Party system closure and openness

The degree of closure of the governmental arena is a central aspect of the stabilization of party systems, and yet little systematic effort has been devoted to its operationalization. The article proposes a new index, examines its reliability and validity, and reports the ranking of 60 party systems. By redefining the units of measurement we suggest new indicators that are uniform and transparent in their logic of construction, can be applied both to specific government-changes and to time periods, and are sensitive to the degree of change. The article finds a hierarchy among the components of party system closure, dominated by coalition formula. While new and established democracies can both produced closed patterns, the analysis of inter-war European party systems shows that closed systems are less prone to authoritarian takeover. The article demonstrates the power of inertia: the completely closed configurations stand out as the most durable ones.


Introduction
The literature on party system dynamics, and more specifically on party system stabilization, is burgeoning, and yet political science lacks reliable indicators of the stability and predictability of party relations. Comparative research would greatly benefit from indices that travel well across political regimes and allow for statistical analyses.
The lack of effective operationalization has both conceptual and measurement-related reasons. The studies on the change and stability of party systems written in the Rokkanian-(Europe), the realignment-(US), or the Mainwaringian (Latin America) traditions focus on the anchors of parties in the society, and not on the patterns of interactions. The latter phenomenon is emphasized by what could be called the Sartorian school. But Sartori (1976) himself was more interested in the variance among institutionalized systems, and less in the dimension of stability.
This is less true about the central author of the Sartorian school, Peter Mair. His concept of party system closure (Mair, 1996) is one of the most important theoretical innovations in recent party system research. The concept refers to the stability of the interactions of parties in the governmental arena. Party systems are closed if the parties stick to old alliances and if the process of governmentbuilding is confined to a small group of established parties.
While Mair needs to be credited for the invention and the imaginative original operationalization of the concept, there are major problems with the latter aspect, hindering the application of the concept to existing party systems. The present article is aimed at elaborating, operationalizing, and validating the concept of closure and at suggesting indicators that are conceptually and empirically superior to the ones suggested by scholars so far. We demonstrate that the existing operationalizations are incoherent and they misrepresent the actual degree of predictability. We offer indicators that are uniform and transparent in their logic of construction, can be applied both to specific governmentchanges and to time periods, and grasp the degree of change more precisely.
The close examination of a wide array of indicators shows that there is a hierarchy among the components of the latent variable of closure. Governmental formula is the most central element of party system closure, while the pattern of alternation is the least central. Closure is shown to covary with the length of democratic past, but the relationship between democratic consolidation and party system closure does not appear as deterministic.
The first section of this article briefly reviews the literature on the operationalization of party system stability, highlighting also the importance of the latter concept within the field of party politics. Mair's theoretical framework is presented in the second section. After the review of the traditional indicators used to measure systemic closure, we turn to the discussion of their weaknesses and to the presentation of new, improved indicators. Section five sets the objectives of the empirical analysis as well as presenting a new data-set on government formation in Europe since 1848. The final section compares how well these new indicators perform in relation to the ones previously employed, providing a new historical ranking of party system closure in 48 European democracies. The main findings of the article are summarised in the conclusion.

Conceptual background
The stabilization and predictability of party systems appears through a wide variety of indicators in the literature. Some authors rely on the Pedersen index of electoral volatility (e.g. Mainwaring and Scully, 1995), others on the volatility of 'old' parties (Meleshevich, 2007). Some works use the 'effective' number of parties as a proxy (Bielasiak, 2002;Morlino, 1998;Tóka, 1997), others the number of 'splits', 'mergers', and 'name changes' (Welfling, 1973). Indices that reflect the concentration of votes or the ideological distribution of political parties (Krupavicius 1999), the affiliation strategies of politicians and voters (Kreuzer and Pettai, 2003), the difference in vote share between the two largest parties (Birch, 2003), or the progressive enhancement of the proportion of the total vote for political parties over time (Lewis, 2006) are also interpreted as measuring stability and consolidation.
These operationalizations all reflect important aspects of party politics but none of them targets specifically the most crucial aspect of party systems: the pattern of inter-party competition (Sartori, 1976). Mair's index of party system closure, on the other hand, directly follows the interactionbased, Sartorian understanding of party systems. A system is considered to be closed if the protagonists and the patterns of their alliances are stable.
