Heather Stoll,
"Dimensionality and the number of parties in legislative
elections," Party Politics, 17 (May, 2011), 405429.
[Available at http://ppq.sagepub.com/content/vol17/issue3/
]
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
(postWorld War II) partydefined dimensionality of
political competition using four measures,
 Table 2. The estimated
OLS coefficients for models 16
 Table 3. The estimated
marginal effect for permissive (nonmajoritarian) 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 partydefined
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)
