Partisan attachments in a multidimensional space

Abstract How do party positions in a multidimensional space affect party identification? This article argues that when parties take consistent ideological positions across dimensions, they clarify their brand, fostering party identifications. An analysis that uses data from the European Social Survey and the Chapel Hill Expert Survey provides evidence for this argument. The results also indicate that the effect particularly holds for the less educated and politically less interested. In addition, ideological inconsistency affects individual parties’ electoral appeal, as parties that take different positions on two dimensions tend to have a smaller partisan base. The results provide important insights into how multidimensional party competition shapes the development of party attachments.

Party attachments play a crucial role in shaping citizens' vote choice and political behaviour (Campbell et al. 1980). Dalton (2016: 1), for example, refers to party identification as 'the most important concept in modern electoral behaviour research' . Citizens who identify with a party rely on this heuristic when choosing between parties, in part because partisans view the world and evaluate political actors through partisan lenses (Bartels 2002;Bisgaard 2015). Given the stable nature of party attachments, especially when conceived as a social identity (Huddy et al. 2015), the impact of partisanship on electoral behaviour ensures a certain degree of political stability (Oscarsson and Holmberg 2020). However, the role of partisanship in politics is not limited to its impact on voters' choices on election day. In particular, party attachments have a mobilising effect (Jung 2017;Moral 2017), as identification with a specific party 'encourage[s] a person to become active in the political process to support his or her side' (Dalton 2016: 7).
Partisanship's central role in turnout and vote choice has led scholars to study the conditions under which citizens are more likely to develop attachments to parties. Much of this work has focussed on voters' individual-level characteristics (Dalton 2007;Huddy and Bankert 2017) or the environment in which they grow up (Kroh and Selb 2009). Substantially less attention has been given to the role of system-level variables and characteristics of the party system in particular (but see Lupu 2015). Similarly, debates about the sources of an alleged decline in party attachments mostly focus on changes in voters' characteristics and preferences (Dalton 2014;Inglehart 2007). While such work offers important insights into the sources of partisanship, we think individual-level factors should be complemented by taking into account the role of context-level factors as well.
The nature of partisanship and the extent to which it is stable or dynamic is the subject of a lively scholarly debate. On the one hand, some argue that once they are formed, partisan attachments are stable and can best be described as an 'unmoved mover' (Campbell et al. 1980;Green and Palmquist 1994). On the other hand, there is work arguing that partisan attachments are highly unstable and that shifts in party attachments are driven by short-term attitudes, like evaluations of the economy or government approval (Fiorina 1981). A more nuanced perspective is taken by scholars who claim that while partisanship is very stable for many voters, it is more dynamic for others (Clarke and McCutcheon 2009). Importantly, however, the dynamism in partisanship appears to be bounded, as work shows most switching takes place between identifying with one specific party and independence (Neundorf et al. 2011;Zuckerman and Kroh 2006). Changes, furthermore, 'are neither rapid nor universal, ' which has led Tucker et al. (2019: 324) to characterise partisanship as a 'very slow mover' . Changes in party identification thus do occur, even if partisan attachments are not fickle. In this article, we theorise that the positions that parties take in an ideological space are a factor that can move party attachments and affect the strength of individuals' attachments with parties. In looking at party positions as a source of dynamics in party attachments, we build on insights from Evans and Neundorf (2020). Studying the dynamics of partisanship in the British context, they found that individuals' core political values shape partisanship, leading them to point to 'ideological shifts by parties' as an important source for understanding the dynamics in citizens' party attachments.
Party systems and the positions that parties take within those party systems likely shape the extent to which citizens develop attachments to parties. The work of Lupu (2013Lupu ( , 2015 offers vital insights in this regard. He theorises that party systems matter through their impact on the 'clarity' of parties' brands. Focussing on the extent to which the parties are ideologically polarised, Lupu (2015) also brings empirical evidence to substantiate his argument. In particular, he shows that in contexts where the ideological distance between parties is on average larger (i.e. parties are more polarised), levels of mass partisanship are higher. This article builds on these insights to study the connection between parties' positions in a multidimensional space and levels of partisanship.
Starting from the assumption that electoral politics and party competition in European democracies are increasingly characterised by competition on two distinct ideological dimensions-one economic and another cultural (Hahm and Hilpert 2022;Hooghe and Marks 2018;Hutter and Kriesi 2019;Kriesi et al. 2006)-we argue that parties' positions on both of these dimensions contribute to the clarity of their 'brands' . Our intuition is that in a multidimensional space, a key feature of the clarity of parties' positions concerns the consistency of parties' positions on the two dimensions. When parties in a party system take consistent positions on the first and the second dimensions (i.e. economically left-wing/culturally libertarian, or economically right-wing/culturally authoritarian), it is easier for voters to distinguish between parties than when their positions on the first dimension are (almost) unrelated to their positions on the second dimension. A large degree of consistency in parties' positions on the two dimensions should thus enhance the clarity of parties' positions, resulting in higher levels of mass partisanship. That is, when economically left-wing parties take libertarian positions and economically right-wing parties take a position on the authoritarian side of the GAL/TAN dimension, this enhances clarity and fosters partisanship.
To test this intuition, we make use of the pooled data of all available rounds of the European Social Survey (ESS), which we combine with information on parties' positions in a two-dimensional space as captured by the Chapel Hill Expert Survey. The results support our expectation and suggest that in party systems where parties' positions on the economic dimension differ more strongly from their positions on the second (GAL/ TAN) 1 dimension, partisanship levels are lower. We also find that the impact of party system ideological inconsistency is stronger for citizens who otherwise lack the resources that help develop strong attachments to parties, such as the less educated and those with lower levels of political interest. Finally, we show that the role of ideological inconsistency in a two-dimensional space is not limited to the party system level but also matters for individual parties. In particular, we find that parties whose positions on the two main ideological dimensions in European politics are more consistent tend to have a larger share of partisans.