Closed party systems can be regarded as 'strong institutions'. In closed systems the relevant actors -voters, politicians, sponsors, activists, etc -are aware that challenging the existing party labels and alliances entails high costs and they adjust their behavior to these expectations. In closed systems the changes in the social context of parties either express themselves through channels that are external to partysystems or gradually transform the major parties from inside. But they do not alter the menu of core players or the fundamental relations among them. Accountability is more easily exercised in such systems because responsibility can be assigned to few meaningful political units (parties or party-alliances) with long time horizon.
The advantage of open systems, on the other hand, is that they provide better conditions for the rise of innovative forces and they constrain the tendencies towards cartelization. The advantages of open systems are less commonly emphasized in the literature because openness is typically discussed either in the context of new democracies which often carry the double burden of inchoate party politics and fragile political institutions, or in the context of those established democracies that shifted towards openness in the midst of declining trust and turnout. One must acknowledge, however, that the adaptability of party systems, as of any system, requires constant innovation. The disadvantages of openness may outweigh its positive implications, but the net consequences need to be measured and not taken for granted.
While many empirical works in the party system literature (e.g. Kreuzer and Pettai, 2003;Mainwaring and Scully, 1995;Morlino, 1998) are based on the behavior of voters or of politicians, the concept of closure reflects the choices made by parties, and specifically by parties that have governing potential. The advantage of this approach is exactly what seems to be its weakness: it says very little about individual politicians and voters. As closure primarily reflects the choices of parties, it becomes possible to investigate whether these choices affect voters or individual politicians. The more disciplined and consistent are the parties in playing the coalition-game, the more loyalty can be expected from the voters (Mair, 1997).
Parties, of course, interact in other spheres as well, not only in the governmental arena. Alliances can be built also on parliamentary, electoral, regional, international, or policy-making levels (e.g. Bardi and Mair, 2008;Smith, 1990). But there are good reasons to focus on the national governmental coalitions. First, the seizure of governmental power is the principal, even if not the only, prize of party competition. Second, to join a particular government or not is a relatively autonomous decision of a party. Therefore it is more likely to betray the party's fundamental character than the developments in the electoral or policy-making spheres, which are typically less under the control of parties. 1 The present article accepts the fundamental thrust of Mair's (1996) approach, but it refines his conceptual apparatus and replaces the existing indicators, used by Mair and others, with new ones. We suggest indicators of closure that are conceptually well justified, uniform, and transparent in their logic of construction, allow the characterization of both individual governments and time periods, and capture the degree of change precisely.
The three components of closure Mair (1997Mair ( , 2001Mair ( , 2007 proposed three major components of party system closure. The first is alternation in government. In this regard three patterns exist: wholesale-, partial-, and non-alternation. In the first case the incumbent government leaves the office in its entirety and is replaced by a completely different group of parties. The second option materializes when the new cabinet is a mixture of parties from inside and outside of the previous government. The third possibility is marked by a complete absence of alternation, as the same parties remain in exclusive control of government over an extended period of time being displaced neither wholly nor partially.
The second major component of the model, government formulae, shows whether the partisan composition of the governments is innovative or familiar. If there are stable groups of parties that tend to govern together, then familiarity, i.e. closure, prevails. If there is a tendency towards previously unseen party compositions, the system is considered to be open, innovative.
The final component is access to government. The relevant difference on this aspect is between, on one hand, systems in which all parties have the opportunity to participate in government and, on the other hand, configurations in which some of the parties are permanently excluded. Closed governments consist exclusively of parties that governed in the past; the open ones include, or are even dominated by, novices.
Mair was not entirely consistent in his use of the three-component model. In Mair (2007) he introduced the frequency of party composition changes as a fourth component. But we do not include the latter phenomenon into our analyses as it refers more to cabinet stability than to the stability of the structure of competition. In fact, there may be systems (e.g. Bulgaria, Lithuania, or Kosovo) where cabinets tend to change only after elections, but the structure of inter-partisan competition is largely unpredictable; and others (e.g. Belgium, Italy, or inter-war Czechoslovakia) where parties collaborate and compete in a structured manner despite frequent governmental changes. The concept of party system closure was originally invented to capture the stability of partisan interactions rather than the regularity with which the latter takes place.
By assessing these three factors one can determine whether a party system is closed or open (Table 1). Party systems are considered to be open when (1) the alternations of governments tend to be partial, (2) no stable configuration of governing alternatives exists, and (3) access to government is granted to all relevant parties, including newly established ones. It is closed when (1) alternations of governments are wholesale or none, (2) the governing alternatives are stable over a long period of time, and (3) governments are confined to a narrow circle of parties. Malta or the US are clear examples of closed systems, while the Baltic countries tend to be open due to the high frequency of partial cabinet alternation, innovative government-composition, and frequent incorporation of new parties into government.
