Party system nationalization

Abstract

The existing measures of party system nationalization and territorial heterogeneity of electoral support, including the Gini-based system-level nationalization score and its complements, can be inappropriate in those research contexts where, as it is in the study of federations, the territorial structure of the state is a substantively important factor of political development rather than one of the possible levels of electoral data aggregation. This problem can be solved by using a normalized version of the Gini coefficient. Alternatively, it is possible to use a new measure, the index of party system nationalization proposed in this study. While both the normalized Gini-based index and the new measure fully satisfy all theory-inspired requirements and yield similar results, the new measure may be preferable because of its relative computational simplicity and intuitively easy understanding.

Keywords

federations measurement party system nationalization political parties

Introduction

Party systems vary in the degree to which there is an equal distribution of party votes across territorial units. A major concept that enables political scientists to capture this variation is party system nationalization. The mainstream definition of this concept is quite straightforward: a party system is fully nationalized if the shares of the vote received by each of the political parties do not vary from one territorial unit of the country to another, and it completely lacks nationalization if each party receives electoral support in only one of many units. There are varying degrees of nationalization in between these extremes. For a long time, research on party system nationalization was focused primarily on the formation of national electorates, with nationalization processes representing ‘a broad historical evolution toward the formation of national electorates and party systems’ leading to the progressive disappearance of ‘peripheral and regional specificities’ (Caramani, 2004: 1). This stream of research, initiated by the studies of party system nationalization in the United States (Stokes, 1967; Vertz et al., 1987), received a continuation in several pioneering comparative inquiries published in the 1970s through the 1990s (Ersson et al., 1985; Hearl et al., 1996; Rose and Urwin, 1975). Yet the decisive breakthrough in comparative research on party system nationalization occurred relatively recently, after the almost simultaneous publication of major studies focused on Latin America (Jones and Mainwaring, 2003), Western Europe (Caramani, 2004), and the world’s largest federations (Chhibber and Kollman, 2004). Since then, the somewhat teleological vision of earlier research, with party system nationalization being viewed as a crucial indicator of the maturity of parties and party systems, has been complemented, or even challenged, by a new approach that conceives the territorial heterogeneity of party support as a property that can be sustained in party systems, irrespective of the levels of their maturity, by a combination of structural factors (Brancati, 2008; Chhibber and Murali, 2006; Harbers, 2010; Morgenstern and Swindle, 2005). There is a new and promising stream of research on federalized (Gibson and Suarez-Cao, 2010) and multilevel (Schakel, 2013) party systems.

The purpose of this study is to make a methodological contribution to this stream of research by focusing on the problems of measurement. The available measures of party system nationalization, while being indispensible for the advancement of this research agenda, are still under discussion (Bochsler, 2010; Kasuya and Moenius, 2008), which explains the necessity to re-examine them. In my assessment, the index that is most often used for measuring the spatial homogeneity of party support, the inverse of the Gini coefficient of inequality, in its currently employed form can be inappropriate in those research contexts where, as it is in the study of federations, the territorial structure of the state is a substantively important factor of political development rather than one of the possible levels of electoral data aggregation. This calls for a new measure of party system nationalization. Of course, for the purpose of broad cross-national comparisons it is essential that this measure be applicable to different research contexts as well. It does not have to work only for federations. The study proceeds as follows. The systematic approach to index-building, as exemplified by Taagepera and Grofman (2003), prescribes that in order to build efficient means of measurement it is essential to formulate a set of requirements to be satisfied by them. This is the subject of the first section of this article. In the second section, I describe the available measures, propose an improvement to one of them, and introduce a new approach to measuring party system nationalization. The third section deals specifically with problems stemming from the application of the indices of party system nationalization to the party systems of federal states. In the fourth section, I test the indices on the empirical real-life data. The empirical test allows for resolving some problems left over from the methodological part of the analysis, and serves as a basis for a practical assessment of the convenience of different measures.

The requirements an index should meet

All the requirements formulated below, with the exception of the last one, are of theoretical nature. They are inspired by the methodological literature on measurement in political science (Monroe, 1994; Taagepera and Grofman, 2003) and by more recent studies focused on the measurement of party system nationalization (Bochsler, 2010). The measurement of inequality has been chosen as a principal point of reference for an important substantive reason: essentially, party system nationalization is a concept pertaining to the equality of political parties’ support across territorial units. In this sense, the measures of party system nationalization are closely related to and comparable with several measures of inequality / unevenness widely employed in political science, including the indices of party system volatility and fragmentation (fractionalization). When exposing the theory-inspired requirements, I relate them to the specific research tasks inherent in the study of party system nationalization. It has to be mentioned that there is a sister concept, party system regionalization (Golosov and Ponarin, 1999), which is simply the inverse of party system nationalization both substantively and computationally. In this section of my analysis, in order to avoid confusion, I will refer exclusively to party system nationalization, even though many indices discussed in the subsequent section were built to measure the sister concept.