Clear party brands and partisanship
Even though partisanship levels vary substantially between countries and over time (Oscarsson and Holmberg 2020), the literature that studies the role of system-level factors on mass partisanship is relatively sparse. This lack of attention to contextual variables is surprising since whether individuals develop attachments to parties likely depends on the parties on offer and their characteristics.
An emerging literature, however, has started to fill this gap and to theorise about how characteristics of the party system can shape the presence and strength of party attachments. The starting point of this work is that for attachments with parties to develop, parties must have distinct 'brands' (Baker et al. 2016;Lupu 2016). These brands result from parties' issue positions, their behaviour during election campaigns, and their coalition behaviour after the elections (see, e.g. Fortunato and Stevenson 2013). By observing parties and their behaviour, citizens form perceptions about what parties stand for and where they are located on some continuum (Lupu 2013: 51). Crucially, party brands are not stable over time, and the clarity of brands can also vary substantially between parties and contexts. Some parties have clear positions and distinctive brands, while for other parties, there is more uncertainty about their location, implying their brands are more diluted.
According to Lupu (2013: 52), a lack of clarity of parties' brands has two important consequences. First, it weakens the perceived fit between voters and a specific party. Second, the dilution of party brands implies that perceived differences between parties are smaller too, weakening the contrast between parties. These phenomena lead to the expectation that when parties' brands are weaker, fewer citizens will develop attachments with parties or hold strong party attachments.
The implications of the branding theory of partisanship have also been tested empirically. Using an experimental approach, Lupu (2013Lupu ( , 2016 has shown that informing respondents in Argentina about similarities between different parties decreased partisanship and weakened partisan attachments. Focussing on the effects of a real-life and fairly sudden dilution in the Brazilian Workers' Party brand, Baker et al. (2016) also find indications that the weakening of party brands leads to dealignment. When the clarity of parties' brands changes, this has consequences for the presence and strength of party attachments.
The testable implications of the idea that more clarity in parties' brands can strengthen party attachments are not limited to rare cases of a more or less sudden change in parties' brands. The branding theory of partisanship also provides us with expectations about differences in levels of partisanship between countries. Work along these lines has primarily focussed on the connection between party system polarisation and levels of mass partisanship. The expectation is that when ideological polarisation is higher, citizens can 'better distinguish party categories from one another' (Lupu 2015: 334-5), which should foster citizens' ability to differentiate between the party that fits them and other parties, and strengthen party attachments. 2 Empirical work lends support to this expectation. Lupu (2015) uses election survey data from the United States and the Comparative Study of Electoral Systems project to show that party polarisation is positively associated with mass partisanship. These findings align with those of Berglund et al. (2005), who conducted a comparative analysis of longitudinal election survey data from six European countries and found higher levels of partisanship in settings where left-right polarisation was higher. Building on these insights, Just (2021) has recently shown that the same mechanisms apply to the development of partisanship among immigrant citizens in Western Europe.
Overall, the literature shows that parties' positions affect how clear their brands are and how many citizens develop attachments to parties.