There is a lack of discussion in the literature about the relationship between the three components. A positive covariation would be in line with the fact that all three components are supposed to be related to the same underlying concept. But since these phenomena are not consequences of closure but components of it, a strictly unidimensional structure is not necessary. Moreover, using ecological systems as analogies, extreme values on all three aspects may be expected to be dysfunctional. Regimes that are completely rigid or open in all regards may not be able to survive. If so, then there could be a certain amount of trade-off between the three components, possibly even producing negative correlations.
The mechanical relationships among the three variables, however, increase the likelihood for a positive covariation. The instance of no-alternation implies familiar coalition formulae and closed access. Open access presupposes innovative cabinet formula and partial or total alternation. Due to these relationships, there can be a certain amount of bias towards positive correlation among the three variables.
One may expect positive correlations also because all three components are part of, and can be under the influence of, the more general phenomenon of party system stabilization. In a sample of 10 countries Enyedi and Casal Bértoa (2011) found that party systems with a low number of parties, stable and relevant party blocs, low electoral volatility, and a high level of polarization tend to have higher party system closure. The positive correlation among the three components may be a result of the impact of these -partly exogenous -variables. Mair does not comment on the relative centrality/ marginality of the three components within the syndrome of closure. On a conceptual basis, and based on historical experiences, the pattern of alternation does not correspond directly to the degree of stability. While the appearance of new parties or of new coalitions of parties implies openness of the system in an unequivocal way, the link between partial alternation and instability is less straightforward. If the incumbent parties have only limited options for partners, for example Christian Democrats can align only with Socialists or with Liberals, as in the classical Benelux pattern, then the predictability of coalitions is relatively high in spite of the partialness of government alternation. Citizens either get a center-left or a centerright government. Partial alternation therefore does not necessarily equal fluidity, contrary to innovative formulae and the inclusion of new parties into the government.

Existing indicators
The concept of party system closure has already inspired a number of party scholars. Some of them used the original measures proposed by Mair (e.g. Linz and Montero, 2001;Müller and Fallend, 2004;O'Dywer, 2006;Rybář, 2004;Toole, 2000), while others developed new, dichotomous, or continuous indicators, and Mair himself kept changing the measures. The original conceptualization suggested a dichotomous operationalization (e.g. Henjak, 2003;Stoychev, 2008): governmental formulae are either innovative or familiar, the governments either include newcomers or not, alternation is either wholesale (i.e. total or none) or partial. Müller-Rommel (2005) applied a score of 0 to no-alternation, innovation, and access; 1 to wholesale alternation, familiar formula, and closed access; and 2 to partial alternation. Enyedi and Casal Bértoa (2011) assigned 0 to partial alternation, innovation, and access; and 1 to wholesale alternation, familiar formula, and closed access.
Some studies (Casal Bértoa and Mair, 2010;Mair, 2007) used continuous variables to grasp the degree of change. For capturing alternation in government Mair (2007) applied Pedersen's (1979) index of electoral volatility to the ministerial turnover (calling it the index of governmental alternation, IGA). Thereby IGA was computed by adding the net change in percentage of ministers (including the prime minister) gained and lost by each party in the cabinet from one government to the next, and then dividing the result by two. Concerning the familiarity/innovation of formulae, Mair's continuous indicator relied on the number of innovative governments as a percentage of all governments in a particular period. 2 Finally, for access Casal Bértoa and Mair created an index of openness (IO) which 'measures the weight new parties have in a particular cabinet as well as the weight such governments (with new parties) enjoy in the party system as a whole' (Casal Bértoa and Mair, 2012: 101). IO is calculated by dividing the number of new governing parties by the total number of governing parties.

