Coalition theory, much of which developed from game theory, is part of the quasi-mathematical rational choice tradition in political science which attempts to construct predictive theories to explain political activity. There are two principal domains of political activity to which coalition theories have been applied: the forming of a government by a coalition of minority parties in a parliament, and the forming of military and diplomatic alliances between states. However, the advocates of coalition theory would claim that it ought to apply to any situation where more than two actors face potential conflicts of interest, and thus co-operation between two or more against one or more opponents is rationally useful. They would further argue that at least the general form of a successful theory would apply to any sample, whether it dealt with a coalition of small firms against a potentially monopolistic rival, a coalition of parties to form a government or a coalition of schoolchildren against the playground bully.
In the example of government formation coalition theories have been quite successful, especially when applied to party systems where the number and sizes of parties, as well as the ideological spectrum of the nation’s politics, leaves no obvious coalition grouping. One of the two principal rules to emerge from early work in this sphere was that the most likely coalition to form will be what is called a ‘minimum-winning’ coalition.
In a parliament where 70 seats are needed to form a government, and there are four parties (A–D), running from left to right of an ideological spectrum, A having 50 seats, B 40 seats, C 20 seats and D 10 seats, it is more likely that a two-party coalition of A and B will form than a three-party coalition of B, C and D. What will almost certainly not form is a coalition of all four, because such a government would have 50 more seats than it needed and, as a party loses potential benefits the greater the number of other parties with which it has to share the value of being in government, there is seldom a good reason to form an over-large coalition. The other principal rule is of ‘ideological connectedness’. Parties will try to co-operate with others nearest to their own political values. Thus one of the minimum-winning coalitions in the example above would be between A and C, but C is not ideologically the closest possible partner for A.
In other examples different factors emerge, such as problems arising from the provision of collective goods and, in the international arena, from the general theory of the balance of power.
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