Explaining the effective number of parties: Beyond the standard model

Accepted Manuscript Explaining the effective number of parties: Beyond the standard model Marc van de Wardt

PII:

S0261-3794(15)30043-3

DOI:

10.1016/j.electstud.2016.11.005

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JELS 1799

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Electoral Studies

Received Date: 21 September 2015 Revised Date:

30 August 2016

Accepted Date: 8 November 2016

Please cite this article as: van de Wardt, M., Explaining the effective number of parties: Beyond the standard model, Electoral Studies (2016), doi: 10.1016/j.electstud.2016.11.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Explaining the effective number of parties: beyond the standard model

Department of Political Science University of Amsterdam

1018 WV Amsterdam The Netherlands

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[email protected]

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Nieuwe Achtergracht 166

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Marc van de Wardt

Abstract

This study casts new light on the conditions determining the effective number of parties in

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elections. The state-of-the-art mostly considers the interaction between the permissiveness of the electoral system and social heterogeneity, labelled the standard model. This study argues that we should move beyond the standard model and also consider voters’ short term ideological

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preferences as well as the diversity of issues on the party system agenda. Moreover, the effects of these variables are expected to be conditioned by electoral system permissiveness. The

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hypotheses are examined on the basis of a longitudinal dataset containing information on 696 elections that took place in 79 countries between 1945 and 2011. Importantly, the hypotheses could only be confirmed on institutionalized party systems. Keywords: Electoral systems, party systems, political parties, political representation

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1. Introduction

A very important feature of party systems is their effective number of parties.1 As famously ar-

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gued by Schattschneider (1960: 69), ‘organization is the mobilization of bias’. That is, the existing supply of parties determines the issues that are organized into politics and thus who can meaningfully participate in politics. On representational grounds, a higher effective number of parties is therefore desirable. However, the effective number of parties also determines the extent to

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which power is concentrated or dispersed and the number of possible interaction streams between parties. Among other things, these factors affect which government coalitions are formed

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and whether they have a reasonable chance of surviving (Sartori, 1990). Electoral fractionalization also introduces greater complexity for voters in deciding whom to vote for, whether the party they vote for will govern and which policies will ensue (Strom, 1990). Considering these crucial consequences, it is crucial to develop an understanding of the underlying causes of the effec-

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tive number of parties.

The rich tradition of comparative politics explains the effective number of parties contesting elections. These explanations have accumulated into the standard model of party system density, which focuses on the interaction between social heterogeneity, measured in terms of

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ethnic fractionalization, and electoral system permissiveness, denoted by average/median district

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magnitude. The model posits that greater social heterogeneity will only translate into a higher effective number parties if the electoral system is permissive enough (e.g. Clark and Golder, 2006; Neto and Cox, 1997; Ordeshook and Shvetsova, 1994; Stoll, 2011). This captures the essence of Duverger’s (1967: 205) theory that societal forces are behind the multiplication of parties, yet the ballot system acts as a brake or accelerator in determining whether societal forces will have their hypothesized effects (see also Clark and Golder, 206). 1 As opposed to the actual number of parties, the effective number weights parties in accordance with their vote share. If all vote shares are equal, the effective number of parties equals their actual number; yet if, for instance, one of the parties has a huge majority, the effective number will only slightly be larger than one.

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This article casts new light on the conditions shaping the effective number of parties. Acknowledging the decline of socio-structural voting (e.g. Thomassen, 2005) and the correlated increase in electoral volatility (e.g. Dalton and Wattenberg, 2000), the article moves beyond the

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standard model that fixates on longstanding ethnic divisions. The study thus brings in two new variables: fractionalization of voter preferences along the ideological left-right dimension and issue diversity on the party system agenda. In so doing, we gain better insight into how the effective number of parties is affected by demand side (i.e. voters) and supply side (i.e. party system

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agenda). Unlike the standard model indicators, both these variables provide considerable variation between elections.

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Derived from a longitudinal dataset containing information on 696 elections that took place in 79 democratic countries between 1945 and 2011, the present analysis contributes continued evidence for the standard model. Yet it also shows that voter fractionalization and issue diversity shape the effective number of parties. Analogous to the standard model, these effects

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are conditioned by the permissiveness of the electoral system. More fractionalized voter preferences will only translate into a higher effective number of parties for as long as voters vote strategically, which happens when median district magnitude (M) is low. The availability of issues on the party system agenda, in turn, starts shaping the effective number of parties when M is higher

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– thus as soon as the electoral system no longer acts as a brake. This provides empirical evidence

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for Lowery et al.’s (2010) important albeit largely untested claim that issue diversity is the ‘something else’ condition that determines the effective number of parties in permissive electoral systems.

Remarkably, the examined causes, including the standard model, only play out in institu-

tionalized party systems, meaning countries that transitioned to democracy before 1989. A likely explanation of why newer democracies fail to conform to the model is their lack of electoral history and unpredictability of party competition, which leaves party elites and voters more challenged to assess which parties will be viable on election day and to act accordingly (Cox, 1997). 2

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Party elites will enter even in the absence of favourable breeding grounds, and strategic voting is less likely to have its reductive effects on the effective number of parties. The hypotheses were, however, confirmed across a wide array of Western and non-Western established democracies. It

explanatory power.

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2. Explanations of the effective number of parties

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is thus party system institutionalization, not geographical location, that determines the model’s

Parties can be counted in many ways. This article examines the effective number of electoral par-

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ties (Laakso and Taagepera, 1979), a measure that takes into account the relative size of parties. The effective number of parties only equals its actual number if all parties have the same vote share; yet if, for instance, one of the parties has a huge majority, the effective number will only slightly be larger than one. Thus, the effective number should be distinguished from the actual

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number. The first tells us about electoral fractionalization and can be used as a proxy for the number of electorally viable parties, while the second counts the number of parties regardless of their electoral sustainability. To determine the carrying capacity of party systems, the state-of-theart – to which this study seeks to add – therefore takes the effective number of parties as the de-

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pendent variable (e.g. Carey and Hix, 2011; Clark and Golder, 2006; Lowery et al., 2010).2

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To explain the effective number of parties, a first strand of literature builds on Duverger (1967) and focuses on the role of electoral institutions (e.g. Cox, 1997; Lijphart, 1990; Rae, 1971; Sartori, 1968).3 Duverger’s law holds that plurality voting, wherein the candidate with the most votes wins an electoral district, will foster a two-party system. Proportional representation (PR), To reach conclusions regarding the carrying capacity of a party system, it makes no sense to give equal weight to all the parties contesting an election. It would be sensible to estimate the UK party system’s carrying capacity as being somewhere around the 3.9 effective parties that contested the latest elections (source: http://www.parlgov.org/explore/gbr/election/2015-05-07/), but not around 66, which is the unweighted number of parties that contested (source: https://en.wikipedia.org/wiki/United_Kingdom_general_election,_2015). 3 In presenting his law that plurality voting produces two-party systems, Duverger (1967: 207-208) also is clearly referring to the effective number of parties. 2

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in turn, is hypothesized to lead to multipartyism. Duverger (1967) offered two causal mechanisms for why plurality voting destroys third parties. In disproportional electoral systems, small parties struggle to convert their votes into seats, the mechanical effect of Duverger’s law, which

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subsequently triggers the psychological effect that ‘instrumentally rational voters eschew wasting their votes on hopeless candidacies’ (Cox 1997: 30).4 Notably, Duverger (1967) stresses that plurality voting leads to a two party-system within the individual constituencies and not necessarily at the country level. In some areas, strong local minorities parties may exist, which explains why

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in cases like Canada, plurality voting fails to produce two-partyism at the country level. Accordingly, Riker (1982: 761) later reformulated the law as: ‘plurality elections rules bring about and

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maintain two-party competition except in countries where […] third parties nationally are continually one of two parties locally […]’. The inclination of voters to vote strategically declines with district magnitude (M), which refers to the number of seats that can be gained in a constituency. The more seats that can be gained, the slimmer the chance that voters will waste their vote

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opting for smaller parties, which, in turn, explains why PR systems foster multipartyism (e.g. Carey and Hix, 2011; Clark and Golder, 2006; Ordeshook and Shvestsova 1994). Examining the effect of strategic voting in various electoral systems, Cox (1997) proposed the M+1 rule as a generalization of Duverger’s propositions. That is, the maximum effective number of parties that

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can exist in a country equals M+1. In other words, in a single member district, the maximum ef-

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fective number of parties equals 2, in two-seats districts it is 3 and so forth. A second strand, from a political-sociological perspective, focuses on the effect of social

heterogeneity. This understands parties as vessels built to represent societal divisions and argues that a more heterogeneous society will produce a higher effective number of parties (Grumm, 1958; Lipset and Rokkan, 1967; Lipson, 1959). More recent studies have operationalized social

4 Consider the example of a voter in the UK who prefers the green party over the labour party. The mechanisms predict that should strategic voting occur, the voter will first decide whether the greens stand a serious chance of winning. Since it turns out a green win would be very unlikely in a single-member district, the voter would then opt for the second choice, labour.

