ect of variance in district magnitude on party system in fl ation

We argue that variance in district magnitude affects party system inflation by shaping the process of withinand cross-district coordination. First, at the stage of within-district coordination, electoral systems with large magnitude variance generate different party systems across districts, with larger districts having more fragmented party systems with a greater number of parties. Second, at the stage of cross-district coordination, district party systems dissimilar to each other make it more difficult for elites from different districts to engage in the projection of district parties onto national-level parties. This in turn leads to the inflation of the number of parties at the national level. Through numerical simulations and an observational study, we demonstrate that variance in district magnitude is positively associated with party system inflation. Party system inflation refers to the extent to which the number of parties at the national level is higher than the average number of parties at the district level (Cox, 1999; Kasuya and Moenius, 2008; Moenius and Kasuya, 2004). When electoral support is homogeneous throughout a country, the same parties will be able to realistically compete for seats in all, or most, districts in the country. In such a case, party system inflation tends to be lower because the party system in each district resembles the party system of the entire country. By contrast, when support for different parties is unequally distributed across districts, there is high variation in party systems across districts, which leads to a large discrepancy in the number of parties at the national level and the average number of parties at the district level, i.e., party system inflation. In practice, the inflation of a party system is determined by a twostep process through which citizens' preferences are converted to the formation of national-level parties: withinand cross-district coordination (Cox, 1999; Ferree et al., 2014). In the first step, withindistrict coordination among voters and district elites affects the party system in each district. District magnitude is one of the most important determinants of within-district coordination and the number of district parties (Cox, 1997; Duverger, 1954; Potter, 2014; Singer and Stephenson, 2009). In the second step, cross-district coordination, or strategic interaction among elites from different districts, conditions how district party systems are projected onto the party system at the national level (Chhibber and Kollman, 2009; Hicken, 2009). In short, the combination of withinand cross-district coordination determines party system inflation at the national level. While we know much about the effect of electoral institutions on within-district coordination among district-level actors (Singer and Stephenson, 2009), what is largely missing in the literature is an investigation of how electoral institutions affect the incentives of crossdistrict coordination. In fact, the existing studies on cross-district coordination often focus on the role of non-electoral institutions, such as federalism, bicameralism, and presidentialism (Chhibber and Kollman, 2009; Hicken, 2009). As a result, we lack a theory about how electoral institutions influence the merging of district party systems to nationallevel party systems. This paper fills this gap by arguing that electoral systems shape not only within-district but also cross-district coordination. However, the feature of electoral institutions that affects the latter is different from the one influencing the former. While district https://doi.org/10.1016/j.electstud. 2018.04. 016 Received 16 February 2017; Received in revised form 17 April 2018; Accepted 20 April 2018 ∗ Corresponding author. E-mail addresses: joanbarcelosoler@wustl.edu (J. Barceló), tmuraoka@wustl.edu (T. Muraoka). 1 Some authors provide a complex conceptualization of party nationalization. On one side, Morgenstern and Swindle (2005) and Morgenstern et al. (2009) suggest a two-dimensional conceptualization of party system nationalization: static—the extent to which a party's level of support at any point in time is homogeneous across districts—and dynamic—the extent to which a party's support levels increase or decrease in unison across districts over time. On the other side, Kasuya and Moenius (2008) provide a two-dimensional conceptual map of party nationalization consisting of two factors: inflation—the extent to which the average size of the district-level party system is inflated to the national level—and dispersion—the extent to which each district's party system contributes to the size of the national-level party system varies across districts (Kasuya and Moenius, 2008, 127). Since the arguments regarding the nature of party competition are tied to party competition at a single point in time and have a more direct connection to the aggregation in the number of parties, we focus on the static and inflation concepts of party system nationalization, for which we simply use the term party system inflation. 2 This argument strictly follows the theoretical framework proposed by Cox (1999), Ferree et al. (2014), and Moenius and Kasuya (2004), which states that elites at the district level organize parties in each district first and then combine some of these district parties into large national parties. Other scholars try to understand party system formation using an alternative approach starting from the national level and working down to the district level (see, e.g., Shugart and Taagepera, 2017). Electoral Studies 54 (2018) 44–55 Available online 01 May 2018 0261-3794/ © 2018 Elsevier Ltd. All rights reserved. T magnitude is the primary factor shaping within-district coordination (Cox, 1997; Duverger, 1954), variance in district magnitude conditions cross-district coordination. Electoral systems in different countries have different variances in district magnitude depending on how legislative seats are allocated to each district (Kedar et al., 2016; Monroe and Rose, 2002; Taagepera, 2007). For example, countries with a nation-wide district, like Israel and the Netherlands, do not have variation in district magnitude simply because electoral competition is held under the single district. Similarly, there is no variation in district magnitude in countries with single member district plurality (SMDP) systems, where every district has one legislative seat, as is the case in India and the United States. By contrast, other countries exhibit great variation in the size of districts. Under proportional representation (PR) systems, the most commonly used system in Europe, some districts have only a few seats while others have a large number of seats. In these countries, there is wide variation in the ways in which seats are distributed to each district, leading to different variance in district magnitude. For instance, in Portugal (2009), the size of a district ranges from 2 to 47, whereas in Norway (2009), it ranges only from 4 to 17. As a result, the former has larger magnitude variance than that of the latter. We argue that variance in district magnitude affects the inflation of the party system through two mechanisms that condition the process of withinand cross-district coordination. First, at the stage of withindistrict coordination, large variance in district magnitude generates considerable variation in coordination incentives in each district. Voters and district elites in smaller (larger) districts have stronger (weaker) incentives to engage in district-level coordination. Such variation in coordination incentives results in the formation of different party systems across districts, with larger districts having more fragmented party systems with a greater number of parties. Second, at the stage of cross-district coordination, different party systems created at the first stage make coordination beyond district boundaries more difficult. Party systems in larger districts are more likely to contain parties that would not gain seats if their districts were smaller. Since voter support for these parties is confined to certain permissive districts, these parties have little incentive to participate in cross-district coordination. The presence of parties that are not competitive in all districts hinders the effort of cross-district coordination, thereby making the projection of district parties onto national-level parties less effective. What results from this process is poor linkage between district and national party systems (Cox, 1999) and inflation of the latter. To test this argument, we rely on two strategies. First, we conduct a simulation exercise to illustrate the effect of variance in district magnitude on party system inflation in a fully controlled environment. The simulation results show a strong positive association between magnitude variance and party system inflation (i.e., poor cross-district linkage). Second, we continue our empirical examination by testing our hypothesis with observational data from 36 elections. The empirical results confirm our theoretical argument, revealing the same pattern as the simulations. Compared to countries with lower variance in district magnitude, countries with higher variance in district magnitude are more likely to have greater party system inflation at the national level vis-à-vis the average number of parties at the district level. The rest of this paper proceeds as follows. The following two sections discuss the existing literature on coordination mechanisms and party system inflation and present our theoretical expectation. The third section describes our empirical strategies. The fourth section tests our argument with simulated data in a fully controlled environment. The fifth section is the empirical part of the study, where we present our findings based on real-world data from 36 elections. The final section concludes the argument. 1. Theoretical background Party system inflation is a