Our task here is to achieve models for predicting the number of parties in a political system according to various institutional features. As mentioned in Chapter 10, the most important of these features has for some time now been recognized to be district magnitude, M. Additionally, according to the reasoning regarding Duverger's rule, also discussed near the beginning of Chapter 11, presidential systems might be expected to be different from parliamentary systems in their number of parties, for a given magnitude. That this should be so, at least for those presidential systems employing concurrent elections and plurality rule for the presidency, was foreshad-owed by Table 10.2, in which nationwide values of effective number of parties (N) are given. Our task here is to go beyond the purely empirical observations of Chapter 10 and seek theoretical explanation.

This discussion builds upon Taagepera and Shugart (1992a, b), in which are developed general models of the relation between magnitude and number of parties. By general models, we mean models for the simplest of general cases, that is, primarily parliamentary systems. When we add to the PR assembly electoral system the complexity of a concurrently elected presidency using plurality rule, it is necessary to make further assumptions in the model. Some of this material has already been discussed in Chapter 11, but the discussion here is more technical.