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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.

Polarization is a key characteristic of party systems, but scholars disagree about how polarization relates to the number of parties in a system. Different authors find positive, negative, or null relationships. This relationship is what one would expect if parties were drawn randomly from a super-population with an effective sample size somewhere between the effective and raw number of parties. I test this claim using multiple datasets which report party positions and seat shares, before extending my analysis to consider vote-level polarization, the range of positions, and polarization in presidential and parliamentary regimes. My work extends the Taageperaan research agenda of building interlocking networks of equations relating key quantities of electoral and party systems.

Scholars studying electoral systems have consistently found that single-member plurality elections tend to constrain the number of parties operating in a polity to a much greater extent than multimember proportional representation systems. This article tests this hypothesis in the post-communist context by examining the effects of proportional representation and single-member district elections on the number of parties in five postcommunist states. It is shown that some postcommunist states, most notably Poland and Hungary, have followed the standard pattern of party consolidation over time in reaction to incentives of electoral systems, while others, most notably Russia and Ukraine, have not. The author argues that the different effects of electoral systems can be attributed to different levels of party institutionalization found in postcommunist states.These findings have policy implications. Under conditions of extreme party underdevelopment, the electoral system that promotes the use of party labels—proportional representation—may be more effective than the plurality system in constraining the number of parties, provided a legal threshold is used. This runs counter to the conventional wisdom that plurality elections offer the greatest constraint on the number of parties.

To date, electoral systems are conceptualised as setting an 'upper bound' to, or defining a 'carrying capacity' for, the number of parties or lists, and their effect is assessed at the district level. This article adds to the empirical study of electoral systems by analysing a vast database of district-level electoral returns. The argument focuses on the demand and supply of viable electoral candidates, which are conditioned by the interplay of strategic entry (by the party rank and file) and strategic voting (by the electorate). Drawing on a database of almost 18,000 electoral districts taken from 15 West European countries, the empirical analysis yields a number of insights: most specifically, (1) district magnitude only becomes binding and effective when a higher social demand meets a lower carrying capacity of the electoral district; (2) the provision of upper tiers undermines the emergence of Duvergerian equilibria within the primary electoral districts. Adapted from the source document.

Abstract. Duverger's propositions concerning the psychological and mechanical consequences of electoral rules have previously been examined mainly through the lens of district magnitude, comparing the properties of single–member district plurality elections with those of multimember proportional representation elections. The empirical consequences of multimember plurality (MMP) rules, on the other hand, have received scant attention. Theory suggests that the effect of district magnitude on the number and concentration of parties will differ with regard to whether the allocation rules are plurality–based or proportional. I test this theory by drawing on a uniquely large–sample dataset where district magnitude and electoral formula vary but the basic universe of political parties is held constant, applying regression analysis to data from several thousand Hungarian local bodies elected in 1994 consisting of municipal councils, county councils, and mayors. The results indicate that omitting the variable of electoral formula has the potential to cause significant bias in estimates of Duvergerian consequences of district magnitude. In addition, the analysis of multi–member plurality elections from the local election dataset reveals counter–intuitively that candidate and party entry may increase with district magnitude under MMP, suggesting important directions for future investigation of MMP rules.

This note helps to explain how cabinet-level concentration of power is constrained by party level concentration of seats. Arend Lijphart's Patterns of Democracy (1999) measures concentration of executive power by the frequency of `minimal winning and one-party cabinets' (MW/OP), and party concentration by the effective number (N) of legislative parties. In his factor analysis, these highly correlated indices are the central features that distinguish consensual from majoritarian systems. The present study establishes a quantitative logical relationship leading from N to the major component of MW/OP, so as to explain the reasons behind Lijphart's empirical observation. The note analyses separately the frequency of various types of cabinet coalitions that Lijphart's book has lumped together. It also offers a new way to visualize the effective number of legislative parties, as twice the minimal number of parties needed to form a minimal winning coalition.