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heterogeneity in terms of a society’s effective number of ethnic groups (e.g. Clark and Golder, 2006; Lowery et al., 2010). A third strand emphasizes the supply side of politics. It does not consider latent societal

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divisions, such as ethnic differences, that could be mobilized by parties, but rather the dimensions of conflict that have actually been built into politics (Lijphart 1984; 1999; Stoll, 2011; Taagepera and Grofman, 1985; Taagepera, 1999). This approach bundles issues on which parties tend to position themselves in a consistent manner into separate issue dimensions, such as the

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economic left-right dimension and the post-materialist dimension. When multiple dimensions are salient, more parties are needed to express these conflicts. Taagepera and Grofman (1985) prof-

parties equals issue dimensions +1.

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fered very specific expectations in this regard, having hypothesized that the number of effective

A fourth, related strand also considers the political supply side, but highlights the diversity of parties’ issue emphases (Lowery et al., 2013). Issue diversity can be conceptualized as how

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narrowly or widely attention for the different issues on the party system agenda is distributed, from complete concentration (all parties emphasize the same issue) to complete diversity (all issues receive equal attention) (Boydstun et al., 2014). Thus, parties can distinguish themselves from opponents on individual issues, which is the main departure from the aforementioned di-

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mensionality approach that a priori subsumes multiple issues into dimensions. As put forward in

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this article, I believe that we should not just focus on issue dimensionality, but also on how parties can set themselves apart from competitors on issues within the same dimension.5 Issue diversity also gets around the methodological stumbling block that the meaning of issue dimensions evolves over time, which makes it problematic to predetermine their structure.

5 Collapsing issues such as education, welfare state expansion and free enterprises into one socioeconomic dimension, together with 19 other issues, reduces the chances for parties to set themselves apart. One might argue that these three issues alone would allow three parties to distinguish themselves: one party that stakes the claim to education (e.g. the Dutch social liberals), one to welfare state expansion (the Dutch labour party) and one to free enterprise (the Dutch liberal party). Yet, for these parties’ survival chances, it also matters how issue attention is distributed across issues within the economic dimension.

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3. Interactions between explanations

So far, I have presented dominant explanations for the effective number of parties as separate

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analytical approaches. However, a growing body of literature suggests that we should focus on the interaction between social and electoral structures, namely, how the electoral system moderates the effect of societal determinants of the effective number of parties. As convincingly argued by Clark and Golder (2006), a purely institutionalist approach fails to reflect Duverger’s

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theory. Duverger (1967: 205) proposes that the influence of the ballot system should be compared to that of a brake or an accelerator. The multiplication of parties results from other factors,

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most notably, aspects of the life of a nation such as ideologies and socioeconomic structure. The ballot system only determines whether these variables will have their hypothesized effects. This compels inquiring which societal factors precisely drive the effective number of parties. Recall that also according to Cox’s (1997) M+1 rule, the ballot system only provides an up-

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per bound to the effective number of parties that can exist and, as such, we should examine what determines whether party systems will reach that upper limit. Furthermore, Cox (1997) found evidence that strategic voting ebbs when M is higher than 5, which means that the electoral system no longer acts as a brake and carries no explanatory power when M is above 5. As argued by

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Cox (1997: 141), something else must reduce the effective number of parties in these systems;

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yet, what that something else is remains a conundrum for the field. Thus, we should not only examine which societal factors explain the effective number of parties, but also at what level of M they play out.

A number of studies has emerged focusing on the interaction between social heterogene-

ity and district magnitude, also known as the standard model of party system density. The standard model posits that social heterogeneity produces a higher effective number of parties as soon as electoral systems are sufficiently permissive (Clark and Golder 2006; Neto and Cox 1997; Orderhook and Shvetsova 1994), that is, when the influence of strategic voting has decreased. To 6

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refer again to the finding of Cox (1997), the influence of strategic voting dwindles when M is higher than 5. In keeping with the standard model, I formulate the following hypothesis:

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Social Heterogeneity Hypothesis (H1). Social heterogeneity only increases the effective number of political parties when district magnitude is sufficiently large, all else being equal.

Moving to the political supply side, Stoll (2011) found evidence that issue dimensionality

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also interacts with electoral system permissiveness. An increase in dimensionality only produces a larger effective number of parties in PR systems. Again, the underlying mechanism is an electoral

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system that acts as a brake. Stoll (2011) assumes that only new parties and already existing electorally marginal parties increase the dimensionality of the party system agenda. As opposed to electorally successful mainstream parties, they are the ones with an incentive to politicize new dimensions of conflict (e.g. De Vries and Hobolt, 2013). Yet, voters will only vote for these par-

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ties and in doing so increase electoral fractionalization (and thus the effective number of parties) when electoral systems are sufficiently permissive. As such, the effect of issue dimensionality on the effective number of parties should only surface in PR systems. Stoll (2011) does not focus on district magnitude, a continuous variable, but includes a dummy that simply distinguishes majori-

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tarian from PR systems. It is still unclear therefore at which value of M the effect of dimension-

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ality plays out. In line with the previous hypothesis, I expect this to happen as soon as the impact of strategic voting fades. This produces the following hypothesis:

Issue Dimensionality Hypothesis (H2). The dimensionality of the party system agenda only increases the effective number of political parties when district magnitude is sufficiently large, all else being equal.

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Finally, Lowery et al. (2010) argue that in permissive electoral systems, when M is higher than 15, the room on the party system agenda will shape the effective number of parties. Since the electoral rules in higher-M systems are very permissive, something else – agenda space –

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should pose limits to the effective number of parties. Whereas Stoll emphasizes voters rewarding issue entrepreneurial parties, Lowery et al. (2013) provide a more general explanation of why a diverse party system agenda matters. They argue that issues can be seen as a raw resource needed by parties to set themselves apart from competitors. Should there be a fragmented issue agenda,

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parties have more opportunities to distinguish themselves in terms of issue salience and policy positions. An anti-immigration party that mobilizes the immigration issue, for instance, not only

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creates space for itself, but also provides new opportunities for other parties to maintain a distinctive identity. Others have to choose whether to emphasize the new issue or not and which position they will adopt towards it (Lowery et al., 2013). Therefore, a more diverse issue agenda should be able to sustain a higher effective number parties once strategic voting no longer acts as

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a brake.

Importantly, Lowery et al. (2013) empirically substantiate their claims by showing that issue diversity increases the effective number of parties in the Netherlands, which due to its extreme M of 150, could be considered a most likely case. To fully test their proposition, in this

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study I also examine whether the party system agenda fails to matter when electoral systems are

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not permissive. Keeping with Lowery et al. (2013), we should find that parties only profit from a more diverse agenda if strategic voting plays little role. This can be formalized as the following hypothesis:

Issue Diversity Hypothesis (H3) Issue diversity of the party system agenda only increases the effective number of parties when district magnitude is sufficiently large, all else being equal.

