¹ See Axelrod, Robert, Conflict of Interest: A Theory of Divergent Goals with Application to Politics (Chicago: Markham, 1970)Google Scholar; de Swaan, Abram, Coalition Theories and Cabinet Formations (Amsterdam: Elsevier Scientific Publishing Company, 1973)Google Scholar; Leiserson, Michael, ‘Coalitions in Politics’ (doctoral thesis, Yale University, 1966).Google Scholar

² For example Grofman, Bernard, ‘A Dynamic Model of Protocoalition Formation in Ideological N-space’, Behavioral Sciences, 27 (1982), 77–90CrossRefGoogle Scholar; Grofman, Bernard, Straffin, Philip and Noviello, Nicholas, ‘The Sequential Dynamics of Cabinet Formation, Stochastic Error, and a Test of Competing Models’, forthcoming in Schofield, Norman, ed., Theory of Social Choice and Politics (Boston, Mass.: Kluwer Nijhoff, 1993)Google Scholar; Laver, Michael and Shepsle, Kenneth, ‘Coalitions and Cabinet Government’, American Political Science Review, 84 (1990), 873–90CrossRefGoogle Scholar; Laver, Michael and Shepsle, Kenneth, ‘Government Coalitions and Intraparty Politics’, British Journal of Political Science, 20 (1990), 489–507.CrossRefGoogle Scholar

³ For example in Castles, Francis and Mair, Peter, ‘Left-Right Political Scales: Some Expert Judgements’, European Journal of Political Research, 12 (1984), 73–88CrossRefGoogle Scholar; Morgan, Michael-John, ‘The Modelling of Governmental Coalition Formation: A Policy-Based Approach with Interval Measurement’ (doctoral thesis, University of Michigan, 1976)Google Scholar; Laver, Michael and Hunt, Ben, Policy and Party Competition (London: Routledge, 1992).Google ScholarBudge, Ian, Robertson, David and Hearl, David, eds, Ideology, Strategy and Party Change: Spatial Analyses of Post-War Election Programmes in 19 Democracies (Cambridge: Cambridge University Press, 1987)CrossRefGoogle Scholar analyse post-1945 election programmes of political parties (the Party Manifestos Project), and provide some information on interval policy positions over time. However, for countries that usually have many parties represented in parliament (for example Israel, Belgium, the Netherlands, Italy, France) often only the results for the major, i.e. the largest, parties are reported.

⁴ For the sake of simplicity, but without losing generality, I do not include D'66 in this argument. D'66 is (at the moment) a smaller party that, generally, is located between PVDA to its left and CDA to its right.

⁵ Castles, and Mair, , ‘Left-Right Political Scales’.Google Scholar

⁶ Using this equation, the combined position of any coalition cabinet can be computed. At the same time, however, it has to be stressed that this formalization is more appropriate for connected coalitions than for non-connected coalitions.

⁷ Grofman, , Straffin, and Noviello, , ‘The Sequential Dynamics of Cabinet Formation’.Google Scholar

⁸ This technique can also be used in multi-dimensional applications, provided of course that there is empirical information on the ordinal ordering of parties in more than one dimension. In practice, however, this will probably mean that the complexity of the analysis increases.

⁹ The solution proposed here gives us the opportunity to treat the interval dimension required in many modern coalitions theories as an ordinal dimension that includes an interval element, and thus do away with the negative consequences of using interval-level information collected at one time point for an analysis that covers a greater time period. At the same time, note that this solution is not simply the same as the one that was used by Leiserson, Axelrod and De Swaan in their (ordinal) coalition theories. Each of these three theories include concepts such as ‘range’ and ‘distance’. However, by using the scales as purely ordinal, their measures had to be more complicated than those proposed here, and their scope was fairly limited. For instance, Leiserson and Axelrod were largely limited to using the concept of ‘range’ of coalition S (terminology introduced by De Swaan) as the ordinal distance between the leftmost and rightmost players of S. Suppose players b, c and d are members of coalition S, and are ordered on ordinal scale R as follows: bRcRd (b is the leftmost player of the three, d the rightmost, and that c is in between). If coalition S includes these players, then the distance of S (D_s) is D_s = d(b, d). Now suppose the total game consists of five players, ordered from left to right, a, b, c, d, e. This means that we can compare the distances of coalition S = {b, c, d} and T = {a, b, c, d, e}. Coalition S is a subset of coalition T, thus D_s ≤ D_T. Distances between parties, or between parties and cabinets cannot be computed. De Swaan made up for the latter point by introducing the ‘pivotal player’ (the player that is in the position to swing the vote from left to right or vice versa) of a coalition. Again, however, because only ordinal scales were used, more complicated distance functions were needed and combined policy position of coalitions could not be computed.

¹⁰ See for example Budge, Ian, Crewe, Ivor and Farlie, David, eds, Party Identification and Beyond: Representations of Voting and Party Competition (London: Wiley, 1976)Google Scholar; van der Eijk, Cees and Niemoller, Kees, Electoral Change in The Netherlands (Amsterdam: CT-Press, 1983).Google Scholar

¹¹ Budge, , Robertson, and Hearl, , eds, Ideology, Strategy and Party Change.Google Scholar