1. Directness of measurement

As any complex phenomenon, party system nationalization can be measured directly and indirectly. From a theoretical perspective, direct measurement is preferable. Since the subject of measurement is a party system as manifested in election results, direct measures use information about the electoral performance of political parties in individual territorial units either in an untransformed (raw) form or upon elementary transformations such as exponentiation, taking roots, or weighting by rank. Such elementary transformations, if necessary, should be employed on the condition that they allow for preserving as much of the raw data content as possible.

2. Decomposability

Party systems consist of individual components, political parties. An important methodological desideratum (and one of the inequality axioms) is the requirement of decomposability, according to which the measures of complex phenomena should be built in a way that allows for disaggregating them into individual elements. In other words, they should be aggregates of individual-level measures. According to Golosov and Ponarin (1999), Jones and Mainwaring (2003), and several other scholars, one way to achieve this in the build-up of a party system nationalization index is to weight the nationalization score of each individual party, however defined, by its national electoral return, and to sum the resulting values:

N = \sum_{1}^{n} (N^{'} s_{i}),

where N is party system nationalization score, N’ is each of the parties’ nationalization score defined in this or that way, s_i is the size of the i-th party defined as its fractional share of the nationwide vote, and sigma stands for summation. Formula (1) allows for creating a methodological toolkit that includes both individual-party and party-system level measures, and combines them in a logically consistent way.

3. Normalization

The requirement of normalization means that the values of the index vary between 0 and 1 (or 100 percent). Some of the indices widely employed in political science do not satisfy this requirement, and it is possible to argue that in certain cases, such as with the effective number of parties, their inability to meet it is a merit rather than a shortcoming (Golosov, 2010). Yet in the measurement of party system nationalization, the requirement of normalization is unavoidable, because in cross-national research formula (1) can yield meaningful results only if the values of N’ are bounded between 0 and 1.

4. Zero-to-one limit

This requirement is related to the previous one but differs from it. The zero-to-one limit requirement means that for any party system where each of the existing parties receives electoral support in only one territorial unit, which corresponds to the common sense notion of a party system that absolutely lacks nationalization, the values of the index should equal zero. At the same time, for any party system where all parties enjoy absolutely even support across all territorial units, which obviously indicates the utmost of party system nationalization, the values of the index should equal one.

5. Scale invariance

This requirement applies to the nationalization scores of individual parties. In science, scale invariance is a feature of objects that does not change if scales of length, energy, or other variables, are multiplied by a common factor. In application to the measurement of party nationalization, it means that party nationalization scores should not be affected by the levels of these parties’ electoral support. Note that small parties’ ability to survive is often contingent upon the presence of the regional bases of support, which suggests that, empirically, small parties tend to be less nationalized than large parties. This empirical bias, however, should be distinguished from the bias of measurement that can be avoided by fulfilling the scale invariance requirement. Besides, only individual-level scores that meet this requirement can be meaningfully engaged in formula (1).

6. Sensitivity to transfers

According to the Dalton’s principle of transfers, if a small amount of income is taken from one person and is given to another (richer) person, then inequality must increase. If applied to party nationalization, this means that the scores of two parties, one of them receiving 75 percent of the vote in one territorial unit and 25 percent of the vote in the other unit, and the other receiving 50 percent of the vote in both units, should not be equal even if these parties do not receive any support in the remaining territories. In the first case, the value should be smaller than in the second.

7. Practical requirements: computational simplicity and intuitively easy understanding

If lengthy procedures are needed to calculate the values of an index, it stands to reason that an alternative should be found that can be used more handily. The applicability of this requirement is severely limited by the fact that party system nationalization is a rather complex phenomenon that demands complex means of measurement. But it does not necessarily mean that the indices used for measuring party system nationalization have to be prohibitively labor-consuming and difficult to understand.

Assessing the indices against the requirements

The world of the indices that, at this or that time, have been employed for measuring party system nationalization / regionalization, is not very densely populated, and some of the obvious options, such as entropy-based measures (Taagepera and Ray, 1977), have not even been tried in the literature. My experimentation with these measures did not yield superior results, which is why I do not report them. Below, I deal exclusively with the indices available in the literature, and with innovations that, as argued below, can be productively employed as alternatives to the existing measures.