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4. Bringing voters into the model

The state-of-the-art mainly focuses on electoral institutions and the party political supply side.

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Hardly any attention has been devoted to the demand side, the voters. Although social heterogeneity taps into the latent demand for parties, structural characteristics such as a country’s number of ethnic groups hardly vary over time.

Lack of attention for voters’ ideological preferences does not sit well with the Downsian

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proximity model of party competition. According to Downs (1957), a unimodal or bimodal distribution of voters’ left-right positions will produce a two-party system, while a multimodal dis-

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tribution will produce multiparty systems. In spite of this being a formal model, it is surprising that up until now, the demand side has hardly been taken into account in the effective number of parties literature.

Remarkably, Lago and Martinez (2011) link the phenomenon of new party entry to de-

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mand on the electoral market. They argue that as on an economic market, market failure can exist in electoral terms when political demands shared by a significant number of individuals are left unsatisfied. In such instances new parties are likely to emerge. By the same token, I expect that more effective parties can be sustained when the electoral market is more diverse. Greater

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fractionalization along the left-right dimension leaves more potential electorates sizable enough

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to sustain parties with sufficient votes. Again, I expect the effect of voter preferences to be moderated by the permissiveness of

the electoral system. Yet, contrary to H1, H2 and H3, fractionalization should matter at low levels of M, when strategic voting plays a role. A concentrated voter distribution should only translate into a lower number of effective parties in conjunction with strategic voting. In instances of a concentrated distribution, some parties will be confronted with very small potential electorates. Still, I expect voters sharing the ideological position of these parties to be discouraged from voting for them only if they perceive them as standing no chance of gaining representation. When 9

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electoral systems are permissive enough, however, the psychological effect will not be triggered, implying that these voters will vote sincerely, even if their party has only a small potential elec-

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torate. This hypothesis can be formalized as follows:

Voter Fractionalization Hypothesis (H4). A more fractionalized voter distribution only increases the effective number of parties at low values of district magnitude, all else being

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equal.

Figure 1. Samples of disagreement scores over left-right voter self-placements To illustrate, figure 1 presents six examples of voter distributions observed in the sample.

The maximum level of fragmentation was encountered during the 2003 Israeli elections, which corresponds to a rectangular distribution of left-right preferences. In turn, voter demand was most concentrated during the Argentinian 1991 elections (figure 1, lower right graph), as can be seen from the strongly peaked distribution. Seeing as six individual groups of voters make up

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about 10% or more of the Israeli electorate, it seems reasonable to expect the vote to be more fragmented there than in the 1991 Argentinian election. Even though the effective number of parties was indeed higher in Israel than in Argenti-

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na, 7.1 against 3.6, I believe that one cannot infer from the voter distributions alone whether the effective number of parties was higher. The reason the Argentinian voter distribution translates into relatively few effective parties is because of a low median district magnitude of 3. Due to Duverger’s psychological effect, Argentinian voters at the flanks are unlikely to cast a vote for an

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extremist party. With such a small potential electorate, these parties do not stand much chance of winning a seat in an electoral constituency. Consider, however, what would have happened if the

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Argentinian 1991 electoral system were very proportional. In that case, voters at the flanks would also have had an incentive to vote sincerely, resulting in a higher effective number of parties.

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5. Institutionalized versus non-institutionalized democracies

To the best of my knowledge, earlier studies on the effective number of parties did not examine how party system institutionalization affects the explanatory power of the model. To justify their case selection, Ordeshook and Shvetsova (1994: 102) argue that ‘the relationships between the

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number of parties and electoral laws concern the properties of systems in equilibrium’, yet they

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do not back up this argument with empirical proof. Neto and Cox (1997: 156) stress that their sample does include ‘many third-world democracies’, yet there is no apparent relationship between being a third world country and having a weakly institutionalized party system.6 Demonstrating how the explanatory power of the standard model diminishes once coun-

tries that transitioned to democracy in the 1990s are included, Clark and Golder (2006) get closest to showing that party system institutionalization matters. In this study, however, I employed a

6 For instance, the supposed third world countries Colombia, Venezuela and India qualify as established democracies according to Lijphart’s (1999: 50) definition.

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split-sample design, which reveals the precise effects of different explanations of the effective number of parties in institutionalized as well as non-institutionalized regimes. Building on Cox’s (1997) theory of strategic entry, I expect that my hypotheses will only

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be confirmed in institutionalized party systems. Formulating the boundaries of his theory, Cox (1997: 157) stresses that would-be third-party candidates are only deterred from entering elections by disproportional electoral laws if it is clear who will ‘bear the brunt of strategic voting’. Notably, voters can only vote strategically when, on the basis of their country’s electoral history,

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they have cues about the electoral viability of the different candidates or parties. The fact that it takes time for voters to acquire this information and to become attached to parties explains, for

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instance, why in the new post-communist democracies disproportional electoral systems often fail to reduce the effective number of parties (Moser 1999).7 By the same token, in the absence of clear expectations regarding one’s own electoral viability and the viability of competitors, it is unlikely that entry decision will be influenced by other variables such as voter distribution and

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party system agenda, which set the carrying capacity of party systems. A final hypothesis is therefore formulated as follows:

Party System Institutionalization Hypothesis (H5). H1 through H4 will only be confirmed in

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sufficiently institutionalized party systems.

6. Research design

To test the hypotheses, I compiled a longitudinal dataset containing information on 696 elections that took place in 79 democratic countries between 1945 and 2011. A country is considered as

7 Party system institutionalization lags in post-communist countries due to the absence of a pre-existing civil society and cleavage structure during their transition to democracy (e.g. Bértoa, 2013).

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democratic as soon as it scores a 6 or higher on the Polity IV political freedom scale (see Carey and Hix, 2011). As discussed above, I distinguished between institutionalized and non-institutionalized

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democracies. In accordance with Clark and Golder (2006), democracies are operationalized as institutionalized if they transitioned to democracy (i.e. first received a Polity IV freedom score of 6 or higher) before 1989; all remaining democracies are classified as non-institutionalized.8

I employed a most different systems design (MDSD) expecting to find evidence for H1

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through H4 in institutionalized democracies because of their higher degree of institutionalization, although their geographical location should not matter. Some studies have only focussed on es-

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tablished Western democracies (e.g. Ordeshook and Shvetsova, 1994). There seems to be no good a priori argument, however, for assuming that the effects of electoral rules, cleavages, dimensions of party competition or voter distributions would fail to play out in institutionalized

7. Variables

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non-Western regimes.

The dependent variable is the effective number of parties receiving votes, which is an inverse

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Herfindahl index (Laakso and Taagepera, 1979). A value of 1 means that one party received all

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the votes; increasing values indicate that votes are more evenly spread out over parties. The indices were obtained from Bormann and Golder (2013). The first independent variable, median district magnitude, is obtained from Carey and

Hix (2011). For example, an electoral system with 50 seats across seven districts with the Ms of 2, 3, 3, 5, 6, 14 and 17 produces a median district magnitude of 5.9 Following previous work

An alternative inclusion criterion whereby countries were included from the point they had been democracies for 30 years and onwards yielded very similar findings (see supplementary appendix, section 1, robustness test #1). 9 In instances of a PR system, the median of all PR systems is calculated; in a non-compensatory mixed system, one calculates the median over all districts of any sort; and in a compensatory mixed system, one 8

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(Clark and Golder 2006; Neto and Cox 1997; Orderhook and Shvetsova 1994), I included the natural log of median district magnitude in the model to capture the intuition that the effect of district magnitude becomes smaller as it increases. Supposing that 120- or 150-member districts

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might allow for 20 or 40 effective parties is unreasonable (Ordeshool and Shvetsova, 1994). Similar to Clark and Golder (2006), I used the measure of cultural fractionalization proposed by Fearon (2003) to operationalize social heterogeneity. Contrary to other ethnic fractionalization indexes, this measure is based on a constructivist notion of societal divisions. Ethnic

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groups are distinguished on the basis of divisions that have a strong descent basis and are locally viewed as most consequential. Fearon (2003) relies mostly on religion, although if religious dif-

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ferences are not seen as being most consequential, ethnic groups are distinguished on the basis of other cultural criteria. Notably, this measure also considers the linguistic resemblance factor between ethnic groups. The more linguistically closer the languages spoken by the different groups, the more the fractionalization index will be reduced.