Critique of existing operationalizations and construction of new indicators
The operationalizations summarized above have merits, but also considerable weaknesses. Dichotomous measures are obviously crude indicators. A large new party in the government represents a larger rupture with the past than a small one. Therefore, in principle, continuous variables that are sensitive to the degree of change should be preferred. The exact construction of continuous variables requires, however, additional theoretical and empirical justifications. As demonstrated below, the existing continuous variables are all flawed in one way or another. Our effort is aimed at correcting their flaws and suggesting new indices that follow a uniform logic. This common logic implies taking the percentage of minister-changes as the basis for all the three variables. 3 One of the fundamental problems with Mair's original operationalization is the way in which governmentchange is defined. Traditionally, as summarized for example by Müller and Strøm (2000), three criteria are used to indicate a change of government: (1) a change in the partisan composition of the government coalition; (2) a change of the head of government; and (3) new elections. Contrary to this standard, Mair defined individual governments exclusively in terms of changes in partisan composition. As a result, if the same coalition continues after an election Mair has one entry in his dataset for the pre-and post-election period, not two. We agree with Mair's decision not to consider changes in prime ministers as relevant end-points. The significance of the replacement of the PM typically does not reach the weight of a new election or the political relevance of a coalition break-up. PM-changes which are not results of elections and are not accompanied by party-composition-changes tend to concentrate in countries where the position of the premier is less important. Elections, on the other hand, are defining political events as they always give the possibility for the reconfiguration of the party landscape. At each new election the citizens and the political class face a dilemma: to continue with the old patterns or to innovate. Continuity in these cases is therefore noteworthy. The challenge arising from a PM's resignation is typically managed by a small group of politicians within the dominant party, while a national parliamentary election 'tests' the entire society. Therefore, we consider both elections and changes in partisan composition as signaling the end of a government.
There is an additional reason for implementing this modification of the unit of measurement: we want to record instance of 'no-alternation'. As reviewed above, according to Mair's original conceptualization a system should be considered to be closed whenever a particular government stays in power continuously. This plausible logic, however, is not well reflected in the scores of closure if one counts individual government as Mair did because cases of no alternation are non-existent in the dataset by definition. To give an example, India was a particularly closed system during its first two decades of democracy according to the Mair's definition but using his operationalization this cannot be demonstrated as India hasn't experienced a single change of partisan composition during this period.
For characterizing time-spans the literature tends to average the scores of consecutive governments, disregarding how long the governments lasted. We suggest taking the duration of the governments into account by multiplying the characteristics of a particular government by the number of years the government lasted. Closure scores were assigned to specific years too. If the country had more governments in a year then their average was used to characterize the particular year.
As far as other aspects of the counting rules are concerned, we largely follow Mair. 'Grand coalitions', i.e. coalitions bringing together the most relevant parties (e.g. Kiesinger's 1966 or Merkel's 2005 cabinets) are included in our dataset, but non-partisan, acting, in exile, provisional, or technocratic governments are not. To name a few, the latter categories include the Poincaré (1926), Brünning (1930), Churchill (1940 or, more recently, the Tosovky (1998), Georgievski (2001), Monti (2010), Papademos (2011), Oreharski (2013), or Letta (until November 2013) governments. While the frequency of such governments has recently increased, their formation, change, or dissolution responds to very idiosyncratic circumstances, and therefore their inclusion would blur the analysis of the regular patterns of party competition.
We start our counting from the moment a so-called founding government is established, provided that a country is both (1) democratic (see above) and (2) independent. Following Casal Bértoa and Mair (2012), we consider founding governments to be those created by the first free election taking place in a country after regime collapse, independence, or after a revised constitution has been approved by an interim Constituent Assembly (see also Müller-Rommel et al., 2004).
The year when a country ceases to be democratic is excluded, except in those cases when the authoritarian transition was preceded by a change of government or by elections taking place during that year.
So far we have discussed how the units of measurement are defined and what the overall logic behind the proposed operationalizations is. Now we turn to the measurement of the three constituting components.

Alternation in government
As mentioned above, Mair (2007) suggested ministerial volatility as the indicator of alternation. Higher volatility was expected to reflect high closure. The implicit logic behind this operationalization is that the most closed party systems are characterized by a bipolar pattern of competition undergoing regular and complete alternation. The primary example is the classical UK pattern. But consider a stable Social Democratic-Green coalition which is enlarged from time to time with a five percent strong Left-Libertarian party. In such situations continuity prevails and change/surprise is marginal. Using Mair's index one would, however, mistakenly conclude that the system is particularly open and unpredictable as the Pedersen index would amount to a mere five percent.