Party brands in multidimensional space
While a useful starting point, previous research on the connection between the clarity of parties' positions and partisanship has exclusively considered the differences between parties in a one-dimensional space. This work focuses on parties' positions on a single left-right scale and examines how the polarisation of parties' positions on this dimension correlates with levels of partisanship.
Even though reliance on a single left-right dimension is defensible in several ways, it remains a simplification of the actual space of competition. In addition, a large number of studies point out that electoral competition-particularly in a European context-is increasingly structured along multiple ideological dimensions, rendering the reliance on a single dimension less appropriate (Borbáth et al. 2022). More specifically, to understand the behaviour of parties and the choices that voters make, we should distinguish between an economic left-right dimension on the one hand and an emerging second dimension that taps cultural positions (Gidron et al. 2020) or a distinction between liberal and authoritarian positions (Bakker and Hobolt 2013; Hooghe and Marks 2018) or a conflict about the consequences of globalisation (Kriesi et al. 2006).
If party competition and voters' electoral choices are structured along multiple dimensions, the question becomes how parties' positions in a two-dimensional space determine the clarity of their brands and, in turn, mass partisanship. It could be argued that what matters is parties' positions and the distance between parties on each of these dimensions (i.e. polarisation on each dimension). However, we contend that there is more than just the distance between parties that should be accounted for to capture brand clarity in a multidimensional space. In a multidimensional space, the ideological consistency of political parties' positions across the two dimensions represents a central element of the clarity of parties' positioning. 3 Citizens will have a hard time figuring out where parties are located if parties lean towards the economic left (right) on one dimension and are authoritarian (libertarian) on the other dimension.
In contrast, distinguishing between parties is much easier if parties are consistently positioned on the same ideological side of different dimensions. That is, the clarity of parties' positions is higher when parties are systematically progressive or systematically conservative on both dimensions. In such a context, the multidimensional party competition can essentially be reduced to a single dimension. Hence, we argue that when the parties in a multidimensional space take consistently left-wing or right-wing positions on all dimensions, this clarifies their ideological brands, making it easier for voters to develop party attachments, resulting in higher levels of mass partisanship.
In conceptualising the role of consistency in parties' ideological positions, we assume that when there is a logical connection between positions on the two main dimensions, whereby economic and social/cultural positions are aligned, this increases clarity. Thus, our focus is on the presence of ideological 'constraint' in parties' positions (Converse 2006).
The differences between our argument that consistency in ideological positions provides clarity and the idea that programmatic distinctiveness more generally is key can be emphasised by focussing on the case of left-authoritarian parties. If what matters is mostly how different parties' positions are from each other, the presence of left-authoritarian parties in a party system should enhance clarity and strengthen partisanship. In contrast, if what matters is how consistent parties' positions are on different dimensions, the presence of left-authoritarian parties should reduce clarity and weaken party attachments.
We are not the first to assume that there is a certain degree of constraint which allows conceiving that one dimension encapsulates different dimensions and issues. This idea of constraint is precisely what has motivated students of party politics (Volkens et al. 2013), as well as scholars of voting behaviour and public opinion (Knutsen 1995), to rely on a one-dimensional summary indicator of the ideological positions of parties that combines positions on economic and non-economic issues. It is argued that there are also psychological underpinnings for this constraint, as 'needs for security and certainty attract individuals to a worldview that both maintains traditional modes of conduct (cultural conservatism) and resists destabilisation of the prevailing economic hierarchy (economic conservatism)' (Malka et al. 2019(Malka et al. : 1047. It should be acknowledged, however, that there is debate about whether-at an empirical level-there is indeed a strong connection between economic and cultural left-right positions. In terms of public opinion, Malka et al. (2019) argue that economic and cultural positions are not typically correlated. At the elite level, and in terms of parties' positions, previous evidence points to some heterogeneity. Rovny and Edwards (2012: 62) show that parties' positions on the economic and cultural dimensions correlate in expected ways in Western Europe, but that in Central/Eastern Europe 'the axis of competition has the opposite slope, linking traditionalism and authoritarianism with the economically redistributive left' .
That there is variation in the extent to which parties' positions on different dimensions are aligned is not a problem. On the contrary, it is this variation that we are interested in studying. What would be problematic is that our conception of ideological constraint in positions on the economic and cultural dimensions contrasts with how these dimensions are in practice constrained in some countries. Reassuringly, a visual assessment of parties' positions on the economic and GAL/TAN dimensions, as captured by the Chapel Hill Expert Survey (CHES), reveals that if parties' positions on the two dimensions correlate, the correlation is positive. This implies that, in practice, when we observe constraint in parties' positions, it takes the form of economically left-wing parties being culturally libertarian, and economically right-wing parties taking more authoritarian cultural positions. In line with Rovny and Edwards (2012), we sometimes see the opposite pattern for Central/Eastern European countries. However, this pattern is not universal, and it also seems to weaken over time (see Online appendix A). 4

Hypotheses
Our argument, that consistency in the ideological positions that parties take on multiple dimensions strengthens party attachments, has a series of testable implications.
First, in terms of the differences between party systems, we expect that in settings where parties on average take positions on the two main dimensions that are more inconsistent, party brands are less clear, and mass partisanship levels are lower. For an individual citizen, this implies that her likelihood of being a partisan will be lower when parties adopt more inconsistent positions on the two dimensions. Accordingly, Hypothesis 1 focuses on the role of inconsistency in positions on the two dimensions as a party system indicator, in line with how previous work has studied the role of polarisation.

Hypothesis 1
The more inconsistent are parties' positions on the two main dimensions on average, the lower is mass partisanship.
While we expect levels of party system inconsistency in positions on the two dimensions to have such an effect in general, we also think it is quite likely that some individuals are more affected than others. At a theoretical level, two lines of reasoning motivate this expectation. First, it can be expected that those who are more politically sophisticated 'possess a mass of stored partisan information that will enable them to resist whatever new communications they encounter' (Zaller 1989: 185). Following this argument, if parties change their positions, this should have less impact on the partisan identification of more politically sophisticated citizens. Second, in line with work that has argued that sophistication helps voters 'muddle through a menu of erratic parties' (Marinova 2016: 47), sophistication should also help voters understand the complexities of a truly multidimensional space. For voters with a lower level of sophistication, in contrast, a lack of constraint in parties' ideological position can be a source of confusion, weaken parties' distinctive brands, and lower the likelihood of developing a partisan attachment.
In line with Lupu (2013: 54), who argued that 'individuals with weaker priors about party brands (…) should update party brands more quickly than those with stronger priors,' we hence theorise that citizens who otherwise have the resources that foster strong attachments to parties will be less affected than individuals lacking those resources by variation in party system inconsistency in positions on the two dimensions. We focus on two proxy indicators of such resources: education and political interest. We expect that as individuals are more educated and more interested in politics, the effect of party system inconsistency on party identification becomes smaller. Hypotheses 2 and 3 summarise our expectations.

Hypothesis 2
The higher an individual's level of education, the smaller the effect of party system inconsistency on partisanship.