Several measures of party system nationalization proposed in the literature are indirect, thus failing to fulfill the first of the requirements formulated above. There is a family of simple indices defined as percentage shares of electoral districts contested by the given party’s candidates or lists, or territorial units in which they run (Caramani, 2004; Rose and Urwin, 1975). Apart from the fact that territorial coverage is not equivalent to any level of voter support, such an approach can be utterly misleading if applied to those countries where parties have to contest specified numbers of districts as a condition for electoral eligibility, or where elections are conducted in nationwide districts. More sophisticated but also indirect measures developed by Chhibber and Kollman (1998), Cox (1999), and Moenius and Kasuya (2004), jointly referred to as ‘inflation scores’, are derived from the empirical fact that sub-national party constellations are normally less fragmented than national party systems. These measures are based on the quantification of resulting discrepancies with the effective number of parties. Unlike the territorial coverage indices, inflation scores can be fully utilized in comparative research. However, they can be defined only for party systems as a whole, not for individual parties, thus failing on the requirement of decomposability. In the analysis below, I leave aside the indirect measures and fully concentrate on the direct ones.

The direct measures of party system nationalization can be built in a limited number of ways allowing for the quantification of the concepts of inequality and/or unevenness. These ways can be dubbed construction principles. For expositional purposes, the construction principles can serve as a basis for the classification of indices. When describing these principles and their applications, I use the following notation. In all formulas below, n is the number of territorial units, p_i is the percentage share of the vote received by the i-th party in each territorial unit, and ${\overset{ˉ}{p}}_{i}$ is the mean percentage share of the vote received by the i-th party across all territorial units. Sigma stands for summation from the largest (1) to the smallest (n) component.

With the first construction principle, the basic tool for measuring territorial variation in party support is the absolute deviation, defined as

d = \sum_{1}^{n} | p_{i} - {\overset{ˉ}{p}}_{i} | .

The absolute deviation served as a computational core for several measures of party regionalization, including the mean absolute deviation, defined as d/n (Rose and Urwin, 1975), and the so called Lee index, defined as d/2 (Abedi and Siaroff, 2006; Hearl et al., 1996). None of these indices is normalized, and they violate other requirements from fourth to sixth, with the single exception of the requirement of computational simplicity, on which parameter they are superior to all measures discussed below. The normalized index was developed by Golosov and Ponarin (1999) who dubbed it the index of party regionalization (IPR). This index, also known as the index adjusted for party size and the number of parties (Caramani, 2004), is defined as

I P R = \sqrt{\frac{n d}{2 (n - 1) \sum_{1}^{n} p_{i}}} .

Since its invention, the IPR has been continuously used in research on party systems as a measure of individual party regionalization and, upon weighting by party size and summing the products as in formula (1), in the capacity of a system-level index (Caramani, 2005; Knutsen, 2010). This measure fully satisfies the requirements of normalization, decomposability, zero-to-one limit, and scale invariance, but it fails on the requirement of sensitivity to transfers. For any party that receives voter support in only two of many territorial units, transfers between these two units will not be registered, which is an unavoidable consequence of the fact that the IPR’s computational core is the absolute deviation. Note, however, that as the number of non-zero components increases, and as the gap between the extreme values widens, the index does become sensitive to transfers.

The second construction principle is based on the conventional measure of inequality, the Gini coefficient (G). By its algebraic build-up, the Gini coefficient weights the sizes of individual components with their ranks:

G = \frac{2 \sum_{1}^{n} (p_{i} i)}{n \sum_{1}^{n} p_{i}} - \frac{n + 1}{n},

where i stands for the rank from 1 for the smallest component to n for the largest one.

The individual-level party nationalization score of Jones and Mainwaring (2003) is the inverse of the Gini coefficient: PNS = 1 – G. Formula (1) uses the PNS to build a system-level measure dubbed the party system nationalization score (PSNS). This measure satisfies nearly all of the requirements formulated above, but there is an important exception, the zero-to-one limit requirement. One of the peculiarities stemming from the algebraic build-up of the Gini coefficient is that its upper bound, rather than being set at 1 for all constellations with maximum inequality, has an upper limit of (1 – 1/n). Strictly speaking, the Gini-based measures are neither fully normalized nor bounded between 0 and 1, but rather between zero and this upper limit. In order to make them meet the theory-inspired requirements, it is necessary to subject the values of the Gini coefficient to simple additional normalization, which is achieved by multiplying them by n(n – 1) (Deltas, 2003). This, upon some algebraic transformations, yields the following formula for the normalized Gini coefficient (NG):

N G = \frac{2 \sum_{1}^{n} (p_{i} i)}{\sum_{1}^{n} p_{i} (n - 1)} - \frac{n + 1}{n - 1} .

The normalized Gini coefficient has never been tried in research on party nationalization. However, it is important to emphasize that, unlike the untransformed Gini coefficient, it fully satisfies all theory-inspired requirements. The normalized party system nationalization score (NPSNS) can be built on the basis of the NG by employing the same procedure as in the build-up of the PSNS.

