1 Introduction

Albeit with a few decades delay (but see Jencks, 1973; Atkinson, 1975), rising levels of economic inequality in the West have been met with growing scholarly attention. Whereas social scientists at first focused on describing and explaining the trend in income concentration and wealth accumulation (Rochat, 2023), more recent scholarship asks how the public views and experiences the changing economic landscape (Mijs, 2021). A burgeoning body of research in political economy has made wide ranging empirical inquiries into the basis of public support for income redistribution (Dallinger, 2010; Dimick et al., 2018; Litwiski et al., 2023), starting from the puzzle that people tend to vote against their interest, counter to Meltzer and Richard (1981). Separately, sociological and social psychological research has ventured to better understand how people perceive inequality and explain its causes, be it meritocratically deserved or the result of a race that was rigged from the starting line (Kluegel & Smith, 1986; Hunt, 2007; Mijs, 2021; Mijs & Hoy, 2022).

These two streams of research have fruitfully come together in new scholarship at the nexus of cognitive beliefs and political attitudes, asking how a person’s understanding of inequality shapes their support for income redistribution (Ahrens, 2022; Alesina & Angeletos, 2005; Alesina & La Ferrara, 2005; Condon & Wichowsky, 2019; Dallinger, 2022; Gspr et al., 2023; Roberts, 2014; Smyth et al., 2010). This scholarship has made great strides in better understanding the link between what people believe and how they lean politically, both in general elections or when considering particular policies.

This paper purports to enrich the burgeoning field of research on the content of people’s beliefs about inequality by making a case for studying also the structure of people’s beliefs. Focusing on “inequality belief systems” foregrounds the various configurations and networks of interrelated but distinct dimensions of social inequality, such as economic, gender and racial inequality, mobility, opportunity, and inequity.

Following fruitful empirical applications of Correlational Class Analysis (CCA) in other fields, we innovate by combining CCA with Exploratory Graph Analysis (EGA) in order to (1) identify construals of inequality, (2) model and visualize these as inequality belief systems, and (3) investigate their sociodemographic correlates. Having identified and analyzed belief systems, we subsequently (4) estimate their predictive power on political attitudes, net of the content of people’s inequality beliefs. Hence, our contribution is to develop a theoretically-informed methodological framework for studying how a person’s perceptions and explanations of various inequalities are interrelated, and how the structure of people’s belief systems shapes how they politically engage with inequality.

We empirically test our inequality belief system framework with an original internationally comparative survey fielded with representative samples of the population in the Netherlands (n = 1,618), and the United States (n = 2,501), collecting detailed measures of the public’s beliefs about inequality. By situating our research in two countries, we add a comparative dimension to the analysis to help bring out general pattern as well as national differences. We believe this to be an important contribution to a literature that has predominantly centered on the United States; a country which stands out as having the highest level of income inequality (Morris & Western, 1999; Atkinson et al., 2011; Neckerman & Torche, 2007) and lowest rate of social mobility in the West (Hout, 2018; Song et al., 2020; OECD, 2018). Moreover, the U.S. public stands out as having an especially strong belief in meritocracy, although we should note that this belief is widespread and growing in most of the Western world (Mijs, 2018b). The Dutch public, in contrast, tends to have a self-image of an egalitarian, progressive, and tolerant country (Duyvendak, 2011; Lechner, 2012). Meanwhile, counter to public opinion, the Netherlands and the US are remarkably similar in terms of wealth inequality and ethnic and racial inequality of opportunity (Mijs et al., 2023). In the Netherlands, like in the US, the wealthiest 10% of the population captures around 70% of all wealth while the bottom half owns next to nothing (Federal Reserve, 2019; Statistics Netherlands, 2015). The two countries also share an ugly history and problematic present in terms of the structural discrimination faced by ethnic and racial minorities. In fact, the labor market discrimination confronting African Americans is virtually indistinguishable from that suffered by Dutch people with a Middle Eastern or North African background (Quillian and Lee, 2023). In short, then, we could characterize these two unequal societies as follows: while the Dutch public tends to not see inequalities, the American public explains it away as the fair outcome of a meritocratic process. This, we feel, makes for an especially interesting comparison of the public’s belief systems.