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As for the dimensionality of the party system agenda, I followed Stoll’s (2011) procedure to calculate raw ideological dimensionality over the issues that parties emphasize in their manifestos.10 Issue emphases were derived from the Comparative Manifesto Project (CMP), which is the largest available cross-national and longitudinal dataset on party policy positions (Budge et

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al., 2001; Klingemann et al., 2006; Volkens et al., 2013).

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Issue diversity on the party system agenda was also measured on the basis of the CMP. For each election, I calculated Shannon’s H entropy over the salience proportions attached to

calculates the median of the PR districts only. Like Carey and Hix (2011), I focus on median district magnitude rather than the mean district magnitude because many countries have a large number of small districts and only a few very large districts. Consequently, the average district magnitude can be quite large as compared to the median. 10 The first step of the measure lies in calculating the salience of seven core ideological conflicts: socioeconomic, religious-ethnic, urban-rural, foreign policy, post-materialist and democratic-authoritarian. Issues were assigned to the seven dimensions based on the classification approach proposed by Stoll (2011). Across all the parties participating in an election, I calculated the relative share of quasi-sentences devoted to each dimension. In a second step, the Molinar (1991) procedure was used to weight each conflict by its salience. A higher score on this variable corresponds to higher dimensionality. 14

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each individual issue by all parties participating in the election (Boydstun et al., 2014).11 Thus, unlike Lowery et al. (2013), who determine party system agenda contents on the basis of speeches by the Dutch queen that reflect the issue priorities of government parties, my measure takes

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into account the issue emphases of all parties operating in a legislature.12 Notably, this measure correlates very low (r=.14) with the raw dimensionality measure, meaning that issue diversity and dimensionality capture fundamentally different aspects of the party system agenda.

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Table 1. Definitions and model specification Definitions Effective number of partiest The effective number of parties in the current election t. LogMt The natural log of median district magnitude in the current election t. Cultural fractionalizationt The Fearon (2003) cultural fractionalization score of a country. Issue dimensionalityt The raw ideological dimensionality (Molinar NP) of the party system agenda in the current election t. Issue diversityt The diversity of issues (Shannon’s H) of the party system agenda in the current election t. Voter fractionalization l-r t-1 The fractionalization (Van der Eijk disagreement score) of voter preferences along the left-right dimension based on the available survey waves between election t and election t-1 (including those in the year of election t). Model specification (1) Effective number of partiest = β0 + β1(LogMt) + β2(Cultural fractionalizationt) + β3(Issue dimensionalityt) + β4(Issue diversityt) + β5(Voter fractionalization l-rt-1) + β6(Cultural fractionalization t*LogMt) + β7(Issue dimensionality*LogMt) + β8(Issue diversity*LogMt) + β9(Voter fractionalization l-r t-1*LogMt) + εt

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Finally, the fractionalization of the electorate along the left-right dimension was calculat-

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ed by means of the Van der Eijk (2001) agreement coefficient (A) for ordered rating scales.13

An inverse Herfindahl index (HHI) produced very similar findings (see supplementary appendix, section 1, robustness test #3). However, I opted for Shannon’s H because it is better suited than the inverse HHI to precision at high and low levels of diversity. Shannon’s H is calculated by multiplying the proportion of the agenda that each issue receives by the natural log of that proportion, then taking the negative sum of those products. Since the number of coding categories (i.e. issue) is constant over time, I opt for the non-normalized Shannon’s H (Boydstun et al., 2014). 12 In instances when the CMP’s coding categories have a natural opposite (e.g. references to welfare state expansion versus references to welfare state), I created a salience scale by summing the proportions of positive and negative mentions. For more detail on how the CMP coding categories were transformed into issues, see Greene (2014). Higher values on this variable denote greater agenda diversity, implying that the parties’ issue emphases are more spread out across issues. 13 The agreement coefficient calculates the weighted average of the level of deviation from unimodality that exists in the simple component layers in which any distribution can be disaggregated. Thus, while a Herfindahl index would only consider the sizes of the different electorates located along a distribution, 11

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Agreement was calculated for each available election over respondents’ left-right self-placement on a scale ranging from 1 (left) to 10 (right). Before calculating agreement, I weighted the respondents’ responses if sample weights were available. Data was derived from the Eurobarome-

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ter and the World Values Surveys. All survey waves between election t-1 and t are used to explain the effective number of parties at t.14 In both surveys, the question wording states that ‘in political matters people talk of left and right’ without specifying the meaning of ‘left’ or ‘right’. Consequently, this question captures voter attitudes on a general left-right dimension and not just on

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economic left-right issues. This dimension functions as the most important heuristic for voters and has been labelled the ‘ideological super-issue’ that subsumes a large array of policy issues

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(Pierce, 1999: 30). Thus, focussing on the general left-right dimension enables study of fractionalization throughout the entire sample period, while the substantive meaning of left and right may evolve. I rescaled the agreement measure in the same direction as the hypothesis, so that 1 reflects maximum disagreement (or fractionalization) and 0, maximum agreement (or concentra-

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tion). As seen in figure 1, as disagreement increases the more a distribution conforms to a rectangular shape. A unimodal distribution, in turn, would indicate maximum agreement, as all vot-

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ers have the same left-right position.15

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8. Statistical approach

the Van der Eijk (2001) scale also considers the distance (i.e. level of the deviation from unimodality) between groups. 14 Agreement was calculated over all available survey waves between election t-1 and t to explain the effective number of parties at t. A drawback to this approach is that in a couple of instances this might violate the rule for a cause to precede its consequence. However, since I arrived at the exact same results (see supplementary appendix, section 1, robustness test #2) if only waves that took place between election years are included, I kept to this approach in order to increase the number of elections in the data. Notably, I arrive at very similar results (see supplementary appendix, section 1, robustness test #2), if only waves that took place between election years are included. 15 Hypothetically, the agreement coefficient may also become negative, i.e. A=-1, when 50% of the electorate can be located at each of the scale endpoints. Whether more parties can exist under fractionalization or polarization makes for an interesting discussion, but it must be noted that, empirically, polarized voter distributions did not occur (see figure 1). I therefore refrained from formalizing what would happen to the effective number of parties if agreement dropped below 0. 16

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The model is estimated by means of OLS, with robust standard errors clustered by countries because feasible generalized least squares and panel-corrected standard errors are unfeasible options (for a discussion, see Clark and Colder 2006). Table 1 depicts the model specification.

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Since the hypotheses express expectations regarding the effect of cultural fractionalization, raw dimensionality, issue diversity and the fractionalization of voter demands at specific levels of M, we cannot simply evaluate the statistical significance of the interaction terms in the regression model (i.e. β6, β7, β8 and β9). Instead, I calculated whether the marginal effect of each

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independent variable on the effective number of parties statistically differs from zero along all

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observed values of M. This procedure is explained in detail in Brambor et al. (2006).

9. Results

Table 2 presents the results for institutionalized (models 1-3) democracies and noninstitutionalized democracies (models 4-6). First, I considered the explanatory power of the

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standard model (models 1, 4); in a second step I added the variables capturing the political supply side (models 2, 5); last, ideological demand was included (models 3, 6). Due to the limited availability of public opinion data, a lot of cases were dropped from models 3 and 6 due to listwise

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deletion. The supplementary appendix (section 3) provides an overview of the included elections in the different models.