The bias in the operationalization stems from the fact that only wholesale alternation is recognized as closure and no-alternation is not. Correcting for this bias means that each party-composition change needs to be placed on a continuum between total 4 and no alternation. The degree of stability is indicated by the distance from that endpoint of the continuum (0 or 100) which is further away. If 85% of a government is changed then the case is an instance of almost total alternation. The figure 85 expresses well this high degree of stability. But if only 10% of the ministers belong to new parties, in other words if the government is identical with some previous government in 90%, then stability is even higher than in the previous case. The numeric value assigned to the latter case should be 90, and not 10. Using this logic, each government-change receives a figure that ranges between 50 and 100, the former indicating openness, the latter indicating closure. In order to have the same range (0-100) for the alternation score as for the other two components 50 was subtracted from it and the result was multiplied by 2.

Government formula
Concerning alternation and access (see below), the construction of percentage-based measures is relatively simple. With the familiarity of government formulae there is more complication. It is probably not accidental that no continuous indicator exists in the literature that could be applied to single governments.
In extreme cases the construction of the variable is easy. If the very same combination of parties has already governed together in the analyzed period, there is a 100 percent familiarity. If the government is based on an entirely new combination of parties, the familiarity figure is 0. In the more complicated case when only part of the new government replicates a previous government we suggest using as an indicator of closure the percentage of ministers who belong to the 'familiar' part of the previous government. The contrast needs to be made with the previous government that is most similar in terms of the list of parties to the analyzed government. A cabinet of Communists, Socialists, and Greens is compared to one with Communists, Socialists, Greens, and Populists rather than one with Communists, Socialists, and Liberals.
In case of party mergers we consider the percentage of ministers belonging to each of the merged parties. If a minister cannot be linked to any of the pre-merger parties then he/she is excluded from the counting unless all the merged parties had already been previously in government together.
What shall we do with single party governments? Again, if the party has never governed before, the adequate closure figure is 0 and the formula is innovative. But what if the party used to be part of a coalition? We propose that the previous coalition partners' percentage should be subtracted from 100. If the Social Democrats, who gave 90 percent of the ministers, decide to continue without the Greens, who dominated only one tenth of the government, then closure is high (90). In the opposite case the innovation is considerable, since a small, marginal party turns into the sole government-party. Closure then equals 10. The index of government formula will range between 0 and 100.

Access to government
The existing continuous indicator of access to government (the ratio between the new governing parties and all governing parties, Casal Bértoa and Mair's IO) also needs to be altered, in two ways. First, the values need to be reversed so that they express the degree of closure, in line with the other two components. Second, in order to capture the magnitude of change, the percentage of ministers who are controlled by particular parties should be taken into account, again similarly to the other two indicators. The proposed measure is therefore the percentage of old governing parties. Old governing parties are considered to be all those parties which have already been constituent parts of a previous government. The indicator again varies between 0 and 100. The ministers of a merged party are considered to be 'old' if the predecessor-parties governed before; otherwise they are considered to be new.

The composite indicator of closure
A country's composite closure score will equal the average score of the three variables. Researchers may consider using our index in two further alternative forms. The first is using the standardized versions (Z scores) of the original variables, the second is projecting them onto a 0 to 1 scale. Sometimes it is beneficial to center the variable around the mean, as Z scores do, but then one must consider that the scores will depend on the specific sample used. The 0 to1 alternative is particularly suitable for regression analyses. In the current paper we opted for the 0 to 100 scale because it can be interpreted as percentage of stability and it clearly communicates the message, just as the Pedersen index does, that stability prevails over change.
In summary, the new indicators suggested above (Table 2) have the following characteristics: they (1) are based on the percentage-change of ministers, (2) are continuous, (3) treat no-alternation as a form of closure, (4) apply specific counting rules when calculating the familiarity of the coalition formulae and, last but not least, (5) compute access on the basis of the percentage of ministers belonging to previously governing parties. In contrast to the existing continuous measures, which were constructed according to diverging logic (e.g. Casal Bértoa and Mair, 2012), the indicators proposed above enable the creation of a composite closure score.
Below we calculate both the cabinet-based and the year-based solutions for all the three major alternatives of operationalization: the dichotomous ones (Müller-Rommel, 2005), the continuous ones suggested by the existing literature (Casal Bértoa and Mair, 2010;Mair, 2007), and our two new measures, out of which we recommend for further analyses the year-by-year measure. As a result, altogether six alternative solutions for measuring closure are contrasted.