In what follows we provide a brief review of the theoretical roots of belief systems and of past applications of CCA and EGA, before detailing the various steps of our methodological framework, discussing our data and measures, and presenting the empirical application. We conclude by discussing substantive takeaways and methodological implications, and consider ramifications for the politics of inequality.

2 Background

2.1 The Quest for Construals

In order to provide a comprehensive understanding of the study’s foundations and motivations, we will begin by delving into the literature on construals and belief systems. This exploration will shed light on the origins and significance of our research in examining the structure of public beliefs on inequality.

When examining sociopolitical attitudes, sociologists of culture distinguish between construals and positions. ConstrualsFootnote 1 are socially patterned structures of meaning upon which actors draw to make sense of various aspects of social life. On the other hand, positions denote individuals’ normative beliefs, which are influenced by the construals they adopt. Notably, construals differ from attitudes in two fundamental ways: firstly, they relate to patterns of association among beliefs, rather than attitudes themselves; secondly, individuals can share similar construals even when their attitudes diverge, provided they understand attitudes to be related in comparable ways (DiMaggio & Goldberg, 2018). Indeed, individuals may hold different normative positions even if they share a common interpretation of the pattern of associations existing between a given set of attitudinal items. For example, both liberal and conservative individuals may share the idea that endorsing redistributive policies is associated with leftist political preferences. Nonetheless, they could diverge in their left-right self-placement, thus occupying opposite normative stances on support for redistribution.

This distinction allowed researchers to investigate two types of heterogeneity in survey data (DiMaggio et al., 2018). First, building on Ferdinand de Saussure’s structuralism, cultural sociologists acknowledged the relational heterogeneity of survey items. Indeed, respondents subjectively attribute meaning to a given question on the basis of the associations that it has with other elements of the questionnaire. For example, two individuals may oppose a welfare program with the same intensity. Yet, the determinants of their positions may be different, since one can stand against it because of its cost, and the other on the basis of the conviction that the program must be revisited to avoid overlaps with other redistributive policies, to minimize inefficiencies in the social safety net. Until the associations between support for the program and other economic and political attitudes are left unexamined, it is impossible to discover this heterogeneity with survey data.

A second, and related point is that of population heterogeneity. Since social actors may have different understandings of the same attitude depending on the features of the cognitive structure in which it is embedded, survey samples are likely to be populated by heterogeneous groups of individuals. Within these groups, the heterogeneity will be associated with the normative positions held by individuals. However, between these groups, the heterogeneity will be located at the level of construal, meaning that analyses based on full samples may yield misleading conclusions.Footnote 2

Empirical studies of construals can be divided into two waves, depending on the procedure utilized to retrieve the sample partitions. The first wave was based upon Relational Class Analysis (RCA) (Goldberg, 2011). Researchers who applied RCA undercovered construals of economic attitudes (DiMaggio & Goldberg, 2018), attitudes toward science and religion (DiMaggio et al., 2018), and of political beliefs (Baldassarri & Goldberg, 2014). The second wave started in 2016, with the development of Correlational Class Analysis (CCA) (Boutyline, 2017). CCA simplifies RCA by using Pearson’s correlations between positions expressed by each respondent as a measure of their similarity (see Method section). Correlated answers are thus indicative of a shared construal. This second wave mostly focused on political attitudes. For example, one contribution showed that Dutch people organize their understanding of political issues in three distinct ways and that these construals are also related to varying degrees of support for populist parties (Daenekindt et al., 2017). Another paper examined attitudes toward populism, pluralism, and elitism (Dekeyser & Roose, 2021) to demonstrate that supporters of populist parties are likely to associate populist attitudes with pluralist attitudes, while supporters of mainstream parties perceive populist attitudes as correlated with antipluralist attitudes. Population heterogeneity also persists concerning support for the European Union, where researchers have found federalist, non-federalist, and instrumental-pragmatist construals (Evd et al., 2022). Finally, CCA was applied to test the validity of well established social-psychological theories across different population strata. Kesberg et al. (2024) applied this techniques in four European countries to investigate whether system justification theory holds for all correlational classes. This theory predict disadvantaged individuals have, paradoxically, the highest likelihood of justifying the existing social order (Jost, 2019). Their results show that this prediction holds only for the justifiers, whereas members of other CCA classes show more unstable associations between measures of social status and system justifications.