Hypothesis 3
The higher an individual's level of political interest, the smaller the effect of party system inconsistency on partisanship.
We theorise that the consistency of parties' positions on multiple dimensions affects the clarity of their brands and hence the presence and strength of party attachments. If so, the role of brand clarity should be visible in the link between average levels of position inconsistency on two dimensions and levels of partisanship (as tested by Hypothesis 1) and in the partisan appeal of specific parties. We thus test the expectation that parties which take more inconsistent positions on the two dimensions will have fewer partisans. 5

Hypothesis 4
The more inconsistent a party's positions on the two main dimensions, the fewer partisans it has.

Data
In order to test our hypotheses, we need data on partisanship, including information on the direction of partisanship. To test the possibility that effects are heterogeneous, we also need information on individuals' levels of education and political interest. Furthermore, we need information on parties' positions in a two-dimensional ideological space.
We have all the required information by combining the data from the European Social Survey (ESS) and the Chapel Hill Expert Survey (CHES). More specifically, we use the pooled data of the ESS, including the nine available rounds. The ESS provides us with biannual surveys in European countries between 2002 and 2018. The ESS measures party attachment based on the question 'Is there a particular political party you feel closer to than all the other parties?' . We use this indicator and code it as a binary variable (1 = yes, 0 = no). The ESS also contains measures of individuals' highest level of education (scaled from 1 = less than secondary education to 4 = tertiary education completed) and their level of interest in politics (scaled from 1 = not at all interested to 4 = very interested).
For information on parties' ideological positions, we rely on the data from the CHES. The CHES project surveys experts regularly about their perceptions of parties' positions on multiple ideological dimensions. The average expert placements of parties are generally considered reliable indicators of parties' 'true' positions (Bakker et al. 2015;Hooghe et al. 2010). An alternative strategy would be to rely on the Comparative Manifesto Project (CMP) data. However, we prefer using the CHES data because they correlate more strongly with voters' perceptions of party positions than manifesto-based positions (Adams et al. 2019;Dalton and McAllister 2015). In addition, it has been argued that the CMP data capture issue salience rather than positions (Lowe et al. 2011). Theoretically, our interest lies with parties' positions, not salience. Finally, for our purposes, we must distinguish between left-wing and right-wing positions, which requires a clear mid-point on the scale on which parties are positioned. For the CHES surveys that ask experts to position parties on 0-10 scales, this is straightforward. In contrast, for scales derived from the CMP project, it is less obvious what the mid-point of each scale is.
To test Hypotheses 1 to 3, we match the individual-level ESS data with party system information from the CHES data at the country-year level. We match ESS and CHES surveys fielded in the same year or the closest CHES survey if no CHES data is available for the ESS survey year. 6 For Hypothesis 4, we aggregate the ESS data at the party level to obtain a measure of the share of individuals in a country that is partisan of a party, and match this to information on the party's position in a two-dimensional space obtained from the CHES data (matching ESS and CHES years in the same way as we do for the individual-level analyses).

Measures
An important point is how we operationalise parties' tendency to take inconsistent positions on different dimensions. Throughout, we focus on the two main dimensions that the CHES data distinguishes: an economic left-right dimension and a GAL/TAN dimension. The latter dimension contrasts parties taking a more libertarian or postmaterialist position and parties that are more traditional or authoritarian. 7 To capture whether the parties in a party system tend to take inconsistent (versus largely consistent) positions on the two dimensions, we construct a measure that gauges the vote-share weighted absolute distance between parties' ideological positions on the economic left-right and GAL/TAN dimensions. The weights ensure that the positions of large parties receive larger importance than those of small parties when assessing the composition of the party system.

Party system inconsistency
where ω j is the share of the vote received by party j, p j 1 is the position of party j on the first (economic) dimension and p j 2 is the position of party j on the second (GAL/TAN) dimension. 8 There is some variation in this indicator within countries over time, but most variation is at the country level, with important differences in average levels of party system inconsistency between countries. As can be seen from descriptive statistics reported in Online appendix D, party system inconsistency is lowest in Southern European democracies like Spain and Portugal and considerably higher in democracies in East/ Central Europe-with the highest levels of party system inconsistency observed in Hungary and Poland.
We invite interested readers to consult Online appendix C, where we offer more details on the properties of our measure of party system inconsistency and illustrate the measure by walking through several hypothetical party systems.
For Hypothesis 4, the focus is on parties, not on the party system level. For individual parties, the inconsistency in their positions on the economic and GAL/TAN dimensions can thus be captured straightforwardly by applying the following equation: where p j 1 is the position of party j on the first (economic) dimension and p j 2 is the position of party j on the second (GAL/TAN) dimension.