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Figure 2 maps the marginal effects of the independent variables for increasing values of logM. A positive value on the y-axis implies that the independent variable increases the effective number of parties, while a negative value denotes the opposite. An effect only differs significantly from zero if the confidence intervals (dashed lines) do not entrap the zero line. Figure 3, in turn, presents the predicted number of effective parties (y-axis) for different values of the independent and moderating (LogM) variables, offering a better sense of the magnitude of the effects.

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Table 2. Explaining the effective number of parties Institutionalized democracies Non-institutionalized democracies Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Logged median district magnitude (logM)t 0.307* -0.058 -0.046 1.195 6.895 28.963 (0.158) (1.412) (2.986) (0.782) (7.995) (70.482) Cultural fractionalizationt 1.186 0.298 4.634 5.376 -4.064 15.082 (1.227) (0.980) (3.798) (3.628) (7.275) (19.838) LogMt* Cultural fractionalizationt 1.123 1.694* 0.800 -1.908 1.017 -5.678 (0.781) (0.947) (2.158) (2.250) (2.574) (7.209) Issue dimensionalityt 0.121 0.811 -0.504 -24.118 (0.585) (0.611) (0.952) (52.915) logMt*Issue dimensionalityt -0.100 -0.245 0.612 8.653 (0.190) (0.158) (0.856) (18.612) Issue diversityt 1.386 -0.195 4.261 30.555 (0.969) (1.960) (3.357) (67.443) logM t*Issue diversityt 0.134 0.911 -2.413 -12.886 (0.418) (0.935) (2.377) (26.274) Voter l-r fractionalizationt-1 7.068*** -28.330 (2.297) (49.742) LogMt*Voter l-r fractionalizationt-1 -3.645*** 5.683 (0.691) (15.612) Constant 3.009*** -1.422 -1.807 2.326* -6.665 -49.769 (0.357) (2.959) (6.680) (1.271) (12.172) (181.241) 2 R 0.183 0.312 0.377 0.115 0.131 0.682 N 573 387 151 86 46 11 Note: Robust standard errors clustered by countries in parentheses. * p<0.1, ** p<0.05, *** p<0.01 twotailed. On the basis of table 2, there appears to be little evidence in favour for the Social Hetero-

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geneity Hypothesis (H1), as the interaction between logM and cultural fractionalization is only statistically significant in model 2 (b=1.69). As explained, however, I am primarily interested in whether the marginal effect of social heterogeneity is positive and statistically significant when the electoral system becomes sufficiently permissive. The marginal effects (figure 2, upper left graph) reveal that when logM ranges between 0.7 and 2.4 – that is, when M ranges between 2 and 11 (80 cases in model 3; 274 cases in sample of established democracies) – higher cultural fractionalization significantly increases the effective number of parties. This is very much in line

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with H1, as the hypothesis holds that ethnic heterogeneity should only have an effect if electoral systems are sufficiently permissive. Accordingly, it makes sense that the effect of social heterogeneity is statistically insignificant when M is below 2. At that point, strategic voting depresses

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the effect of societal divisions. Given Cox’s (1997) finding that strategic voting only starts to ebb when M is higher than 5, it is remarkable that social heterogeneity already starts affecting the effective number of parties in two-member districts. Most likely, this is due to the fact that ethnic minorities tend to be regionally concentrated, meaning that within their constituencies they can

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profit from strategic voting. Other work on the standard model has also shown that the effect of social heterogeneity already sets in earlier (e.g. Clark and Golder, 2006). Notably, the effect of

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cultural fractionalization becomes insignificant when logM is above 2.4 (M>11), although this is mostly due to listwise deletion in the full model. Indeed, the effect persists if marginal effects are calculated on the basis of model 1.16 So overall, there is quite some evidence for the standard model. To get a sense of the magnitude of the effect, figure 3 (upper left graph), demonstrates

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that holding the other variables at their means, the effective number of parties would increase from 3.8 to eight parties if cultural fractionalization increased from its minimum to its maximum in electoral systems where logM=2.4. This is a sizable effect. As for the Issue Dimensionality Hypothesis (H2), the regression coefficients and figure 2 (up-

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per right graph) fail to confirm that dimensionality affects the effective number of parties. For

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each value of logM, the effect of dimensionality entraps the zero line, meaning that the marginal effect never differs from zero. Figure 3 (upper right graph) reveals that the effect of dimensionality on the predicted effective number of parties changes direction if logged district magnitude increases from 0 to 5. Nonetheless, this finding carries little weight since figure 2 has revealed that these effects are statistically insignificant. This does not mean, however, that the party system agenda, seen as the supply side, does not matter. Quite the contrary is true: whereas the interaction between issue diversity on the par16

Available upon request. 19

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ty system agenda and logM is statistically insignificant in models 2 and 3, the marginal effects in figure 2 (lower left graph) provide evidence that a more diverse party system agenda produces a higher number of effective parties when logM ranges between 1.8 and 3.7 – that is, when M

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ranges between 6 and 41 (44 cases in model 3; 159 cases in sample of established democracies). This confirms the Issue Diversity Hypothesis (H3) that greater issue diversity will increase the effective number of parties when the electoral system is permissive enough. Holding all other variables at their means and assuming that M equals 41 (logM=3.7), figure 3 (lower left graph) shows

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that the effective number of parties increases from 2.9 to 6.4 if issue diversity moves from its

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1 2 3 4 Log of median district magnitude

5

Marg. effect of issue dimensionality -2 -1 0 1 2

1 2 3 4 Log of median district magnitude

0

1 2 3 4 Log of median district magnitude

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1 2 3 4 Log of median district magnitude

5

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Marg. effect of voter l-r fractionalization -15 -10 -5 0 5 10

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Marg. effect of issue diversity -5 0 5 10

Marg. effect of cultural fractionalization -10 0 10 20 30

minimum to its maximum. Again, this is a very strong effect.

Figure 2. Marginal effects of the independent variables on the effective number of parties (yaxis) for all observed values of logged median district magnitude (x-axis) on the basis of the full model specification (table 1, model 3). A positive value on the y-axis implies that the independent variable increases the effective number of parties, while a negative value denotes the opposite. An effect only differs significantly from zero, in case the confidence intervals (dashed lines) do not entrap the zero line. Finally, table 2 shows that the interaction between voter fractionalization and logM (b=3.6, model 3) moves in the expected direction and that it is statistically significant. In line with

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the Voter Fractionalization Hypothesis (H4), the marginal effects (figure 2, lower right graph) reveal that greater fractionalization only fosters a higher effective number of parties when logM ranges between 0 and 1 – that is, when M ranges between 1 and 3 (32 cases in model 3; 185 cases in

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sample of established democracies). It makes perfect sense that this effect becomes insignificant when M is 3 since a fragmented voter distribution should only contribute to a higher effective number of parties when voters vote strategically, which happens when M is below 5 (Cox, 1997). From figure 3 (lower right graph) we can derive that if logM equals 0 (i.e. M=1) and the other

Pred. eff. number of parties 3 4 5 6 7

Pred. eff. number of parties 3 4 5 6 7 8

.2 .3 .4 .5 Cultural fractionalization

1

LogM=0

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2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 Issue diversity LogM=1.8

1.5 2 2.5 Issue dimensionality

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Pred. eff. number of parties 2 4 6 8 10

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Pred. eff. number of parties 3 4 5 6 7

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disagreement shifts from its minimum to its maximum.

