Abstract
Forming an idea of the number of parties competing at elections or winning seats in legislatures is fundamental to disaggregated approaches to mapping party systems. We set out a method for systematically relating the behaviour of any `number of parties' index to the size of the largest party's vote and the numbers of parties in competition. This approach shows that the `effective number of parties' (N 2) can confuse real changes in party competition with mathematical quirks in the way that the index is calculated. We also demonstrate that N 2 (and its main rival the Molinar index) behaves in hard to predict and anomalous ways under some configurations of party support. We conclude that the Molinar index should not be further used, and that the N 2 score's behaviour can create problems in quantitative applications. Even in less formal historical or comparative analyses N 2 always needs to be carefully interpreted. There is no `perfect' measure of the weighted number of parties, but averaging N 2 scores with a simple measure of largest party predominance (1/V 1) produces a highly correlated measure (Nb), but one with lower maximum scores, less quirky patterning and a readier interpretation. A more radical solution is to `spatialize' N 2 (or Nb) scores, which allows analyses to take more account of variations in the party competition conditions lying behind any given index number.
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