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Heather Stoll, "Dimensionality and the number of parties in legislative elections," Party Politics, 17 (May, 2011), 405-429. [Available at ]

First paragraph:
What is the relationship between the number of political parties competing in legislative elections and the dimensionality of the space that structures political competition? Several scholars have postulated that the former is a function of the latter. For example, Lijphart (1984, 1999) has argued that a positive association exists between the number of parties and what he calls the number of issue dimensions. Others have proposed similar if more complicated hypotheses (e.g. Taagepera, 1999; Taagepera and Grofman, 1985; Taagepera and Shugart, 1989). All have found empirical support for their arguments.

Figures and Tables:
Table 1. The average (post-World War II) party-defined dimensionality of political competition using four measures,
Table 2. The estimated OLS coefficients for models 1-6
Table 3. The estimated marginal effect for permissive (non-majoritarian) and restrictive (majoritarian) electoral systems.
Appendix 1 Measuring raw ideological dimensionality
Appendix 2 Countries and elections

Last Paragraph:
(Second paragraph of Conclusion) We began by arguing that how we conceptualize dimensionality has important implications for its relationship with the number of electoral parties, and we offered a three fold schema for doing so. Most importantly, we distinguished between what we called the raw and the effective party-defined dimensionality, where the former simply counts the number of conflicts or dimensions that are salient to political parties and the latter counts only those salient conflicts that are independent once party positions are taken into account. We then argued contrary to the literature that there is a mathematical relationship between the effective dimensionality and the number of electoral parties: the effective dimensionality must always be less than or equal to the number of electoral parties minus 1. This makes it unsurprising that the literature has found a strong relationship between the number of electoral parties and Lijphart's (1984, 1999) measure of dimensionality, which is a measure of the effective dimensionality. However, such a finding does not convey any new information of interest because it primarily confirms the mathematical relationship that follows from the variables' definitions. Moreover, within these deterministic bounds, exploring this relationship involves theorizing simultaneously about party positions and conflict salience - a difficult task (e.g. Laver and Hunt, 1992)

Last updated April 2011