2.2 From Construals to Belief Systems

As stressed by the literature on construals, attitudes are not held in isolation. Rather, they are embedded in broader systems of meaning. This intuition was already present in the work of Converse, who first studied how voters organize their normative positions about politics. Observing that the term ideology was dangerously muddled by its different uses, the political scientist defined a belief system as a “configuration of ideas and attitudes in which the elements are bound together by some form of constraint” (Converse, 2006, p. 6). In his seminal contribution, Converse argued that the “mass public” was unable to develop an organized belief system as a consequence of their low level of political information. Furthermore, he theorized that political identity was the organizing force of political belief systems.

The main limitation of this work is in the mismatch between the theoretical conceptualization of belief systems and their methodological inquiry. While positing that beliefs are part of a wider attitudinal network, Converse backed his theory with simple correlations between survey items, and with qualitative evidence. To overcome this limitation, Boutyline proposed the application of social network analysis to standard survey data and termed the newborn discipline as belief network analysis (Boutyline & Vaisey, 2017). In this approach, attitudes become nodes of a network model whose weighted ties represent the absolute values of pairwise correlations between survey items. Adopting standard measures of node centrality, Boutyline indeed showed that partisan identity is remarkably pivotal in this system. More recently, DellaPosta (2020) expanded belief network analysis to study the dynamics of belief networks. The author computed correlation networks for 44 years of data from the General Social Survey to examine polarization trends. Interestingly, his work showed that even though polarization of already polarized issues did not increase, a growing number of sociopolitical issues have become polarized along political identity. This was primarily visible through network communities. In correlational networks, attitudes can form cohesive sub-groups in which nodes are more likely to interact with items of the same sub-structures rather than with outsiders. The number of communities found in the networks decreased over time, signaling heightened polarization in the U.S. public.

Meanwhile, research in political psychology has started to address networks of beliefs with an alternative approach. This research is based on a formalized theory of political belief systems, which is organized around three pillars (Brandt & Sleegers, 2021). First, elements of a belief system must be connected, although with varying intensity, at least for a part of the population. This is necessary to state that a set of attitudes form a system, and this idea was already present in the work of Converse, who highlighted how belief systems are constrained by political ideology. Second, the relationship between elements of the system must be causal, meaning that an individual changing his or her mind on a particular attitude will re-align his or her beliefs on related topics. Third, belief systems are shaped by a vast array of exogenous forces, such as sociodemographic factors, peer influence or communication flows. This means that the study of a belief system can not be detached from the examination of its social determinants.