The third construction principle is based on one of the basic statistical measures of dispersion, the standard deviation (σ), defined as

σ = \sqrt{\frac{\sum_{1}^{n} (p_{i} - {\overset{ˉ}{p}}_{i})^{2}}{n - 1}} .

Upon a minor adjustment, the standard deviation was used in the pioneering studies of party system regionalization (Ersson et al., 1985; Rose and Urwin, 1975) as the variability coefficient: CV = σ/ ${\overset{ˉ}{p}}_{i}$ . The variability coefficient is not normalized. However, normalization can be easily achieved if we divide the CV by the square root of the number of territorial units, which results in the normalized coefficient of variation (NCV), defined as

N C V = \frac{σ}{{\overset{ˉ}{p}}_{i} \sqrt{n}} .

When closely examining the formula above, I discovered that it can be rewritten in an entirely different shape that makes use of the Herfindahl-Hirschman index of concentration (HH). If expressed on the basis of the raw sizes of components (not absolute shares, which is normally the case), the HH is defined as

H H = \frac{\sum_{1}^{n} x_{i}^{2}}{(\sum_{1}^{n} x_{i})^{2}},

where x_i is the size of the i-th component.

The use of the Herfindahl-Hirschman index for the reformulation of the NCV is possible because the HH is related to the standard deviation (Feld and Grofman, 2007; Golosov, 2010). The HH, conventionally transformed into the Laakso and Taagepera (1979) effective number of parties (ENP = 1/HH), is one of the most widely used aggregate quantities in contemporary political science. Similarly to the Gini coefficient, it is essentially a weighting scheme, with the size of the component serving as its weight. The HH-based alternative formula for the NCV is

N C V = \sqrt{\frac{H H - \frac{1}{n}}{1 - \frac{1}{n}}} (see Appendix 1 for a mathematical proof) .

The new index proposed in this study is derived from the NCV by dividing it by the square root of the Herfindahl-Hirschman index and squaring the quotient. Upon a simple algebraic transformation, this gives the new measure, dubbed the coefficient of party regionalization (CPR):

C P R = \frac{n - \frac{1}{H H}}{n - 1} .

If we replace HH with the full expression, this formula can be rewritten as

C P R = \frac{n - ((\sum_{1}^{n} p_{i})^{2} / \sum_{1}^{n} p_{i}^{2})}{n - 1} .

When using this formula, it is important to take into account that summation is performed not on the shares of the vote received by the given party nationally, as in the familiar measure of party system fragmentation, but rather on the shares of the vote received by this party in each of the territorial units, as in the computation of the IPR and the Gini-based party nationalization score. For example, when computing the value of the index for a party that contests elections in a country consisting of three territorial units and receives 60 percent of the vote in one of the units and 15 percent in each of the remaining units, the CPR is computed as follows:

\begin{matrix} C P R = \frac{3 - ({(60 + 15 + 15)}^{2} / (60 + 15^{2} + 15^{2}))}{3 - 1} \\ = \frac{3 - 2}{3 - 1} = 0.5 \end{matrix}

This is an intuitively plausible score for a party that, while enjoying some support nationwide, still relies on a heavily concentrated regional base. Note that in the computation of the CPR, percentage shares of the vote can be replaced with absolute shares. This does not affect the results and can be handier with certain sets of data.

The CPR fully satisfies all requirements to the measures of party system regionalization. The same applies to its logical complement, the related individual-party measure of party nationalization dubbed the index of party nationalization (IPN). It is defined as 1 – CPR. Formula (1) transforms the IPN into a system-level measure, the index of party system nationalization (IPSN). Among the measures overviewed above, only the NPSNS and the IPSN fully satisfy the theory-inspired requirements. This is why I select these two measures for further examination. However, given that the non-normalized Gini coefficient, transformed into the PSNS, is the measure that is most prominent in contemporary research on party system nationalization, I found it useful to test it as well.

Indices of party system nationalization and the study of federal states

The main difficulty in the quantitative assessment of party system nationalization is that it necessarily involves two different categories of the units of analysis, the political parties, and the territorial units of the country. These units necessarily vary in size. While it is certainly possible to achieve scale invariance on this parameter, the question is, is that desirable? In other words, is it useful to take into account the varying sizes of territorial units’ population when measuring party system nationalization? This problem has been recognized already in the early studies (Ersson et al., 1985). In the recent literature, a stand for measures that take the unequal sizes of territorial units into account has been taken by Bochsler (2010: 16) who argues that ‘using non-weighted measures of territorial homogeneity, electoral strongholds in a small and low-populated administrative unit affect our results equally as strongholds in a large and highly populated unit’ and cites the case of Canada, where he contends it would be inappropriate to view the impact of the small province Prince Edward Island as equal in importance to that of Quebec. Acting on these premises, Bochsler (2010) transforms the conventional PNS index into a new measure that corrects for the unequal sizes of territorial units. Earlier, the non-normalized indices of this kind were proposed by Rose and Urwin (1975) and Ersson et al. (1985).

