(Page 2 of 22) - Ideological Space Dimensionality and the Number of Competitors authored by Stoll, Heather.

are often given only supporting roles to play in the above stories, a problem that is even more acute
in the empirical analyses. This is surprising given the large body of literature linking institutions to
the number of parties competing in elections (e.g., Cox 1997). At the empirical level, quantitative
tests of these hypotheses have for the most part not moved beyond description. For example,
standard errors for estimated regression coeﬃcients are provided by neither Taagepera and Grofman
(1985) nor Taagepera and Shugart (1989). Further, all existing studies test their hypotheses using
one of the variants of Lijphart’s (1981, 1984, 1999) measure of issue dimensionality, the validity of
which has been questioned elsewhere (Stoll 2004, 2005).

This paper attempts to address these issues. Theoretically, we take a ﬁrst step towards ﬂeshing

out earlier arguments. To begin, we distinguish between what we call the raw and eﬀective ideo-
logical dimensionality. We then hypothesize that the raw dimensionality is positively related to the
number of parties, but that this relationship is conditional upon the restrictiveness of the electoral
system. Empirically, we provide rigorous tests of these arguments. Using an original time series
cross-sectional data set of legislative post-war elections in advanced industrial democracies, which
includes at its core a new measure of ideological space dimensionality, we ﬁnd empirical support
for our hypotheses. Raw dimensionality interacts with electoral system restrictiveness (speciﬁcally,
with the proportion of seats distributed in an upper tier) to positively shape electoral fractional-
ization in legislative elections after controlling for other political institutional variables. However,
this relationship cannot properly be viewed as causal. Moreover, the substantive signiﬁcance of
raw dimensionality is dwarfed by that of one of the political institutional variables, the size of the
upper tier.

We initially deﬁne the key independent variable of ideological dimensionality; develop hypothe-

ses about the relationship between this variable and the dependent variable of the number of parties;
utilize a new measure of dimensionality and an original time series cross-sectional data set to test
our hypotheses; and then conclude.

Deﬁnitions, Deﬁnitions: All About Dimensionality

At an abstract level, the paper’s key independent variable is the number of salient, fundamental
conﬂicts

structuring competition between political parties in advanced industrial democracies,

which we will call the particized dimensionality. These cleavages are salient and hence particized
because they appear on the party-deﬁned political agenda: over the course of an electoral campaign,
parties implicitly take positions on them, mostly notably in electoral platforms (also known as
manifestos).

Four additional features of the deﬁnition employed in this paper deserve note. The ﬁrst three

pertain to the types of cleavages that we consider potentially salient. First, we focus on ideological
conﬂicts: latent conﬂicts that provide links across the substantive policy issues on which parties

We use the terms ‘cleavage’, ‘conﬂict’, and ‘dimension’ interchangeably throughout, reﬂecting both usage in the

literature and our own belief that that they are all appropriate labels for the same abstract concept.

The same conﬂicts are likely, but not guaranteed, to drive both political debate between elections and the

production of public policy. While systematic evidence of the former is spotty due to the practical diﬃculties
involved in collecting such data, evidence does exist in support of the latter (see, for example, Klingemann et al.
1994). Hence, by implication if not by direct evidence, we should feel reasonably conﬁdent that the between-election
set of particized cleavages is linked both to the set of cleavages generated during the election campaign, the focus of
this paper, and to public policy.