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The Laakso-Taagepera index of the effective number of parties, while satisfying most of the requirements of this aggregate quantity, tends to produce unrealistically high scores for party constellations in which the shares of the largest parties exceed 50 percent, and can produce misleading results in several other situations. After reviewing the structural properties of the Laakso-Taagepera index and supplements or alternatives to it proposed in the literature, this article proposes a new index that eliminates several problems inherent in the mathematical form of indices using the Herfindahl-Hirschman measure of concentration as computational core. The proposed index is tested on a set of party constellations from recent elections in new democracies and non-democratic electoral regimes. The results confirm that the new index works better than earlier proposed alternatives in measuring the effective number of components in highly fragmented and highly concentrated party systems. [Reprinted by permission of Sage Publications Ltd., copyright holder.]

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' ( N2) can confuse real changes in party competition with mathematical quirks in the way that the index is calculated. We also demonstrate that N2 (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 N2 score's behaviour can create problems in quantitative applications. Even in less formal historical or comparative analyses N2 always needs to be carefully interpreted. There is no `perfect' measure of the weighted number of parties, but averaging N2 scores with a simple measure of largest party predominance (1/ V1) 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' N2 (or Nb) scores, which allows analyses to take more account of variations in the party competition conditions lying behind any given index number.

I propose an alternative index to operationalize the variable number and size of parties in a party system. To support it, I present a critical overview of the two most common indices, Laakso and Taagepera's effective number of parties and Kesselman and Wildgen's hyperfractionalization, showing the causes of their weakness. Then I explain the computational logic of my alternative, "number of parties," and compare it with the other two, using hypothetical cases. After that, I contrast the Laakso-Taagepera index with mine, using data from actual elections between 1945 and 1981. I conclude that my index outperforms the other two as an operationalization of the variable number and size of parties.

This article explores how the party-defined dimensionality of political competition relates to the number of parties competing in legislative elections. It demonstrates that a mathematical relationship between the number of electoral parties and the literature's concept of dimensionality follows from the variables' definitions; conversely, it argues that exploring the relationship between the number of electoral parties and a different concept of dimensionality conveys new information. Hence, it first argues that how we conceptualize dimensionality matters. Redirecting attention to the latter relationship, it then hypothesizes that party system fragmentation will go hand-in-hand with the appearance of new conflicts on the political agenda when the electoral system is permissive. Using a time-series cross-sectional dataset that includes at its core a new measure of dimensionality, it finds reasonable support for the hypotheses; however, at the elite level, new parties are found to play less of a role in politicizing new conflicts than expected. [Reprinted by permission of Sage Publications Ltd., copyright holder.]

This article explores how the party-defined dimensionality of political competition relates to the number of parties competing in legislative elections. It demonstrates that a mathematical relationship between the number of electoral parties and the literature's concept of dimensionality follows from the variables' definitions; conversely, it argues that exploring the relationship between the number of electoral parties and a different concept of dimensionality conveys new information. Hence, it first argues that how we conceptualize dimensionality matters. Redirecting attention to the latter relationship, it then hypothesizes that party system fragmentation will go hand-in-hand with the appearance of new conflicts on the political agenda when the electoral system is permissive. Using a time-series cross-sectional dataset that includes at its core a new measure of dimensionality, it finds reasonable support for the hypotheses; however, at the elite level, new parties are found to play less of a role in politicizing new conflicts than expected.

The Laakso—Taagepera index of the effective number of parties, while satisfying most of the requirements of this aggregate quantity, tends to produce unrealistically high scores for party constellations in which the shares of the largest parties exceed 50 percent, and can produce misleading results in several other situations. After reviewing the structural properties of the Laakso—Taagepera index and supplements or alternatives to it proposed in the literature, this article proposes a new index that eliminates several problems inherent in the mathematical form of indices using the Herfindahl—Hirschman measure of concentration as computational core. The proposed index is tested on a set of party constellations from recent elections in new democracies and non-democratic electoral regimes. The results confirm that the new index works better than earlier proposed alternatives in measuring the effective number of components in highly fragmented and highly concentrated party systems.