Methods
In order to test Hypotheses 1, 2, and 3, we estimate mixed linear probability models in which the dependent variable captures whether a respondent is a partisan (coded as 1) or not (coded as 0). We estimate mixed models to account for the nested structure of the data by specifying three levels, with individuals nested in country-years and countries, with random country-year and country intercepts. We add a limited number of individual-level controls to the model: focussing on the socio-demographic variables gender (woman = 1, man = 0), age, and education, along with political interest. Each of these variables is known to predict partisanship; with men, older citizens, the more educated and those with a higher level of interest having a higher likelihood of being partisan (Dalton 2007). Our interest is in the effect of party system inconsistency. Still, to isolate its impact, we must account for other party system features that might be correlated with ideological inconsistency. An alternative mechanism would be that it is not the extent to which parties' positions on the two dimensions are inconsistent which affects partisanship, but more generally, how far away from the centre are these positions. According to this logic, when parties differentiate themselves from the main diagonal, this increases the ideological distance between parties and might increase brand clarity and partisanship. To account for this alternative mechanism, we systematically include controls for the extent of party system polarisation on each of the two main dimensions in the models. To operationalise party system polarisation, we follow Lupu (2015) and use a measure that relies on the weighted distance between parties' positions on a specific dimension and the 'centre of gravity' of the party system on that dimension. 9 We also control for the effective number of electoral parties (ENEP) in the most recent election (Gallagher 1991). 10 Finally, given that the ESS surveys are not election surveys, but because we know that partisanship levels are higher during elections (Michelitch and Utych 2018), we add a control for the number of months (proxied as the number of days divided by 30) since the last general election in the country. Given that the interview date varies between respondents in a specific country-year, this is technically an individual-level variable. Descriptive statistics for all variables included in the individual-level models are reported in Online appendix E. For Hypotheses 2 and 3, we additionally specify a random slope (for either education or political interest) and add an interaction between these indicators and our measure of party system inconsistency.
The main models focus on a dichotomous measure of partisanship, but we also verify whether results hold when using a measure that accounts for the strength of individuals' party attachments. This indicator ranges from 0 to 4 (0 = no particular party, 1 = not at all close, 2 = not close, 3 = quite close, 4 = very close).
Testing Hypothesis 4 requires shifting the focus to the party level. We use the ESS data as a starting point to calculate the share of citizens in a country-year that identify with the different parties in a party system. We then match parties with information from the CHES data to examine whether parties that take more inconsistent positions on the economic and GAL/TAN dimensions tend to have a smaller share of partisans. We estimate OLS models, in which we control for differences in mass partisanship between countries using country fixed effects. The observations in these models are parties, and parties can be included multiple times in the dataset (as many times as there are ESS rounds). We account for the clustering of observations in countries and parties by double-clustering the standard errors at these two levels. Including country fixed effects in the models should account for significant system-level differences between settings that impact individual parties' partisan appeal. However, to isolate the role of party inconsistency, we must consider several party-specific characteristics. Mirroring the controls for polarisation in the individual-level analyses, we include specific parties' positions on the economic left-right and GAL/TAN dimensions. We further probe the robustness of the results when incorporating differences between niche and mainstream parties and the party's age. 11 Descriptive statistics of the variables included in the party-level models are listed in Online appendix K.
Our reliance on ESS and CHES data allows us to test our hypotheses with a varied sample of democracies in Western and Central/ Eastern Europe.