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variables are held at their means, the effective number of parties increases from 1.7 to six if voter

.41

.51 .61 .71 .81 Voter l-r fractionalization LogM=0

LogM=3.7

.91

LogM=1

LogM=5

Figure 3. Predicted effective number of parties based (y-axis) for all observed values of the independent variables (x-axis) on the basis of the full model specification (table 1, model 3). A higher value on the y-axis implies that more effective parties are predicted. The different values of logged median district magnitude are depicted by the coloured lines. Notably, figure 2 shows that greater voter fractionalization will contribute to fewer effective parties when district magnitude is very high – that is, when logM is equal to or greater than 2.9 (M ≥18, 21 cases in model 3; 72 cases in sample of established democracies). This negative 21

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relationship is also plotted in figure 3 (lower right graph) for a hypothetical situation where logM equals 5 (M=150) and all other variables are held at their means. Although I anticipated that the effect of voter fractionalization would become statistically insignificant when strategic voting

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ebbs, it appears that fragmentation, counterintuitively, may limit the effective number of parties when M is high. As shown in figure 4, however, this effect emerges due to listwise deletion. Figure 4 (left-hand graph) plots the predictive margins for high-M (logM≥3) systems. Diamonds depict the cases that could be included in a model that separately tests H4 as well as in model 3

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(the full model); crosses indicate that a case was dropped from model 3 because of listwise deletion. We can clearly see that the effect of fractionalization becomes negative for high-M elections

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because the Israeli 2003 elections were omitted from the full model. The right-hand graph depicts the marginal effects when H4 is tested separately without the other variables that produce listwise deletion. As anticipated, the effect of voter preferences becomes insignificant at higher levels of M. Therefore, the empirical evidence in favour of a negative effect of voter fractionali-

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zation at high values of M is not robust. Still, the fact remains that in some rare instances, most notably in the case of the Netherlands, we find increasing fragmentation corresponding with a lower effective number of parties. In the conclusion and discussion I offer an explanation as to

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why.

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Figure 4. Left graph: predicted effective number of parties (y-axis) for increasing levels of voter fractionalization (x-axis) when logM=3 or higher. Right graph: marginal effects of voter fractionalization on the effective number of parties (y-axis) for all observed values of logged median district magnitude (x-axis) when H4 is tested separately without the variables producing listwise deletion

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Finally, the insignificant interaction effects in models 3 through 6 reveal that none of the hypotheses are confirmed for non-institutionalized party systems. In the supplementary appendix

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(section 2), I present the marginal effects plot. As can be seen, the independent variables fail to matter regardless of the value of logM. In line with the Party System Institutionalization Hypothesis (H5), explanations of the effective number of parties only surface if party systems are institutionalized.

10. Conclusion and discussion

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Parties are key actors in democracies, making it imperative to learn about the conditions determining their effective number. Existing explanations mainly focus on the interaction between social heterogeneity and electoral system permissiveness (Clark and Golder, 2006; Lowery et al.,

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2010; Neto and Cox, 1997), namely, the standard model of party system density. Through this study I sought to develop a better understanding of the role of voters’ ideological preferences and the structure of the party system agenda. Both variables are important given the changes that are taking place among electorates. The decline of socio-structural voting and increased electoral

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volatility (e.g. Thomassen, 2005), in particular, suggests that we look beyond longstanding societal divisions, as the standard model posits. What is more, parties have reacted to electoral de-

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alignment by engaging in issue competition (Green-Pedersen, 2007). They go up against each other over the contents of the issue agenda, selectively emphasizing the issues on which they have a handling advantage and downplaying those favouring their opponents. Contents and structure of the party system agenda can thus change rapidly over time, meaning it is critical to

selves.

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develop a better understanding of how issues can act as a resource for parties to sustain them-

This study’s pooled time-series analyses, based on 79 countries from 1945 onwards, provide convincing evidence that district magnitude conditions the effect of ethnic heterogeneity,

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agenda diversity and fragmentation of voters’ left-right preferences: social heterogeneity and

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greater issue diversity on the party system agenda increase the effective number of parties when electoral system are sufficiently permissive. It must be emphasized, however, that social heterogeneity already starts increasing the effective number of parties when strategic voting still takes place (M<5), while the effect of issue diversity emerges when district magnitude is higher (M=6). The latter provides evidence for Lowery et al.’s (2010) largely untested claims that issue diversity determines the carrying capacity for parties in permissive electoral systems where strategic voting no longer matters. In turn, more fractionalized voter preferences will only increase the effective number of parties as long as voters vote strategically – that is, when M is low. Notably, the hy24

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potheses could only be confirmed for institutionalized democracies, Western and non-Western. This strengthens the conception that it is electoral history, understood as parties and voters having clear expectations, rather than geographical location that determines the explanatory power

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of our models. This study sought to surpass the standard model, offering a more complete picture of the forces affecting the effective number of parties in institutionalized democracies at different levels of district magnitude. Still, it also raises questions for further research. It remains a challenge to

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understand why in very proportional electoral systems like the Netherlands, more concentrated left-right preferences among electorates yield more effective parties. One potential explanation is

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given by resource partitioning theory, which explains why markets often appear to be partitioned between two non-competing subpopulations of market-centre generalists and peripheral specialists. If resources are concentrated in the centre of a market, concentration among generalist organizations will increase, leaving very few large generalists to dominate the market. Yet, at the

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same time, this makes room for specialists at the edges of the market (e.g. Carroll, 1985; Popielarz and Neal, 2007).

One could argue that mainstream parties can fruitfully be viewed as generalists and niche parties as specialists. Thus, when an electoral systems is permissive and voters’ left-right prefer-

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ences are concentrated, the party system could become partitioned into a few large mainstream

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parties catering to the dense centre of the voter distribution and numerous niche parties that offer more extreme position and/or emphasize issues that cannot easily be subsumed in the leftright dimension (Meguid, 2005). This could explain why in permissive electoral systems where niche parties are less likely to suffer from strategic voting, a concentrated voter distribution could actually increase the effective number of parties. The Netherlands (M=150), for instance, has witnessed the emergence of an increasing number of niche parties, such as a green party, an animal rights’ party, two Protestant parties, a pensioners’ interest party and various right-wing populist parties. It would therefore be interesting to study resource partitioning in party systems. Ad25

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ditionally, the question of how the effective number of parties relates to entry and exit decisions among parties deserves further attention. The effective number of parties that can live is determined by the carrying capacity of a party system (e.g. the ballot structure and the other variables

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considered by this study), but this does not tell whether party numbers are supressed through increased mortality or inhibited entry.

The results also have societal implications. They lead to arguments such as (a) despite concentrated left-right preferences, electoral minorities should also be represented; (b) parties

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should be able to act as vessels representing societal divisions; and (c) a more diverse party system agenda should sustain more effective parties. If a country values the representativeness of its

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electoral system, it should opt for a district magnitude of at least 6 because then condition (a) (b) and (c) are accounted for. But as they say, there is no such thing as a free lunch: a higher district magnitude goes hand in hand with electoral fragmentation, which could threaten government stability. Therefore, it is important that this study shows precisely how different independent var-

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Sozialforschung (WZB).

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Manifesto

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Supplementary appendix This appendix presents additional information regarding several tests that were carried out to assert the robustness of the findings (see section 1). Furthermore, it presents the marginal effect

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plots for non-established democracies, as these were omitted from the manuscript in order to save space (see section 2). Lastly, it provides a detailed interview of the elections that were included in the different analyses (see section 3).

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Section 1

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To recap, the manuscript provides evidence in favour of the Social Heterogeneity Hypothesis (H1), the Issue Diversity Hypothesis (H3) , the Voter Fractionalization Hypothesis (H4) and the Party System Institutionalization Hypothesis (H5). H1, H3 and H4 hypotheses posit that the effects of cultural heterogeneity, issue diversity and voter fragmentation along the left-right dimension are conditioned by the logged median district magnitude (M). H5, in turn, proposes that the aforemen-

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tioned hypotheses will only be confirmed in institutionalized democracies. Since H5 proved to be true, the robustness tests focus on institutionalized democracies only. Finally, I will only present the marginal effects, as in contrary to regression coefficients from interactions, these show pre-

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cisely for which values of the moderating variable (logged median district magnitude), the independent variable has a statistically significant effect on the dependent variable (effective number

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of parties). For a detailed explanation see Brambor et al. (2006). I carried out the following tests to ensure that the findings are robust against: (1) an al-

ternative operationalization of institutionalized democracies, (2) only including public opinion data that was gathered in between election years, and (3) an alternative operationalization of issue diversity. Each of these tests produced essentially similar findings, which strengthens the validity of the conclusions in the manuscript. Let me discuss each of these test in turn.

