofield, N., ‘Bargaining Set Theory and Stability in Coalition Governments’, Mathematical Social Science, III (1982), 9–31CrossRefGoogle Scholar, for further details of the methods involved in computing the bargaining set.

¹⁵ In comparing our results with those of Browne and Franklin, of course, account must be taken of the fact that they predict proportion, while we predict numbers, of cabinet seats. This should not affect the slopes much, but our constant of about one portfolio reflects, given a mean cabinet size of about twenty portfolios, a proportionate constant of about 0·05.

¹⁶ We also verified that this systematic misprediction was not purely a result of the lumpy nature of the dependent variable.

¹⁷ See Schofield, N., ‘The Relationship Between Voting and Party Strength in an Electoral System’, in Holler, M., ed., Power, Voting and Voting Power (Wurzburg: Physica Verlag, 1981).Google Scholar

¹⁸ See, for example, Schofield, N., ‘Social Equilibrium and Cycles on Compact Sets’, Journal of Economic Theory, XXXIII (1984), 59–71.CrossRefGoogle Scholar

¹⁹ See Schofield, , ‘Generic Instability of Majority Rule’Google Scholar, for a formal proof.