Results
We start with an analysis of the individual-level data of the ESS, allowing us to evaluate whether citizens living in party systems where parties-on average-take more inconsistent positions on the economic and GAL/ TAN dimensions are less likely to develop a party attachment. Model 1 in Table 1 tests Hypothesis 1. Before focussing on the primary indicator of interest-party system ideological inconsistency-it is reassuring that all individual-level control variables have the expected relationship. We see that women are less likely to be partisans, while age, education, and political interest are positively correlated with partisanship.
Our focus, however, is on the coefficient of our indicator of party system inconsistency. Model 1 of Table 1 shows that the coefficient has the expected negative sign and is significant at the 0.01 level. In substantive terms, it suggests that a one-unit increase in party system inconsistency is associated with a two percentage points lower likelihood that an individual identifies with a party. Considering the range of the party system inconsistency measure, the estimated effect of this indicator is quite substantial. All else equal, the likelihood that an individual identifies with a party decreases from 51% when party system inconsistency is at its lowest observed value (0.3) to 40% when inconsistency is at its highest observed value (5.8). Importantly, we find indications of a reasonably strong association between party system ideological inconsistency and partisanship while controlling for other party system features. In particular, the models account for the extent to which parties are polarised on the economic and the GAL/TAN dimensions. The estimates for these variables suggest very weak associations between partisanship and dimension-specific polarisation. This contrasts with earlier work on the connection between polarisation and partisanship (Lupu 2015). However, it should be kept in mind that we concentrate on dimension-specific polarisation and a restricted sample of European democracies.
Overall, the results of Model 1 in Table 1 support our first hypothesis. In settings where parties take more inconsistent positions on the economic and GAL/TAN dimensions, individuals' propensity to identify with a party is lower. Furthermore, our results also suggest that, in a multidimensional context, the level of inconsistency in parties' positions seems to matter more for the development of partisanship than the extent to which parties are ideologically polarised.
Having found evidence in line with Hypothesis 1, we now turn to our expectations regarding heterogeneity in the role of party system ideological inconsistency. Based on the assumption that individuals with more resources that foster the development of party attachments would be less influenced by contextual factors, we hypothesised that education (H2) and political interest (H3) moderate the effect of party system inconsistency. Models 2 and 3 in Table 1 provide tests for these hypotheses. First, in Model 2 we add a cross-level interaction between individuals' level of education and party system inconsistency. The interaction coefficient has the expected positive sign and reaches significance (at the 0.001 level). This interaction suggests that the negative effect of party system inconsistency is significantly reduced for individuals with a higher level of education. To aid the interpretation of this interaction, the top graph in Figure 1 shows the average marginal effect of party system inconsistency at different levels of education. This plot shows that the effect of party system inconsistency differs significantly between the least (education = 1) and most (education = 4) educated respondents. Furthermore, the graph clarifies that the negative effect of party system inconsistency is limited to respondents with a lower level of education. In fact, the estimated effect of party system inconsistency is only different from zero for respondents who have less than secondary education (education = 1).
The estimates of Model 3 in Table 1 suggest a similar moderation effect for political interest. The coefficient of the interaction term between political interest and party system ideological inconsistency is positive and significant at conventional levels (p < 0.001). The negative effect of party system inconsistency is significantly reduced as respondents are more politically interested. This is also what the bottom graph in Figure 1 shows. In line with what we observed for education, the graph indicates that the negative effect of party system inconsistency is limited to respondents at the lower end of the political interest scale (interest = 1).
Overall, the results of our individual-level analyses suggest that the degree of inconsistency in party positions on the two ideological dimensions is a feature of the party system which is relevant for the development of party attachments. As parties, on average, take more inconsistent positions on the economic and GAL/TAN dimensions, the likelihood that an individual identifies with a party is significantly reduced. Notably, the results also point out that party system inconsistency is not affecting all citizens equally. In fact, the negative association between inconsistency and partisanship is limited to individuals who otherwise lack resources that encourage the development of a party attachment, such as the least educated and the least politically interested. While we focus on the association between party system inconsistency and a dichotomous indicator of partisanship here, the results in Online appendix F show similar patterns when using the strength of party attachments as a dependent variable instead. To account for omitted country-level variables, such as differences in party system structures between Central/Eastern Europe and Western Europe, we also verify whether the results hold when we add country fixed effects. By doing so, our estimates capture variation within countries over time. As can be seen from the results in Online appendix G, this produces substantively very similar findings. 12 In supplementary analyses, we also explore the possibility that the effects are conditioned by respondents' age (see Online appendix I). It could be argued that younger age groups, who are less likely to have developed a strong party attachment, are more strongly influenced by system-level factors. Surprisingly, however, we find that the older age groups are somewhat more affected by variation in party system inconsistency. This could signal that the groups of voters which are less used to inconsistency in parties' ideological positions react more strongly to parties taking inconsistent positions on the two dimensions. However, more research is needed to validate and understand these observed age differences.