Methodologically, the study of belief systems relies on an innovative psychological perspective labeled as the “network approach” (Borsboom et al., 2021). In psychometrics, researchers have begun to question the latent variable measurement model, which holds that a disease is an unobservable variable that influences the set of its (observable) indicators, i.e., symptoms. An alternative perspective is of diseases as emergent phenomena produced by the intricate set of dependencies among their symptoms (Robinaugh et al., 2020). Following from this perspective, network models started to populate psychology, leading to the establishment of network psychometrics (Epskamp, 2016). Within this stream of research, one of the most adopted methods is Exploratory Graph Analysis, a dimensionality assessment technique based on the estimation of a partial correlation network, followed by a community detection algorithm (see Sect. 3.3). EGA is extensively used in psychometrics (Borsboom et al., 2021), and a burgeoning field of research has started to apply it to sociopolitical attitudes. EGA was applied to assess the dimensionality of attitudes toward science in Germany (Wingen et al., 2022), the Netherlands, and Colombia (Sachisthal et al., 2019). Researchers also investigated the dimensionality of prejudice and stereotypes (Nariman et al., 2020; Sayans-Jimnez et al., 2019) of national identity (Phua et al., 2020), the structure of the risk belief system (Zhu et al., 2020), and the relationships between the content, the structure of a belief system, and the levels of affective polarization (Turner-Zwinkels et al., 2023). More directly relevant to this paper, EGA has been fruitfully applied to study political belief systems (Di Cicco et al., 2023), liberal and conservative moral foundations (Turner-Zwinkels et al., 2020), and attitudes toward inequality (Franetovic & Bertero, 2023). The latter authors applied EGA to 22 variables of Chile’s ISSP Social Inequality module, showing that attitudes toward inequality, redistribution, taxation, and wages form a unified belief system in this highly unequal country. Furthermore, the authors partitioned the sample according to different measures of social stratification, showing that Chileans with lower social status have a more multidimensional understanding of inequality (more network communities), and a denser belief system (greater network connectivity).

In sum, new research on belief systems departs from the CCA literature mainly in three points. First, this new strand of literature adopts partial, rather than simple, correlations. This has important advantages, as partial correlations are indicative of the unique variance shared between elements of the system, and this enhances the consistency with the formal theory, which predicts causal influence between them; also, partial correlations allow for parsimony, reducing the risk of working with spurious associations (Turner-Zwinkels & Brandt, 2022). Second, unlike Belief Network Analysis, which renders the absolute value of between-item correlation as network edges, partial correlation networks allow modeling signed edges. As such, partial correlation networks are better equipped to deal with the population heterogeneity highlighted by the literature on construals, being able to discern the cases in which a given association is positive or negative. Third, both Belief Network Analysis and partial correlation network literatures largely avoid dealing with sample heterogeneity. Indeed, researchers of both streams highlight that cross-sectional analysis of attitudinal data “assumes a single network of which each person’s beliefs are a noisy realization” (Boutyline and Vaisey, 2017, p.1397), and admit that they provide limited insight into within-person belief systems (Brandt & Morgan, 2022). Consequently, some studies argue for the adoption of longitudinal data and personalized network estimation (Brandt, 2022; Borsboom et al., 2021). However, these models are data intensive, and assume stationarity. Therefore, other studies laud the potential of combining CCA with network estimation, to mitigate the homogeneity assumption at the core of the latter procedure (Hunzaker & Valentino, 2019; Turner-Zwinkels & Brandt, 2022).

3 Data and Methods

3.1 Data

Our empirical application is based on an original survey fielded with representative samples of the population in the United States and the Netherlands in August and September of 2020, respectively.

U.S. participants were recruited through Prolific Academic, a survey firm specializing in social science research, founded by academics in Oxford, UK. Prolific has worked with researchers at top institutions around the world and compares favorably to other survey firms that offer high-quality alternatives to Amazon Mechanical Turk (Palan & Schitter, 2018). Our survey was fielded with Prolific’s active panel of 138,363 participants based in the U.S. We gathered 2502 participants using a quota sample stratified by gender, age, and race/ethnicity to match U.S. Census Current Population Statistics (Census Bureau, 2020). After removing one observation who straight-lined, we obtained a sample of 2,501 participants that matches population statistics on race and gender, skewing slightly toward a younger demographic.Footnote 3

Participants in the Netherlands were recruited from the Longitudinal Internet Studies for the Social Sciences (LISS) panel. The panel was established in 2007 with a true probability sample of 4,500 households randomly drawn from the population register by Statistics Netherlands (2020). Panel members are provided with a computer and internet connection if necessary and paid upon completion (Leenheer and Scherpenzeel, 2013). LISS data are widely used in social science research and have been found to provide a similar or better quality than reputable international surveys like the European Social Survey (Berning & Schlueter, 2016; Revilla, 2012; Scherpenzeel, 2009, 2018). We targeted a sample of 1500 respondents. Response rates were higher than anticipated (89%), yielding a sample of 1645. Missing values motivate the listwise deletion of 25 participants, and we further excluded 2 participants who straight-lined. We thus obtain a final sample size of 1,618, which matches population statistics on gender but skews strongly to an older demographicFootnote 4.