It has to be recognized that there are research tasks quite consistent with this line of reasoning. If we look at party system nationalization from the perspective of the progressive homogenization of the vote, which was quite characteristic of the early research on the subject, then the peculiarities of the vote in Prince Edward Island should concern us to a lesser degree than the specific vote patterns of Quebec. Indeed, the impact of the Quebecois upon the overall heterogeneity of party support in Canada is much greater. Probably, a perfect solution for such research contexts can be secured by artificially dividing each of the countries under examination into the specified number of units, aggregating the precinct-level data at this level, and using these aggregates for the assessment of party system nationalization. Yet in different research contexts, the vision of administrative divisions as mechanical aggregates of electoral precincts is highly irrelevant. Such is the study of federal states. Consider a hypothetical federation that consists of 11 very unequal units, with half of the population residing in one of them, and the rest in the remaining 10. The sets of parties operating in each of the federal units are entirely different from those of other units. If our purpose is to assess the impact of federalism on the development of this country’s party system, or vice versa, then the primary fact that has to be recognized is that the country completely lacks a nationwide pattern of party competition, and the degree of party system nationalization is zero. In other words, this party system is completely federalized, as was the case with the so called ‘old republic’ in Brazil. This certainly bears important implications for our understanding of this model of federalism. However, the story told by any index that properly corrects for the varying sizes of territorial units will be different. Given the size of the largest unit, such index, however defined, is bound to assume moderate values, indicating some intermediate level of party system nationalization. Yet in the study of federalism, the presence of fully regionalized parties matters irrespective of the sizes of territorial units where they operate.

The above argument applies primarily to the measures of individual party nationalization, such as the NPNS and the IPN. Political parties can be purely regional if they are represented in one federal unit only, or they can enjoy a broader national support. The ability to clearly express this difference lies at the core of the measurement of party nationalization in federal states. True, system-level measures, such as the NPSNS and the IPSN, if built in accordance with formula (1), do appear to vary depending on the sizes of units in which individual parties operate. A purely regional party, even if it receives 100 percent of the vote in Prince Edward Island, reduces the nation-level IPSN score of Canada only by 0.005, while with a purely regional party taking all votes in Quebec the deduction would be 0.26. However, it is important to take into account that in such cases the variation in the values of party system nationalization indices stems not from the varying sizes of territorial units but rather from the varying sizes of parties, as clearly expressed in the indices’ algebraic structure. Thus in a completely regionalized party system, in which purely regional parties take all votes in small and large territorial units alike, the lack of party system nationalization can be properly captured only of we build system-level measures on the basis of individual-level indices that are not adjusted for the varying sizes of territorial units. In general, I can conclude that while in certain research contexts indices that correct for the inequality of territorial units can be useful, the study of federal states does not belong to this category.

From the methodological perspective, there is also the important problem of the level of electoral data aggregation. In nearly every electoral system, the data can be aggregated at the constituency level or, alternatively, at the level of precincts. In federations, there is necessarily one more level, the level of federal units. This level is normally, but not necessarily, higher than the constituency level: as an exception, consider the case when federal elections are conducted in a nationwide electoral district. Obviously, the level of federal units is more appropriate when research goals are directly related to the problematic of federalism, because only in this way the peculiarities of federal units can be properly estimated and analyzed. No less obviously, there is no level of aggregation that is perfect for performing all research tasks. Indeed, the very possibility of choosing different levels of data aggregation makes the means of measurement capable of combining generality and validity by devoting greater attention to context (Adcock and Collier, 2001).

Testing the indices on real-life data

Indices remain abstract until they are tested on real-life data. When making the selection of cases for trial, I pursued the strategy of maximizing the geographical diversity of the sample rather than its chronological scope. The main purpose was to include as many federations that exist in the contemporary world as possible. The selected cases are listed in Table 1. The sample is fairly representative of the general population of the world’s federations as of January 2012. I did not include Nepal, Sudan, and Iraq because of their very limited experience with federalism; the United Arab Emirates and the Federated States of Micronesia because of the lack of party systems; and the Comoros and Ethiopia because of the unavailability or low quality of the electoral statistics. I had to exclude Venezuela because the idiosyncratic pattern of coalition politics in this country makes it extremely difficult to identify the levels of support of individual parties across the federal units. All other federations are included irrespective of their size, levels of economic development, or other factors. In addition, I included two countries that, while not federations in the strict sense of the term, still have systems of multi-level governance similar to federalism, South Africa and Spain. Each of the countries enters the sample with only one election to the lower chamber of the national legislature. Two countries, Germany and Mexico, enter the sample twice. The reason is that both countries employ mixed electoral systems, as a result of which every election produces two different sets of results, one in the plurality section of the electoral system and the other in the proportional representation section. The data sources are reported in Appendix 2.