1. Alternative operationalization of established democracies 32

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In line with Clark and Golder (2006), democracies are operationalized as institutionalized in case they transitioned to democracy (i.e. first received a Polity IV freedom score of 6 or higher) before 1989, whereas all remaining democracies are classified as non- institutionalized. So this

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would entail that also countries like Argentina and South-Korea that transitioned to democracy shortly before 1989 will be included in the analyses. Since the hypotheses are more likely to play out in institutionalized democracies, I also ran the models on a case selection that only considers

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a democracy as established from the moment it has been a democracy for at least 30 years.

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Figure 1. Marginal effects of the independent variables on the effective number of parties for increasing values of logged median district magnitude (full model specification) Notes: 90% confidence intervals

On the basis of a full model specification (N=110), examining all the hypotheses simul-

taneously, figure 1 shows that this analysis produces very similar findings as those presented in figure 2 of the manuscript. Notably, the effect of issue diversity (bottom-left) becomes even stronger within this most-likely case setting, since in contrary to the manuscript, the effect also persists when logM is above 3.7, thus when M is higher than 41. 33

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2. Only including public opinion data gather in between elections

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Agreement over voters’ left-right preferences was calculated over all available surveys waves in the World Values Surveys (WVS) and Eurobarometer (EB) surveys between election t-1 and t to explain the effective number of parties at t. To maximize data availability, also waves that took place in the same year as election t were included. Unfortunately, exact data on the month of

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fieldwork is unavailable in WVS and this information is also difficult to find for all the EB waves that are being considered. Therefore a drawback of this approach is that in a couple of instances

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− when public opinion data is gathered in election year t, but coincidentally after the elections −

the rule for a cause to precede its consequence might be violated. So in this robustness check, I demonstrate that all else being equal, the Voter Fractionalization Hypothesis (H4) also holds when public opinion data gathered in elections years is excluded. All else being equal (N=124), figure 2

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depicts a very similar patterns as in the manuscript (see manuscript, figure 2, bottom-right). Given that I arrive at very similar results if waves that took place in election years are excluded, I included these elections in the analyses presented in the manuscript to increase the number of elections. That is, some countries only carried out public opinion surveys in election

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124 to 153.

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years. Including these elections enabled me to increase the sample size of the full model from

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Figure 2. Marginal effects of voter fragmentation on the effective number of parties for increasing values of logged median district magnitude (full model specification) Notes: 90% confidence intervals 3. An alternative operationalization for issue diversity

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Boydstun and her co-authors (2014) provide good arguments why one should calculate issue diversity by means of Shannon’s H instead of an inverse Herfindahl index (HHI). They demon-

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strate that Shannon’s H more consistently captures changes in attention diversity due to its higher sensitivity when diversity is very high or low. Since previous research on the effect of issue diversity relied on the HHI, however (Lowery et al., 2013), I also tested the Issue Diversity Hypothesis (H3), utilizing the HHI. All else being equal (N=151), figure 3 below shows that this produces very similar findings as those presented in the manuscript (see manuscript, figure 2, bottom-left)

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Section 2

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Figure 3. Marginal effect of issue diversity of party system agenda on the effective number of parties for increasing values of logged median district magnitude (full model specification) Notes: 90% confidence intervals

Since the hypotheses could not be confirmed for non-established democracies, I refrained from

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presenting the marginal effect graphs in the manuscript to save space. Instead these are present-

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ed below. Figure 4 depicts the results when the hypotheses are evaluated separately. This is done because a very limited number of cases have observations on all the variables of interest (N is 11 in the full model). In turn, figure 5 presents the results based on the full model. As can be seen from figure 4 and 5, the effects of the independent variables are either statistically insignificant for all values of district magnitude, or the effect is in the opposite direction. Agenda diversity (figure 4, bottom-left) only increases the number of effective parties when M is low, whereas it should surface when M is high. And voter-left right fractionalization should exert a positive effect when M is low instead of a negative effect when M is high (figure 4 and 5, bottom-right). 36

5

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Marg. effect of issue dimensionality -2 0 2 4 6

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Figure 4. Marginal effects of the independent variables on the effective number of parties for increasing values of logged median district magnitude in non-established democracies (separate models) Notes: 90% confidence intervals

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Marg. effect of issue dimensionality -100 -50 0 50 100

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Figure 5. Marginal effects of the independent variables on the effective number of parties for increasing values of logged median district magnitude in non-established democracies (full model specification) Notes: 90% confidence intervals

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Section 3 Appendix 1. Elections included in model 1-6, table 2

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Elections 1983,1985,1987,1989,1991,1993,1995,1997,1999,2001,2003,2005,2007,2009,2011 1946,1949,1951,1954,1955,1958,1961,1963,1966,1969,1972,1974,1975,1977,1980,1983,1984,1987,1990,1993,1996,1998,2001,2004,2007,2010 1949,1953,1956,1959,1962,1966,1970,1971,1975,1979,1983,1986,1990,1994,1995,1999,2002,2006,2008 1946,1949,1950,1954,1958,1961,1965,1968,1971,1974,1977,1978,1981,1985,1987,1991,1995,1999,2003,2007,2010 1985,1989,1993,1997,2002 1986,1990,1994,1998,2002,2006,2010 1949,1953,1957,1958,1962,1963,1965,1968,1972,1974,1979,1980,1984,1988,1993,1997,2000,2004,2006,2008,2011 1993,1997,2001,2005,2009 1958,1960,1962,1964,1966,1968,1970,1974,1978,1982,1986,1990,1991,1994,1998,2002,2006,2010 1948,1953,1958,1962,1966,1970,1974,1978,1982,1986,1990,1994,1998,2002 1947,1950,1953,1953,1957,1960,1964,1966,1968,1971,1973,1975,1977,1979,1981,1984,1987,1988,1990,1994,1998,2001,2005,2007,2011 1979,1984,1986,1988,1990,1992,1994,1996,1998 1985,1988,1991,1994,1997,2000 1948,1951,1954,1958,1962,1966,1970,1972,1975,1979,1983,1987,1991,1995,1999,2003,2007,2011 1973,1978,1981,1986,1988,1993,1997,2002,2007 1990,1994,1998,2002,2005,2009 1974,1977,1981,1985,1989,1989,1990,1993,1996,2000,2004 1985,1991,1996,2001,2006,2011 1989,1993,1997,2001 1957,1962,1967,1971,1977,1980,1984,1989,1991,1996,1998,2004,2009 1948,1951,1954,1957,1961,1965,1969,1973,1977,1981,1982,1982,1987,1989,1992,1997,2002,2007,2011 1949,1951,1955,1959,1961,1965,1969,1973,1977,1981,1984,1988,1992,1996,1999,2003,2006,2009 1948,1953,1958,1963,1968,1972,1976,1979,1983,1987,1992,1994,1996,2001,2006,2008 1962,1967,1972,1976,1980,1983,1989,1993,1997,2002 1952,1953,1955,1958,1960,1963,1967,1969,1972,1976,1979,1980,1983,1986,1990,1993,1996,2000,2003,2005,2009 1976,1982,1983,1987,1991,1995,2000 1946,1948,1952,1956,1959,1963,1967,1971,1972,1977,1981,1982,1986,1989,1994,1998,2002,2003,2006,2010 1946,1949,1951,1954,1957,1960,1963,1966,1969,1972,1975,1978,1981,1984,1987,1990,1993,1996,1999,2002,2005,2008,2011 1999,2003,2011 1949,1953,1957,1961,1965,1969,1973,1977,1981,1985,1989,1993,1997,2001,2005,2009 1989,1994,1999 1987,1992,1995,1998,2001 1976,1979,1980,1983,1985,1987,1991,1995,1999,2002,2005,2009,2011