We took several steps to secure data quality. First, to accommodate people differently impacted by COVID-19, working and not working, with and without care duties, we provided an extended window during which participants could take the survey, spanning two working days and a weekend day. Further, we designed the survey to be short: the median time of completion was 11 min. Second, we tested our questions and treatment design in two pilot surveys (n = 100 and n = 150). Third, to minimize selection bias, we gave our survey a non-descript name (“Social topics in [country]”) and offered relatively generous compensation ($2.50 for our U.S. participants and €2.50 for the Dutch, corresponding to an hourly rate of approximately $14 or €14). Data and code are available at: https://github.com/arturobertero/inequality_belief_systems.

3.2 Measures

To ground our key variables in the international scholarship on inequality beliefs, where possible we use the same measures and question wording as used in the International Social Survey Programme’s (ISSP) Social Inequality module and the European Social Survey (ESS). We focus on three sets of variables pertaining to perceptions, explanations and attitudes about wealth and racial and ethnic inequality, following a longstanding distinction in the literature on inequality beliefs, namely that between (1) descriptive views of the nature and extent of inequalities in society, (2) explanatory accounts of their underlying causes, and (3) popular attitudes about what society ought to be (Kluegel & Smith, 1986; Mijs, 2018; McCall, 2013). Hence, we conceptualize as distinct dimensions what people think their society looks like, in terms of inequality, why they believe this is the case, and how they feel about this. Unless otherwise noted, these items are measured on a 7-point scale ranging from “strongly disagree” to “strongly agree”. We report their wording and labels in Table 1. Descriptive statistics of these variables in each country are made available in the Supplement.

Perceptions of inequality are assessed by four items: “Differences in income in [country] are too large”, “Differences in wealth in [country] are too large”, “Children in poor families do not have the same opportunities for getting ahead as children in rich families”, and “[Black/ethnic minority] children do not have the same opportunities for getting ahead as white children”.

Following the ISSP, we measure lay explanations of inequality on a 5-point scale, ranging from “not important at all” to “essential”. Participants are presented with a set of factors, for each of which they are asked to assess its importance: “This question is about factors that may be important for achieving economic success. How important would you say is...”. The factors listed are the following: (1) coming from a wealthy family, (2) having highly educated parents, (3) having a good education, (4) hard work, (5) knowing the right people, (6) race or skin color, (7) legal or immigration status, (8) religion, and (9) being born a man or woman.

We measure attitudes about inequality through the following three items: “Society is fair when hard-working people earn more than others”, “[Racial/ethnic] diversity makes [country] stronger”, and “For society to be fair, differences in people’s standard of living should be small”.

Table 1 Label and wording of each inequality belief item
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3.3 Analytical Strategy

Our analysis is structured into four phases that are symmetrically applied to the United States and the Netherlands. Figure 1 summarizes our four-step analytical strategy.

We start by segmenting national samples into groups of people sharing construals of inequality, applying CCA (Boutyline, 2017). Second, we study construals as belief systems, through partial correlation networks, and we assess their dimensionality with EGA (Golino et al., 2017). Third, we isolate sociodemographic predictors of membership to each CCA class using a set of logistic regressions. Finally, we examine whether inequality belief systems have an independent effect on support for redistribution, controlling for the position people have on these topics. We reduce the original variables to mean indexes according to EGA communities, and we use them as controls in a second set of regression models where CCA membership predicts support for redistribution.