Goals of the empirical analysis and data-set
The empirical analysis below serves three purposes. The first goal is to learn about the relationships between the three constituting variables of party system closure. To what extent does closed pattern on one dimension imply closure on the other? Which of the three variables is most central for the overall phenomenon of closure? Is a unidimensional conception of party system closure warranted? The second task is to establish whether the index proposed by us has more attractive features in terms of reliability and validity than the existing ones. Finally, the third purpose of the exercise is to provide data about the frequency of closed and open patterns and to establish a ranking of European party systems in terms of closure, opening the way for further studies that treat closure as a dependent or independent variable. In order to achieve these three goals we rely on a new data-set that covers European governments between 1848 5 and 2013.
The dataset comprises European party systems under democratic conditions. We consider a country to be democratic when (1) it has obtained a score of 6 or more in the Polity IV index, (2) elections take place according to universal (at least male) suffrage, and (3) cabinets are formed on the basis of a parliamentary majority. The dataset contains information on cabinet duration, the partisan composition of cabinets, and on the number of ministers belonging to each governmental party. The dataset covers 165 years, 46 European democracies, 64 different historical party systems, 630 elections, 6 and 1483 cases of government formation.
However, before scrutinizing the empirical data we need to make a couple of caveats in relation to the issue of the time-frame. In the analyses below we present data for the entire life-span of 60 European party systems. This implies a very short time period in some instances, for example only two years (from 1946 till 1948) in the case of the first Greek party system, and a longer period in others, such as Denmark (over a century, from 1911 to 2013). This focus on the core dataset will be complemented by the analysis of various subsamples: young (less than 23 years old), inter-war, recent , and East and West European party systems. Investigating multiple subsamples is not only in line with general methodological recommendations aimed at increasing the number of observations (King et al., 1994), it also has the advantage of providing samples within which the age, geographical area, historical era, or length of time of the party systems are held constant and therefore the comparability of the cases is less disputable. Obviously, for most of the actors a governmental formula that hasn't been used for many decades can represent as much change as a completely new formula. Since no obvious temporal threshold can be defined, the best strategy is to examine the relationship on samples with both varying and uniform time frames.

Closure and openness in Europe
The covariation among the three variables is best demonstrated with the help of the government-based dichotomous operationalization. Table 3 shows that out of the logically possible combinations some almost never occur. For example closed alternation, open formula, and closed access was found only in a small minority of the cases. Partial alternation went together with closed formula and closed access somewhat more frequently. Total or no alternation often co-occurred with open formula and open access. The pure types of open and closed patterns were even more numerous. Within the universe of young party systems the most frequent pattern is a mixed one: partial alternation, innovative formula, and governments including no new party. In the overall sample of party systems the completely closed pattern occurs most often.
The counting above does not consider how long the various patterns last. Examining the number of years spent under a particular pattern, we found that the completely closed configuration stands out as the most durable one. Out of the 2032 years taken into account, 1445 (71%) were spent under governments which were, in terms of coalition patterns, copies of earlier governments. The fundamental inertia of European party systems has long been documented in terms of the behavior of citizens and the identity of parties (Bartolini and Mair, 1990), but apparently a similar degree of inertia exists also at the level of government-building.
We found the three variables to be positively related to each other according to all forms of operationalization. But the degree of coherence varied considerably. The reliability analyses and factor analyses (Table 4) showed that formula is the kernel of closure. Formula had in all cases the largest loading on the main factor and contributed  most to the Cronbach alphas. This was the case in the three subsamples as well, again according to all forms of operationalization (data not presented). Alternation and access have been found to be least tightly related. Apparently, party systems that tend to experience partial alternation do not necessarily allow new actors to join the circle of governing parties easily, and open access to government may occur even under the circumstances of total alternation. The weak relationship between these two components undermines the unidimensionality of the construct. These results do not imply, however, that the composite variable of closure lacks internal homogeneity. The variables based on year-by-year measurements are particularly coherent: the factor analyses indicated that they are structured around one principal component, the Cronbach alphas were above 0.7 (the conventional psychometric standard), and the inter-item correlations were around 0.5.
In order to check the inter-temporal reliability of the measures we have compared the closure index of 18 Western European democracies 7 (the relatively stable part of our sample) in 2000 and in 2013. The scores of the two timepoints correlated almost perfectly (between 0.94 and 0.98), indicating that all indices are highly reliable. The mean correlation coefficient for the six scales taking into account all periods was 0.64 (in the sample of new party systems 0.59, of inter-war democracies 0.75, of post-1990 party systems 0.67). The year-based index promoted by the current study correlated on average at 0.62 with the other five constructs (0.57 in the new democracy, 0.75 in the inter-war, and 0.7 in the post-90 sample), indicating the criterion-validity of the index (Adcock and Collier, 2001). The new year-based measure also reflects well the theoretical expectations concerning the internal structure of closure as it shows formula as the most central component and alternation as the least central component of the syndrome.