Table 1.

The descriptive characteristics of the sample.

Country	Federal units	Number of units	Year of elections
Argentina	23 provinces, 1 autonomous city	24	2011
Australia	6 states, 2 territories	8	2010
Austria	9 Länder	9	2008
Belgium	3 regions	3	2010
Bosnia and Herzegovina	2 autonomous entities	2	2010
Brazil	26 states, 1 federal district	27	2010
Canada	10 provinces, 3 territories	13	2011
Germany	16 Länder	16	2009
India	28 states, 7 union territories	35	2004
Malaysia	13 states, 3 federal territories	16	2004
Mexico	31 states, 1 federal district	32	2009
Nigeria	36 states, 1 territory	37	2003
Pakistan	4 provinces, 1 capital territory, federally administered territories (counted as 1 unit)	6	2008
Russia	21 republics, 46 provinces, 9 territories, 1 autonomous province, 4 autonomous districts, 2 federal cities	83	2011
Spain	17 autonomous communities, 2 autonomous cities	19	2011
South Africa	9 provinces	9	2009
St Kitts and Nevis	2 islands	2	2010
Switzerland	26 cantons	26	2011
United States	50 states	50	2008

Sources: See Appendix 2.

Table 1 provides information about the constitutional denominations and numbers of federal units in the included countries and the years of elections. It has to be mentioned that when collecting the electoral data I did not use the category of ‘others’, which practically means that a nationalization score was assigned to every party, however small. Overall, the aggregation was based on 652 individual-level party observations. However, when calculating party nationalization scores for Germany and Malaysia, I counted the CDU-CSU coalition and the Barisan Nasional as single parties because of the arguably consolidated nature of these entities and the lack of intra-coalition electoral competition. Of course, there can be a substantive justification for a different approach. If these coalitions’ constituent parties were counted separately, the results would be sensibly different for Germany and entirely different for Malaysia. This situation is quite illuminative in illustrating one of the difficulties inherent in research on party systems (Wolinetz, 2006), but such difficulties are not to be dealt with in this analysis. The electoral returns of non-party candidates were lumped together on the assumption that from the specific angle of measuring party system nationalization each of them represents one regional party, which renders the disaggregation of this category pointless.

Table 2 gives the values of the indices. The purpose of this exposition is not to arrive at any substantive conclusions regarding party system nationalization in federal states, which certainly requires more extensive empirical research, but rather to assess the reported values of the indices against common-sense expectations based on our already acquired knowledge, thereby resolving several questions left over from the earlier methodological inquiry. One of these questions is whether the noticed deficiency of the non-normalized PNS, the lack of 100 percent limit, affects the results of cross-national analysis. The sample includes only one federation in which there is no national party system whatsoever, St Kitts and Nevis. Each of the islands constituting this small federation has a two-party system that is entirely different from the other island’s pattern of party competition (Lewis, 2002). Another country that has to be recognized as lacking a national party system is Bosnia and Herzegovina where the party systems of the two federal units are almost entirely different. There are several parties that try to cross the boundary, but so far without much success (Hulsey, 2010). Obviously, these two countries should receive very low party nationalization scores. In the case of St Kitts and Nevis, the score should be zero. In fact, however, the relative placement of these two countries by the non-normalized PSNS is such that it rates party nationalization in St Kitts and Nevis higher than in India, and in Bosnia and Herzegovina, at the same level as in Switzerland. Of course, such characterizations are utterly counterintuitive, if not to say entirely flawed. Two other indices reported in Table 2 place St Kitts and Nevis at the bottom of party nationalization rating, followed, as it should be, by Bosnia and Herzegovina. Needless to argue at length, such cases are crucial because one of the primary purposes of index-building is to develop measures that attribute realistic values to all observed phenomena.

Table 2.

The values of the indices.

Countries	Party system nationalization score	Normalized party system nationalization score	Index of party system nationalization
Argentina	0.77	0.76	0.81
Australia	0.86	0.84	0.90
Austria	0.83	0.81	0.88
Belgium	0.54	0.31	0.37
Bosnia and Herzegovina	0.57	0.13	0.15
Brazil	0.62	0.60	0.66
Canada	0.75	0.73	0.81
Germany, plurality	0.84	0.83	0.91
Germany, proportional	0.84	0.83	0.90
India	0.38	0.36	0.39
Malaysia	0.80	0.79	0.82
Mexico, plurality	0.77	0.76	0.83
Mexico, proportional	0.77	0.76	0.83
Nigeria	0.62	0.61	0.67
Pakistan	0.51	0.41	0.46
Russia	0.80	0.80	0.87
South Africa	0.78	0.75	0.80
Spain	0.76	0.74	0.81
St Kitts and Nevis	0.50	0.00	0.00
Switzerland	0.57	0.56	0.59
United States	0.83	0.82	0.90

Sources: See Appendix 2.