Fig. 1
figure 1

Summary of the analytical strategy

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3.3.1 Correlation Class Analysis

We isolate people holding different construals on inequality with CCA (Boutyline, 2017). This technique groups individuals displaying similar patterns of correlations between a set of survey items. CCA establishes the best number of sample partitions, and assign each individual to one of them. Respondents are assigned to the same correlational class if they share a construal. This happens when they agree on the patterns of relationship existing between attitude items, independent of their positions on the topic. CCA refines (ibid.) and improves (Sotoudeh and DiMaggio, 2021) Goldberg’s Relational Class Analysis (Goldberg, 2011) by adopting Pearson’s correlation as a measure of similarity between respondents’ answers. CCA starts by computing correlations between the vectors of survey answers expressed by each respondent. Then, it groups individuals whose response vectors are linearly dependent. This means that two individuals—A and B—are grouped together if A’s responses can be obtained by scaling, inverting or shifting B’s answers. Thus, CCA groups are possibly composed of individuals holding different positions on inequality. Hence, by disentangling positions from construals, the identification of CCA subsamples can be combined with the estimation of regression models to highlight population heterogeneity (DiMaggio et al., 2018). We estimate CCA with the corclass package, version 0.2.1 (Boutyline, 2017). We specify the default value of the filtering treshold (0.01), meaning that absolute row correlations below this value are set to 0 to reduce noise and enhance the reproducibility of our findings.

3.3.2 Exploratory Graph Analysis

We apply EGA (Golino et al., 2017) to study CCA construals as different belief systems, and to assess their dimensionality. Starting from each correlation matrix, this method estimates a regularized partial correlation network, which we interpret as an inequality belief system. Secondly, EGA fits a community detection algorithm on the belief system, and equates the number of communities in the network to the number of dimension of the selected variables (Golino et al., 2020). In the remainder of the Section we detail how EGA perform the two procedures.

EGA starts by estimating a Gaussian Graphical Model (GGM) which renders survey variables as network nodes connected by weighted, signed, and undirected network edges (Lauritzen, 1996). This network is estimated using the Graphical Least Absolute Shrinkage and Selection Operator (glasso) (Friedman et al., 2008). Glasso identifies partial correlations among variables, which helps in eliminating spurious connections, creating a sparse network that optimally represents the real interdependencies among the variables. To select the best model, the Extended Bayesian Information Criterion (EBIC) (Chen & Chen, 2008) is computed for various levels of sparsity, and the model with the lowest EBIC is chosen. This procedure was extensively validated in dedicated studies (Foygel and Drton, 2010; Epskamp et al., 2018; Epskamp, 2016; Epskamp & Fried, 2018).

After the network model is estimated, EGA uses the Walktrap community detection algorithm to identify communities within the network (Pons and Latapy, 2005). These communities represent clusters of closely related variables, which are therefore interpretable as the dimensions of perceptions, explanations, and attitudes toward inequality. The algorithm involves simulating random walks within the graph: starting from a node, the walk proceeds to a neighbor based on the probabilities derived from the edge weights. Mapping random walks helps retrieve communities, as they are characterized by denser connections. This process groups nodes that share more substantial connections into the same cluster, uncovering the dimensions in the data similarly to factor analytic techniques (Christensen & Golino, 2021; Golino et al., 2020).

Finally, to evaluate the robustness of all network models shown in the article, we perform parametric bootstrap analyses. A detailed description of this procedure and its result is made available in the Supplement. We estimate EGA networkks, their dimensionality, and their stability with the EGAnet package, version 2.0.5 (Golino and Christensen, 2024). We use the default values of the EGA function. These estimate GGM networks with the combination of the glasso and the EBIC, and detect their communities through the Walktrap algorithm.

3.3.3 Sociodemographic Determinants of Inequality Belief Systems

In the third phase we fit logistic regression models predicting the likelihood of belonging to the different CCA groups of each country. These models fetch the sociodemographic determinants of different inequality belief systems. Equation 1 shows the specification of the models estimated for each country separately, describing the conditional probability of belonging to an indicated CCA group.

$$\begin{aligned} P(Y=1 | X_1, X_2, \ldots , X_n) = \frac{\exp \left( \beta _0 + \sum _{i=1}^{n} \beta _i X_i\right) }{1 + \exp \left( \beta _0 + \sum _{i=1}^{n} \beta _i X_i\right) } \end{aligned}$$
(1)

where \(P(Y=1 | X_1, X_2, \ldots , X_n)\) represents the probability of belonging to the indicated CCA group given \(X_1, X_2, \ldots , X_n\); \(X_i\) are the sociodemographic variables, where \(i = 1, 2, \ldots , n\); \(\beta _0\) is the intercept; and \(\beta _i\) are the coefficients for the sociodemographic variables.