While the analysis above provides some ground to single out the new, year-based index as the one with the strongest conceptual rationale and most attractive psychometric features, does the index also provide us with valid measurement? This would be an easy question to answer if we had a straightforward theory about the relationships between closure and other phenomena. Closure, as discussed in the introduction, is part of a larger syndrome of stabilization and consolidation. In the literature these concepts are often related to the consolidation of democracy (e.g. Mainwaring, 1999;Morlino, 1998;Pridham, 1990). But some scholars also warn us that above certain levels the degree of institutionalization and stabilization may become irrelevant (Mainwaring and Scully, 1995) or even dangerous (Schedler, 1995) for the democratic quality of a polity. The reason why students of democracy should pay attention to the stabilization of party systems is rather that inchoate systems may be conducive to the breakdown of democracies Mitchell, 2000, 2003). Therefore the most adequate test is to examine the party systems of the inter-war period and check how the indicators of closure help us to predict whether a democracy survived or collapsed.
According to all measures, the democracies with closed party systems survived at a higher rate and the differences between the cases of survival and collapse were statistically significant (below 0.05). The association reached the highest level using our new, year-based measure (Table 5, first row), providing an additional argument for relying on this index in the future. 8 Party system closure can be considered to be the 'necessary condition' for the survival of democracy within the framework of QCA (Ragin, 2008;Schneider and Wagemann, 2012). 9 Among the six indicators, only our new, year-based measure passes the consistency threshold of 0.9 (Table 5, second row). 10 All in all, the association between the two variables appears to be the closest according to the indicators promoted in this article.
As a very last step in demonstrating the differences among the indices, we analyze the actual rankings of party systems. For the sake of simplicity only the three yearbased measures are contrasted. According to the results, as can be seen in Table 6, there is a high degree of similarity between the rankings produced by the various forms of operationalization. The rankings based on the old dichotomous and continuous measures correlate particularly highly with each other, at 0.99. The new index is also closely related to the old dichotomous measure (0.81) and old continuous measure (0.8) indices. All three forms of operationalization place Malta, Switzerland, UK, Greece, In spite of the high correlation among rankings, the new index shows a number of countries (particularly Montenegro, Czechoslovakia, Ukraine, France IV, Albania, and Romania) to be considerably more structured, while others (Turkey, Russia, San Marino, Czech Republic, pre-war Finland, and current Lithuania) are more more inchoate than the older measures. The difference between the scales becomes somewhat more understandable if one zooms in on certain specific regions. Given that the 11 Eastern European new EU states have similar timeframes and since they are the ones that are scrutinized most intensively from the point of view of stabilization, a close look at this region can help us best to make sense of the differences among the three indices. According to all of them the majority of the Eastern Central European party systems appear in the open half of the continuum (Table 7). While Hungary is categorized according to all measures as a relatively closed system, and Latvia as an extremely open one, the ranking slightly differs for the other countries. Within the regional framework the new index (rightmost column) placed Slovenia, Romania, and Croatia higher, and Slovakia, Czech Republic, Bulgaria, Estonia, Lithuania, and Poland lower than the others.
The differences are in line with what the literature tells us about these party systems. Bulgaria and Lithuania are among the least institutionalized systems in the region, with the largest electoral volatility and the highest number of new parties at elections, while Romania and Slovenia have considerably more stable party landscape. The previous operationalizations misplace the latter two party systems because they give too much weight to frequent but only minor changes in government. In Slovenia most governments have been built around the same political parties (e.g. LDS and SD or SLS and SDS, seven times each), but because they often incorporated new (mostly minor) actors (e.g. SKD, DeSUS, Zares, NSi, PS, DLGV), alternation and formula acquire values close to 0 according to the old operationalizations. Our proposed index reflects much better the fact that the coalition patterns tend to be familiar. As a result Slovenia appears more closed than, for example, Bulgaria where governments are often formed by parties established right before elections (e.g. NSDV, GERB).