The values of the NPSNS and the IPSN are extremely closely correlated (Pearson’s r = 0.999).¹ Even the relative placements of individual countries given by these two indices almost coincide, even though there are three discrepancies: on the parameter of party system nationalization, the IPSN rates Germany (in the plurality section of its electoral system) higher than Australia; Mexico, higher than Malaysia and Argentina; and Canada and Spain, higher than South Africa; while the reverse is true of the NPSNS. However, I failed to find any theoretically consistent or empirically plausible explanation to these very minor discrepancies.² In fact, it is remarkable that the two indices, absolutely different in their algebraic build-up, produce so similar results for a vastly diverse sample of cases. Of course, the sample is very small. In order to exclude the possible small-sample bias, I ran a bivariate analysis on a much larger sample of 652 individual-level party observations. The picture did not change: the values of the party nationalization score and the index of party nationalization for individual parties turned out to be correlated at 0.995 (Pearson’s r). To finalize the series of empirical tests, I extended the scope of inquiry to non-federal states and performed a binary analysis on a set of recent election results from 35 new democracies and electoral authoritarian regimes.³ When constructing the sample, I combined the obvious criterion of data availability with two other priorities, increasing the geographical diversity of the sample and facilitating a comparison between the new measures proposed in this study and a variety of indices developed in the earlier literature. Table 3 reports a matrix that correlates the IPSN and the NPSNS with seven earlier proposed measures: the PSNS as defined above, three different modifications of the PSNS developed by Bochsler (2010), the original inflation score of Cox (1999), and two modified inflation scores of Moenius and Kasuya (2004). In order to provide for full data compatibility, I used the CLEA database (Kollman et al., 2013) as the source of the values of older indices and for my own calculations. The CLEA dataset differs from the data previously used in this study in one important respect: the data is aggregated on the constituency level, not on the federal unit level.⁴ Since the number of constituencies is normally much greater than the number of federal units, this almost completely eliminates previously observed discrepancies between the PSNS and the NPSNS, as a result of which the IPSN is strongly associated with both. Yet in the study of federations, as argued above, the choice of the unit of aggregation is highly consequential. All indices are highly correlated, which indicates that they measure the same phenomenon, albeit in different ways. At the same time, the IPSN and Gini-based indices tend to yield very similar results, while inflation scores form a group of their own, which corresponds to their different build-up.

Table 3.

Correlation matrix for nine indices of party system nationalization (Pearson’s r; n = 35).

	IPSN	NPSNS	PSNS	PSNS_s¹	PSNS_w²	PSNS_sw³	I_1⁴	I_2⁵	I_3⁶
IPSN	1	0.998	0.997	0.941	0.954	0.922	–0.899	–0.855	–0.837
NPSNS		1	0.999	0.939	0.952	0.924	–0.886	–0.837	–0.819
PSNS			1	0.934	0.958	0.916	–0.892	–0.843	–0.826
PSNS_s				1	0.824	0.832	–0.801	–0.778	–0.744
PSNS_w					1	0.918	–0.929	–0.889	–0.891
PSNS_sw						1	–0.839	–0.819	–0.811
I_1							1	0.953	0.921
I_2								1	0.988
I_3									1

1. Bochsler Standardized Party Nationalization Score; 2. Bochsler Weighted Party Nationalization Score; 3. Bochsler Standardized and Weighted Party Nationalization Score; 4. Cox Inflation Score; 5. Moenius and Kasuya Inflation Score; 6. Moenius and Kasuya Weighted Inflation Score.

Note: All correlations significant at 0.01.

Source: CLEA database (Kollman et al., 2013).