We include the following sociodemographic variables: (i) gender, measured in categories “Female”, “Male”, and “Other”; (ii) age, in categories “18–27”, “28–37”, “38–47”, “48–57”, and “58+” years old; (iii) origin (native-born = 0; foreign-born = 1); (iv) race/ethnicity (non-white = 0; white = 1); (v) education, in categories “high school or less”, “some college”, and “college or more”; (vi) work status (not employed = 0; employed = 1); (vii) household income, in categories “low” (less than $19,999), “medium” ($20,000 to $99,999), and “high” ($100,000 or more); (viii) marital status (not married = 0; married = 1); (ix) political ideology, measured as a continuous scale ranging from 0 (strong Democrat/far-left) to 10 (strong Republican/far-right); and (x) religion, in categories “catholic”, “protestant”, “other” and “none or not declared”. Descriptives of sociodemographic variables in each country are included with the Supplement.

3.3.4 Inequality Belief Systems Predict Support for Redistribution

The fourth part of the research requires estimating the impact inequality belief systems have on support for redistribution, despite respondents’ positions on the topic. Support for redistribution is measured on a 7-point scale ranging from “strongly disagree” to “strongly agree” with the statement that “It is the responsibility of the government to reduce the differences in income between people with high incomes and those with low incomes”. We perform a set of stepwise linear regression models where CCA membership predicts the level of support for redistribution, controlling for all items on which CCA was performed. To avoid collinearity between the attitude items, we exploit the equivalence between the number of communities of an EGA network and the dimensionality underlying the corresponding data (Golino et al., 2017). We fit EGA on the full sample of the U.S. and the Netherlands, assessing the dimensionality of these belief systems at the population level. Then, for each country, we reduce variables belonging to the same cluster to mean indexes. Confirmatory Factor Analysis and Cronbach’s alpha of each index are provided in the Supplement. For each country we fit an OLS where we estimate the impact of inequality belief systems (e.g. the membership to a certain CCA group) on support for redistribution, controlling for EGA indexes and sociodemographic variables described in Sect. 3.2. Equation 2 describes the linear regression models estimated for each country and controlling by the same sociodemographic variables included in section 3.3.3 regression models.

$$\begin{aligned} Y = \beta _0 + \sum _{i=1}^{n_1} \beta _{1i} X_{\text {CCA}_i} + \sum _{j=1}^{n_2} \beta _{2j} X_{\text {EGA}_j} + \sum _{k=1}^{n_3} \beta _{3k} X_{\text {Sociodem}_k} + \epsilon \end{aligned}$$
(2)

where Y represents support for redistribution; \(X_{CCA_i}\) are the CCA groups, where \(i = 1, 2, \ldots , n_1\); \(X_{EGA_j}\) are the EGA community indexes, where \(j = 1, 2, \ldots , n_2\): \(X_{Sociodem_k}\) are the sociodemographic variables, where \(k = 1, 2, \ldots , n_3\); \(\beta _0\) is the intercept; \(\beta _{1i}\) are the coefficients for CCA groups; \(\beta _{2j}\) are the coefficients for EGA indexes; \(\beta _{3k}\) are the coefficients for sociodemographic variables; and \(\epsilon\) is the error term.

4 Results

4.1 Identifying Construals on Inequality Using CCA

Correlational Class Analysis (CCA) of the Dutch and American samples reveals two construals across each of the two populations based on the patterns of correlations between people’s beliefs about inequality. Figure 2 shows the Pearson’s correlations between the 16 variables studied for individuals belonging to each of the four CCA groups detected (US1, US2, NL1 and NL2). Since the variables capture perceptions, explanations and attitudes about inequality, the correlations tend to be positive across construals. However, there are several differences, which we highlight in what follows.

