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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.]

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.

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.

This paper develops a novel argument as to the conditions under which new political parties will form in democratic states. Our approach hinges on the manner in which politicians evaluate the policy implications of new party entry alongside considerations of incumbency for its own sake. We demonstrate that if candidates care sufficiently about policy outcomes, then the likelihood of party entry shouldincreasewith the effective number of status quo parties in the party system. This relationship weakens, and eventually disappears, as politicians' emphasis on "office-seeking" motivations increases relative to their interest in public policy. We test these predictions with both aggregate electoral data in contemporary Europe and a data set on legislative volatility in Turkey, uncovering support for the argument that party system fragmentation should positively affect the likelihood of entry when policy-seeking motivations are relevant, but not otherwise.

This paper proposes a new method to evaluate the number of relevant parties in an assembly. The most widespread indicator of fragmentation used in comparative politics is the "Effective Number of Parties", designed in 1979 by M. Laakso and R.Taagepera. Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of "relevant"parties. This index however produces misleading results in single-party majority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sartori's definition of relevance, without requiring additional information (such as policy positions) in its construction. We thus advocate for the use of our "Effective Number of Relevant Parties"in future comparative research.

This paper proposes a new method to evaluate the number of relevant parties in an assembly. The most widespread indicator of fragmentation used in comparative politics is the "Effective Number of Parties", designed in 1979 by M. Laakso and R.Taagepera. Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of "relevant"parties. This index however produces misleading results in single-party majority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sartori's definition of relevance, without requiring additional information (such as policy positions) in its construction. We thus advocate for the use of our "Effective Number of Relevant Parties"in future comparative research.