Given that both the NPSNS and the IPSN fully satisfy all theory-inspired requirements to the aggregate quantities of this kind, and that the results yielded by the two indices are nearly identical, the question of choice between these alternatives is practical rather than substantive: which of them is easier to use and understand? The core algebraic expression for the NPSNS, formula (3), is rather clumsy and obviously lacks any intuitively comprehensible content. It is usual to explain the meaning of the Gini coefficient, from which the NPSNS is derived, not in algebraic but rather in geometrical terms, as the ratio of the area that lies between the line of equality and the Lorenz curve, which is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth (Gastwirth, 1972). At the same time, the core algebraic expression for the IPSN, formula (4), has a merit of very easy interpretation. Its main component, if rewritten as 1 / HH, is a number-equivalent index that has been for a long time understood as the effective number of components (Blackorby et al., 1982). If a number-equivalent index evaluated for any multi-component system achieves a value of n, we can say that the system is as fragmented as if there were n components of equal size. Thus, substantively, the coefficient of party regionalization can be understood as the difference between the overall number of territorial units and the number of territorial units in which the given party is effectively present, normalized as a result of division by (n – 1). If a party is effectively present in all territorial units, which means that its shares of the vote are equal, then the CPR assumes the value of 0. If the levels of its electoral support are uneven, then the values lie between 0 and 1, because the effective number of territorial units for the given party is smaller than the overall number, and the larger the difference, the greater the values of the CPR. For a party that receives votes in only one territorial unit, the value of the index is necessarily 1. If inversed and built into formula (4), these values determine the system-level scores of the IPSN in an intuitively understandable way.⁵ From the point of view of computational convenience, the Gini coefficient is as highly labor-consuming as any index that involves ranking the units of analysis by size, which is a procedure that has to be performed for each of the parties separately. The calculation of the IPSN does not require the reordering of the data. Thus for practical reasons, the IPSN can be preferable to the NPSNS, even though from the substantive point of view, the two indices are largely equivalent and can be used interchangeably.

Conclusion

My analysis of the measures of party system nationalization has demonstrated that the index most widely employed in contemporary research, the party system nationalization score, can produce misleading results if the number of territorial units in countries under examination is small, which is often the case in the study of federal states. Instead, it is possible to use the normalized version of this index. In addition to the normalized party system nationalization score, the system-level homogeneity of party support can be estimated with a new measure proposed in this study, the index of party system nationalization. While producing values that are very highly correlated with the values of the normalized party system nationalization score, the new index has the merits of computational simplicity and intuitively easy understanding. The utility of fully normalized indices in the study of federal states is greatly enhanced by the fact that in federations the existing territorial structure is not just a level of electoral data aggregation but also a substantively important phenomenon. The boundaries of member states are not mere technicalities. Quite the reverse, they are derived from politically meaningful and highly consequential decisions and continuously shape the electoral arenas of federal states. Thus for the proper study of the party systems of federal states, it is important to use the tools of measurement based on the robust notion of the territorial structure of the state.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

Appendix 1. Conversion of the customary NCV formula into the HH -based formula

We know that $σ = \sqrt{\frac{\sum_{1}^{n} (s_{i} - {\overset{ˉ}{s}}_{i})^{2}}{n - 1}}$ , $H H = \frac{1}{n} + \sum_{1}^{x} (s_{i} - {\overset{ˉ}{s}}_{i})^{2}$ (Golosov, 2010: 173), and ${\overset{ˉ}{s}}_{i} = \frac{1}{n}$ . Then

Appendix 2. Data sources for Tables 1 and 2

Argentina: Ministerio del Interior, http://www.elecciones2011.gov.ar; Australia: Australian Electoral Commission, http://results.aec.gov.au/; Austria: Bundesministerium für Inneres, http://www.bmi.gv.at; Belgium: Direction Générale Institutions et Population, http://polling2010.belgium.be; Bosnia and Herzegovina: Centralna izborna komisija Bosne i Hercegovine, http://www.izbori.ba; Brazil: Tribunal Superior Eleitoral, http://www.tse.jus.br; Canada: Elections Canada, http://www.elections.ca/; Germany: Der Bundeswahlleiter, http://www.bundeswahlleiter.de; India: Election Commission of India, http://eci.nic.in; Malaysia: BERNAMA, http://web7.bernama.com/events/elect2004/; Mexico: Instituto Federal Electoral, http://www.ife.org.mx; Nigeria: Constituency-Level Elections Archive (CLEA), http://www.electiondataarchive.org/; Pakistan: Election Commission of Pakistan, http://www2.ecp.gov.pk/vsite/complete/; Russia: Tsentralnaya izbiratelnaya komissiya Rossiiskoi Federatsii, http://www.izbirkom.ru; South Africa: Independent Electoral Commission of South Africa, http://www.elections.org.za; Spain: Ministerio del Interior, http://www.infoelectoral.mir.es; St Kitts and Nevis: Psephos, Adam Carr’s Election Archive, http://psephos.adam-carr.net/countries/s/stkitts/stkitts2010.txt; Switzerland: Bundesverwaltung Statistik Schweiz, http://www.bfs.admin.ch/; United States: Office of the Clerk of the US House of Representatives, http://clerk.house.gov/member_info/electioninfo/2008/2008Stat.htm. All internet resources were accessed in December 2012 through September 2013.

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