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Country name Argentina Australia Austria Belgium Bolivia Brazil Canada Chile Colombia Costa Rica Denmark Ecuador El Salvador Finland France Germany Greece Greek Cyprus Honduras India Ireland Israel Italy Jamaica Japan Mauritius Netherlands New Zealand Nigeria Norway Panama Philippines Portugal

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Model 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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1988,1992,1996,2000 1977,1979,1982,1986,1989,1993,1996,2000,2004,2008 1948,1952,1956,1958,1960,1964,1968,1970,1973,1976,1979,1982,1985,1988,1991,1994,1998,2002,2006,2010 1947,1951,1955,1959,1963,1967,1971,1975,1979,1983,1987,1991,1995,1999,2003,2007,2011 1966,1971,1976,1981,1986,1991,1995,2000,2001,2002,2007,2010 1983,1987,1991,1995,1999,2002,2007,2011 1945,1950,1951,1955,1959,1964,1966,1970,1974,1974,1979,1983,1987,1992,1997,2001,2005,2010 1946,1948,1950,1952,1954,1956,1958,1960,1962,1964,1966,1968,1970,1972,1974,1976,1978,1980,1982,1984,1986,1988,1990,1992,1994,1996,1998,2000,2002,2004,2006,2008,2010 1989,1994,1999,2004,2009 1963,1968,1973,1978,1983,1988,1993,1998,2000 1949,1953,1957,1961,1965,1969,1972,1976,1980,1983,1987 1946,1949,1951,1954,1955,1958,1961,1963,1966,1969,1972,1974,1975,1977,1980,1983,1984,1987,1990,1993,1996,1998,2001,2004,2007,2010 1949,1953,1956,1959,1962,1966,1970,1971,1975,1979,1983,1986,1990,1994,1995,1999,2002,2006,2008 1946,1949,1950,1954,1958,1961,1965,1968,1971,1974,1977,1978,1981,1985,1987,1991,1995,1999,2003,2007,2010 1949,1953,1957,1958,1962,1963,1965,1968,1972,1974,1979,1980,1984,1988,1993,1997,2000,2004,2006,2008,2011 1947,1950,1953,1953,1957,1960,1964,1966,1968,1971,1973,1975,1977,1979,1981,1984,1987,1988,1990,1994,1998,2001,2005,2007,2011 1948,1951,1954,1958,1962,1966,1970,1972,1975,1979,1983,1987,1991,1995,1999,2003,2007,2011 1973,1978,1981,1986,1988,1993,1997,2002,2007 1990,1994,1998,2002,2005,2009 1974,1977,1981,1985,1989,1989,1990,1993,1996,2000,2004 1996,2001 1948,1951,1954,1957,1961,1965,1969,1973,1977,1981,1982,1982,1987,1989,1992,1997,2002,2007,2011 1949,1951,1955,1959,1961,1965,1969,1973,1977,1981,1984,1988,1992,1996,1999 1948,1953,1958,1963,1968,1972,1976,1979,1983,1987,1992,1994,1996,2001,2006,2008 1960,1963,1967,1969,1972,1976,1979,1980,1983,1986,1990,1993,1996,2000,2003,2005 1946,1948,1952,1956,1959,1963,1967,1971,1972,1977,1981,1982,1986,1989,1994,1998,2002,2003,2006,2010 1946,1949,1951,1954,1957,1960,1963,1966,1969,1972,1975,1978,1981,1984,1987,1990,1993,1996,1999,2002,2005,2008,2011 1949,1953,1957,1961,1965,1969,1973,1977,1981,1985,1993,1997,2001,2005,2009 1976,1979,1980,1983,1985,1987,1991,1995,1999,2002,2005,2009,2011 1992,1996,2000 1977,1979,1982,1986,1989,1993,1996,2000,2004,2008 1948,1952,1956,1958,1960,1964,1968,1970,1973,1976,1979,1982,1985,1988,1991,1994,1998,2002,2006,2010 1947,1951,1955,1959,1963,1967,1971,1975,1979,1983,1987,1991,1995,1999,2003,2007,2011 1983,1987,1991,1995,1999,2002,2007,2011 1945,1950,1951,1955,1959,1964,1966,1970,1974,1974,1979,1983,1987,1992,1997,2001,2005,2010 1948,1952,1956,1960,1964,1968,1972,1976,1980,1984,1988,1992,1996,2000,2004,2008 1983,1996,2007 1995,1999,2002,2006,2008 1974,1977,1978,1981,1985,1987,1991,1995,1999,2003,2007,2010 2000,2006

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South Korea Spain Sweden Switzerland Trinidad and Tobago Turkey United Kingdom United States of America Uruguay Venezuela West Germany Australia Austria Belgium Canada Denmark Finland France Germany Greece Greek Cyprus Ireland Israel Italy Japan Netherlands New Zealand Norway Portugal South Korea Spain Sweden Switzerland Turkey United Kingdom United States of America Australia Austria Belgium Canada

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1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3

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1973,1977,1979,1981,1984,1987,1988,1990,1994,1998,2001,2005,2007,2011 1995,1999,2003,2007,2011 1973,1978,1981,1986,1988,1993,1997,2002,2007 1990,1994,1998,2002,2005,2009 1981,1985,1989,1989,1990,1993,1996,2000,2004 1973,1977,1981,1982,1982,1987,1989,1992,1997,2002,2007,2011 1976,1979,1983,1987,1992,1994,1996,2001,2006,2008 1983,1990,2000,2005 1977,1981,1982,1986,1989,1994,1998,2002,2003,2006,2010 1999,2005,2011 1997,2009 1985,1987,1991,1995,1999,2002,2005,2009,2011 1992,1996 1986,1989,1993,1996,2000,2004,2008 1982,1998,2002,2006,2010 1991,1999,2007,2011 1991,1999,2002,2007,2011 1974,1974,1979,1983,1987,1992,1997,2001,2005,2010 1996,2000 1991,1996 1991,1995,1999 1991,1994,1997,2001 2000 1996,1998,2002 1992 1978,1982,1986,1990,1998,2002 1992,1995,1999 1946,1951,1956 1999,2003 1990,1994,1998,2002 1999 1993,1995,1998,2002 1992,1996,2000 1994,1998,2002 1993,1998,2002 1994,1999 1992,1997,2002 2000 1998,2001 1992,1996,2000

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Denmark Finland France Germany Greece Ireland Italy Japan Netherlands New Zealand Norway Portugal South Korea Spain Sweden Switzerland Turkey United Kingdom United States of America Bangladesh Benin Bulgaria Croatia Czech Republic Czechoslovakia Dominican Republic Estonia France Guatemala Hungary Indonesia Latvia Lithuania Macedonia Madagascar Malawi Mali Mexico Moldova Mongolia

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3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

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1990,1996,2001 1993,1998 1980,1985,1990,2001 1991,1993,1997,2001 1996,2000 2000 1994,1998,2002 1952,1956,1960,1960,1965,1970,1977,2001 1998 1992,1992,1995,1996,2001 1991,1994,1997,2001 2000 1996,1998,2002 1992,1995,1999 1946,1951,1956 1990,1994,1998,2002 1993,1995,1998,2002 1992,1996,2000 1994,1998,2002 2000 1998,2001 1991,1993,1997,2001 1996,2000 1994,1998,2002 1952,1956,1960,1965,1970,1977 1997 1998 1999 1998 1998 1998,2002 2000 1997 2000 1998

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Nicaragua Paraguay Peru Poland Romania Serbia & Montenegro Slovakia Sri Lanka Taiwan Thailand Bulgaria Croatia Czech Republic Estonia France Hungary Latvia Lithuania Macedonia Mexico Moldova Poland Romania Slovakia Sri Lanka Bulgaria Czech Republic Estonia Hungary Latvia Macedonia Mexico Poland Romania Slovakia

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4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6

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References

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All references are listed in the manuscript

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