Finally, we also explored the differences between party systems where parties take constrained versus unconstrained positions using an alternative indicator-one that focuses on the weighted share of all parties that take positions in the left-authoritarian and right-libertarian quadrants of a two-dimensional space. While the main effect of this blunter indicator is not significant at conventional levels, we find significant interaction effects when focussing on individual-level heterogeneity based on education or political interest (see Online appendix J).
At the individual level, there is support for our theoretical argument that the consistency in parties' positions on multiple dimensions defines the clarity of their brands and in turn affects party attachments. In addition, the implications of our theory extend beyond the association between ideological inconsistency and partisanship at the party system level. If taking more inconsistent positions on the two main ideological fault lines dilutes parties' brands, we should also see the consequences of a lack of clarity for individual parties. We hence hypothesised (H4) that parties with more inconsistent positions on the economic and GAL/ TAN dimensions would have a smaller share of partisans.
A look at the partisan strength of several parties and where those parties are positioned in a multidimensional space offers suggestive evidence for our hypothesis. Take, for example, the contrast between the Swedish Social Democrats (SAP) and the Swedish People's Party (FP). The SAP is a party that generally takes left-wing positions on both the economic and GAL/TAN dimensions. In the 2006 CHES survey, the estimated position of the SAP was 3.2 for the economic dimension, while it was 4.2 for the GAL/TAN dimension (on 0-10 scales). On the other hand, the FP takes positions that reflect more inconsistency. While the party is economically right-wing (7.4 in the 2006 CHES), its GAL/TAN positions reflect a more libertarian position (3.6). According to our theory, we would expect the SAP to have a larger partisan base than the FP. And that is precisely what we find. In the 2006 EES Survey, 23% of Swedish respondents indicated feeling close to the Social Democratic Party, while only 6% reported identifying with the Swedish People's Party. Similarly, the Swedish Democrats (SD)-who take a clearly authoritarian position on the GAL/TAN dimension (9.2 in the 2014 CHES survey) but a more centrist position on the economic left-right dimension (5.4 in the 2014 CHES survey) have a small partisan base. For example, in the 2014 ESS survey, only 3.8% of all Swedish respondents indicated identifying with the SD.
Descriptive statistics in Online appendix K show that almost 70% of the observations in the party-level analyses are parties that take a position along the main diagonal-i.e. in the left-libertarian or right-authoritarian quadrants of a two-dimensional space. Of the less than 30% of parties that take inconsistent positions, slightly more are in the right-libertarian quadrant (15.5%) than in the left-authoritarian quadrant (13.3%).
To verify whether differences in the parties' partisan appeals reflect a more general association with parties' positions in a multidimensional space, we proceed with a regression analysis. We focus on the party level and analyse the relationship between inconsistency in parties' positions on the two main dimensions and the share of individuals in a country-year that identify with these parties. The relevant results are presented in Table 2. The coefficient of interest is that of party ideological inconsistency. Across all models in Table 2, the coefficient has the expected negative sign and reaches statistical significance. Importantly, we find indications that party inconsistency matters for the partisan appeal of parties when accounting not only for country-level differences but also when we control for other characteristics of parties that likely affect the magnitude of their partisan base. More specifically, the effect of party inconsistency holds when we consider differences between niche and mainstream parties (Model 2) and the fact that more established parties, captured here by the age of parties, have a larger share of partisans (Model 3). 13 In substantive terms, the association between party inconsistency and partisan strength is quite sizeable. For example, taking the estimates from Model 2 in Table 2 (the smallest estimated effect), a party that has the same position on the economic and GAL/TAN dimensions (party inconsistency = 0) is predicted to have a partisan base that includes 7.1% of the respondents in a survey. When the inconsistency in the party's positions is at its observed maximum (8.8), this share drops to 2.8% of respondents. These results offer support for Hypothesis 4 and suggest that ideological inconsistency is a factor that defines the clarity of parties' positions in a party system and the brand of individual parties. Parties that consistently take positions on the left (or the right) on both dimensions have clearer brands and attract more partisans. 14 Connecting our party-and system-level analyses, the final model in Table 2 explores whether the effect of a party's inconsistent positions on the two dimensions is conditioned by the overall level of ideological inconsistency in the party system. We add party system inconsistency and an interaction between this variable and party inconsistency. From a theoretical point of view, we might expect that the extent to which inconsistency is a source of confusion for voters depends on whether citizens are used to parties taking inconsistent positions on the two dimensions. The estimates of Model 4 in Table 2 offer evidence in line with this intuition. Figure 2 plots the average marginal effect of an individual party's inconsistency score on the partisan share, conditional on the party system's level of ideological inconsistency. The graph shows that the negative effect of party inconsistency on partisanship is particularly strong when there is not much inconsistency in the party system, that is, when most parties take positions on the main diagonal. However, as ideological inconsistency becomes more normalised in a country, the negative effect of a party taking more inconsistent positions becomes more muted and indistinguishable from zero-and it even turns positive at very high levels of party system inconsistency.