Within the spectrum of the 11 new member states we can also check the validity of the closure indices by contrasting the closure-averages of the post-Communist decades with the averages of electoral volatility and parliamentary fragmentation. The correlation matrix indicated that closure is related, as expected, to low fragmentation and low volatility. The new index covaried more strongly with both fragmentation and volatility (-0.66, .sig 0.03 and -0.51, sig. 11) than the old ones (continuous -0.43, sig. 0.19, and 0.06, sig. 0.97, dichotomous -0.61, sig. 05, and -0.09, sig. 0.8). 12 The cases of post-independence Montenegro, presentday France, and inter-war Czechoslovakia illuminate further the differences between the indices. The existing rankings place Montenegro among the open systems while our index ranks it among the closed ones. In fact in Montenegro the same coalition of parties (DPS, SDP, and DUA) has governed the country since the adoption of independence in 2006. The old operationalizations misclassify the case because they give too much weight to one very minor change -the fact that in 2009 the Bosniak minority represented by one single minister was incorporated into the coalition. The same could be said about the French party system during the 5th Republic. According to the old forms of operationalization, this case is in the open segment of the continuum, appearing as even less stable than Bulgaria or Lithuania. But in fact governmentbuilding in France has been relatively well structured around two clearly opposed party blocs, the center-right and the center-left. The existing ways of measurement misclassified France because they gave excessive weight to small parties (e.g. CDP, CR, MDD, PSD, ADD, GE, MDC, NC, LP, or W) and to minor reshuffles of governments, thereby not only decreasing closure on access but also exaggerating the innovative character of the formula.  As far as inter-war Czechoslovakia is concerned, our index classifies it as closed, in line with the literature that considers it as a highly stable system (Capoccia, 2005).
The other indices treat it as open due to the large number of cabinet reshuffles. In fact the Czechoslovak governments were dominated by the same five parties (RSZML, CNSS, CSDSD, CND, and CSL) throughout the entire period, one of them, the RSZML, was never out of government, and the five parties cooperated so closely that they were even considered to be one political entity, the 'Petka'. This underlying stability is reflected only by the new indicators.

Conclusions
The principal outcome of this article is a new operationalization of party system closure. The existing operationalizations were incoherent, did not fit the original conceptualization, did not capture well the degree of predictability, and were unsuitable for measuring time periods. They fell short of the standards of symmetry, precision, applicability, and homogeneous logic. The new indicators are more uniform and transparent in their logic of construction. They follow the original three-component model of closure, and are all based on percentages of ministers controlled by parties. The beginning and the end of governments are defined in terms of both party configurations and elections and therefore we are able to record 'no alternation', in the spirit of the original conceptualization of the concept of closure. The new indicator of government formula can be applied to specific government-changes and to time periods. The temporal dimension is taken care of by taking into account the number of years spent under a particular pattern. The theoretical justification for the new index was complemented with empirical analyses. Across 19 inter-war European party systems, closure was shown to covary with the survival of democracy. Examining 60 European party systems from 1848 to 2013, and then double-checking the results on various subsamples, the analysis has shown that the three constituent components of closure are positively related, but they do not attain a perfect unidimensionality. It seems that, both conceptually and empirically, government formula is more central to party system closure than alternation.
The analysis found that the most frequent governmental pattern is characterized by a combination of partial alternation, innovative formula, and no new party included into the government. But most of the time we live under closed patterns: governments which are formed after complete or no alternation, containing no new parties and reproducing earlier coalition formulae.
Finally, the application of the new measures to 60 European cases demonstrated that closure can be achieved in new democracies with authoritarian elements (Montenegro, Georgia), but it is more common in wellestablished democracies (UK, Switzerland, Norway, etc). The concentrated party systems (Malta, UK, Spain after 1979) scored high, but some fragmented systems (Switzerland, Norway, Sweden) also achieved high ranking. The post-war systems tend to be much more closed than the ones that existed during the early 20th or late 19th centuries, and Eastern Europe lags behind the West in terms of closure (Casal Bértoa, 2013). Countries that have permissive institutions (i.e. small thresholds in front of the formation and electoral and governmental success of new parties) tend to have more open systems, but the ranking proves that party system closure is far from being determined by institutional rules.
The proposed formula for closure appears as most relevant for multiparty parliamentary democracies, but in fact it can be applied to two-party systems and to presidential regimes as well, though in those cases it may not capture the dynamics of party politics to the same extent. This article demonstrated its utility for European democracies, but hopefully researchers will consider its applications also for other regions.