Conclusion and discussion
Partisan attachments play a crucial role in electoral politics and political behaviour. Individuals' identification with a party shapes their views and their choices. Also, the ties between citizens and parties stabilise electoral outcomes and are even considered an indicator of party system institutionalisation (Dalton and Weldon 2007). Much work that has studied the sources of party identification has focussed on individual-level characteristics that facilitate acquiring a party attachment, including political interest and access to political news (Brader and Tucker 2008), as well as the role of the environment in which individuals grow up (Huddy and Bankert 2017;Kroh and Selb 2009). An emerging literature, however, has drawn attention to the roles that political parties themselves can play in fostering the development of party attachments. Much like the influence of parties' positions on vote choice Figure 2. party inconsistency and party system inconsistency. (Downs 1957), this work argues that parties' positions can promote the development of party identification. Importantly, this argument does not assume that party positions have such an effect because issue opinions drive partisanship (rather than vice versa) (Fiorina 2002). It focuses instead on how party positions help clarify the 'brand' of a party (Baker et al. 2016;Lupu 2016). The branding literature's fundamental idea is that citizens have a broad notion of where each party is positioned, and the clarity of these positions allows citizens to distinguish between parties-which fosters the development of partisan attachments.
In this article, we have argued that in a context where parties compete along multiple ideological dimensions, a key feature of their brand relates to the consistency of their positions on different dimensions. Our intuition is that parties that consistently take economically left-wing/culturally liberal or economically right-wing/culturally authoritarian positions have a clearer ideological 'brand' than parties that are progressive on one dimension but conservative on the other dimension. Consequently, in contexts where parties, on average, take more inconsistent positions on the two dimensions, partisanship should be lower. Furthermore, for individual parties as well, their positioning in a multidimensional space should have an incidence on the strength of their partisan base. Using data from the ESS public opinion and CHES expert surveys, our analyses offer evidence that aligns with our expectations. We also find that this feature of party competition does not affect all citizens equally. It is especially those who otherwise lack resources that foster the development of a party attachment-the less educated and the less politically interested-that appear to be influenced by the extent to which parties take consistent ideological positions and have clear ideological brands.
Our results indicate that the ideological consistency of parties' positions, beyond the mere distance between parties on specific dimensions, define the clarity of parties' brands and can encourage the development of party attachments. Importantly, in supplementary analyses reported in Online appendix L, we show that the negative effects of party inconsistency appear to be driven mainly by parties that take right-libertarian positions. In contrast, left-authoritarian parties do not seem to suffer from the inconsistency of their ideological positions. Maybe left-authoritarian parties are simply not perceived as inconsistent by citizens, or perhaps left-authoritarian parties are more successful in focussing citizens' attention on their position on the libertarian/authoritarian dimension only. Unfortunately, with the data at hand and without information on how individuals perceive parties' positions in a multidimensional space, we cannot examine the causes of this heterogeneity in the effects of differences between party types-but this is an important avenue for future research.
Given that it is more and more accepted that a focus on a single (economic) ideological dimension is insufficient to understand and explain party competition and electoral behaviour, our findings have important implications. As competition moves from a one-to a two-or a multidimensional space, our work suggests a level of complexity is added to parties' brands that can inhibit the development of party identifications. If competition is truly multidimensional and public opinion is spread along multiple dimensions, our results also imply a conundrum in terms of representation. On the one hand, in the absence of left-authoritarian parties, for instance, voters who are left-wing economically and have authoritarian preferences lack representation (Hillen and Steiner 2020;Lefkofridi et al. 2014). On the other hand, parties in the left-authoritarian quadrant of a two-dimensional political space can dilute parties' ideological brands and weaken the development of party attachments. And the consequences of this brand dilution are particularly strong among the less educated and less politically interested, implying growing inequalities in who develops attachments to parties. Our analyses of the interaction between an individual party's tendency to take inconsistent positions on the two dimensions and the level of inconsistency in the party system overall offer a vital nuance, however. More specifically, these results suggest that the negative effects of a party's inconsistency are limited to contexts where inconsistency is limited overall-where most parties take positions on the main diagonal.
Like any study, our work has limitations and leaves open questions for further research. Importantly, our analyses are purely observational. While we have accounted for important confounders in our models, the estimates should not be taken as indicators of the causal effect of position inconsistency on partisanship. Owing to our design that takes a broad comparative perspective to study the connection between ideological inconsistency and partisanship in many countries, we lack insights into the mechanisms that connect inconsistency and party attachments. The ESS, unfortunately, does not ask respondents to position parties on (multiple) ideological dimensions, meaning we cannot test to what extent uncertainty about parties' positions drives the effect. In future research, we plan to address these limitations, relying on a combination of experiments and original survey research. For now, our intuition is strengthened by the observation that party (system) ideological inconsistency indeed correlates in expected ways with partisanship. Notes 1. That is, a dimension distinguishing green, alternative and libertarian positions from traditional, authoritarian and nationalist positions.
2. The idea that more ideological polarisation between parties clarifies the differences between them, and in this way helps voters to choose between parties, is also what motivated the APSA Committee on Political Parties (1950) to argue that political parties should take more distinct positions. Even though much empirical work provides evidence that supports this role of ideological polarisation (for an overview, see Dassonneville and Çakır 2021), it is important to acknowledge that ideological polarisation not only has beneficial effects on democracy. In particular, as parties take more extreme positions, there not only is a heightened risk of political gridlock, parties also alienate voters in the centre (Fiorina et al. 2008) and cause a decline in fundamental political attitudes-like political trust (Hetherington and Rudolph 2018). 3. It should be stressed that we think this theory complements the role of polarisation, which by itself also influences clarity and in that way partisanship. Empirically, we ensure to capture the independent effect of the consistency in parties' positions by including controls for polarisation in the models. 4. Empirically, we account for differences in the structure of party systems between Central/Eastern Europe and Western Europe, and between countries more generally, by means of additional analyses that include country fixed effects. We also present the results of an additional test in which we include a dummy variable to distinguish between countries in Western Europe and countries in Central/Eastern Europe. 5. It should be stressed that our expectations relate to partisanship, not parties' electoral success. To be sure, partisanship is a strong predictor of vote choice (Campbell et al. 1980), and parties that have more partisans on average will gain a larger share of the vote. However, partisanship is not the only determinant of electoral success. Newly emerging parties-that have not had the time to build a strong partisan base-can win elections too, sometimes benefiting from the saliency of an issue they own or perhaps the presence of a charismatic leader. 6. Details on the survey-years that are matched can be found in Online appendix B. 7. In the 2006 CHES survey, for example, the question wording used to ask experts about the positions of parties on a GAL/TAN dimension is the following: 'Parties can be classified in terms of their views on democratic freedoms and rights. 'Libertarian' or 'postmaterialist' parties favour expanded personal freedoms-for example, access to abortion, active euthanasia, same-sex marriage or greater democratic participation. 'Traditional' or 'authoritarian' parties often reject these ideas; they value order, tradition and stability, and believe that the government should be a firm moral authority on social and cultural issues.' (Hooghe et al. 2010: 14). 8. Because of the inclusion of the weights that add up to 1 within a country-year, there is no need to account for the number of parties that is present in a particular party system. Empirically, the index of party system inconsistency and the effective number of parties correlate only weakly (Pearson correlation of 0.115). 9. The equation to capture polarisation on a specific dimension is: where ω j is the share of the vote received by party j, p j is the position of party j on the dimension, and p is the vote-share weighted average position of all parties on the same dimension. 10. Information on the ENEP is retrieved from Gallagher's website: https:// www.tcd.ie/Political_Science/people/michael_gallagher/ElSystems/Docts/ ElectionIndices.pdf. 11. In line with previous research, we define niche parties as parties belonging to the radical left, radical right and green party families (O'Grady and Abou-Chadi 2019). Information on the age of parties is retrieved from the Integrated Party Organization Database (Giger and Schumacher 2015), and was complemented with information from ParlGov. Information on the age of parties is only available for countries in Western Europe, restricting the sample for this additional analysis. 12. We also estimated models in which we include a dichotomous indicator to distinguish between countries in Western Europe and countries in Central/Eastern Europe. As can be seen from Online appendix H, the main effect of party system inconsistency is somewhat reduced when we account for differences between Central/Eastern Europe and Western Europe, and is no longer significant at the 0.05 level. However, the estimates of the models that examine the moderating role of individuals' level of education and their political interest are substantively very similar to those of the main results. 13. We have also explored the possibility that the effect of party age is curvilinear but found no evidence of such a pattern. 14. As can be seen from additional analyses in Online appendix M, including a control for right-wing populist parties does not substantively change the results of the party-level models.