Fig. 2
figure 2

Item correlation matrices for construals of inequality—US & NL

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Respondents in both countries are fairly evenly split between two construals. In the United States, 53.1% of the sample belongs to a first construal of inequality, while the remaining 46.9% of individuals belong to a second (n = 1,327 and 1,174). Both groups present highly positive correlations between perceptions of inequality, regarding income and wealth differences, and opportunities for poor people and ethnic or racial minorities (p_income, p_wealth, p_poor, p_black). In addition, explanations concerning the importance of race, migration, religion, and sex (e_race, e_migra, e_relig, e_sex) in the configuration of inequalities are positively associated in both groups. However, while the US1 construal is characterized by a near absence of negative correlations between items, in the US2 construal it is possible to detect negative associations. Among them, the importance of people’s hard work (e_work) stands out as negatively related to perceptions of inequality, belief in equality as a distributive criterion (a_equality) and the relevance of coming from a wealthy family (e_weafam) and knowing the right people (e_people). Moreover, the importance of individuals’ religion (e_relig) is inversely correlated with perceptions of inequality, in terms of income, wealth and opportunities for poor and black Americans.

In the Netherlands, the NL1 construal includes 52.7% of the Dutch sample, while the NL2 construal fits the remaining 47.3% of individuals (n = 853 and 765). As in the U.S., perceptions of inequality are positively correlated with each other, but to a lesser extent. Structuralist explanations of inequality, such as the importance of race, migration, religion and sex tend to be positively associated, even more strongly than in the U.S.. However, in the Netherlands, null and negative correlations between items are more frequent. In particular, the NL2 group is characterized by strong inverse associations of the belief in meritocracy as a desirable distributive criterion (a_merit) with other items. Specifically, people with this construal strongly and negatively relate belief in meritocracy with all perceptions of inequality, and with belief in diversity and equality (a_diversity, a_equality), such that the more they support the former, the less they agree with the latter, and vice versa. The NL1 group, on the other hand, also shows negative correlations between belief in meritocracy and other items, but in a milder form. Likewise, the NL1 construal differs in its inverse association between perceptions of income and wealth inequality and individualistic explanations regarding the importance of education (e_edu) and hard work (e_work), which in NL2 are neutral.

The cross-national comparison of construals reveals some notable differences, in particular with regard to beliefs about meritocracy (a_merit), hard work (e_work), and religion (e_relig). In the U.S., belief in meritocracy correlates positively with all other items, except for a negative association with the perceived importance of education (US2). This would suggest a strong endorsement of merit-based principles in American society, aligning positively with attitudes toward diversity and equality. In the Dutch construals, in contrast, attitudes toward meritocracy correlate negatively with perceptions of inequality and attitudes toward diversity and equality. This suggests a more ambiguous stance toward meritocracy among the Dutch population, possibly reflecting skepticism about the effectiveness of merit-based systems in addressing social inequalities.

Another difference between the two countries is the role of hard work in explaining inequalities. In the U.S., its relationship with other inequality beliefs varies between the construals. In the US1 construal, hard work is positively associated with belief in meritocracy, diversity, and equality, and shows no significant association with perceptions of inequality. In the US2 construal, the perceived importance of hard work contrasts with other explanations and clashes with positive attitudes toward equality. Moreover, negative correlations between these perceptions and hard work suggest that people whose beliefs fit the US2 construal may emphasize its importance only when they perceive low levels of inequality. In the Netherlands, by contrast, hard work consistently correlates positively across both construals, with only minor differences such as the negative associations with perceptions of inequality in one construal (NL1) which are non-significant in the other (NL2).

A final difference between the two countries to note, concerns people’s understanding of the role of religion in explaining inequalities. Such views vary by construal, with differing emphasis between the U.S. and the Netherlands. In the U.S., beliefs about the importance of religion positively correlate with other perceptions, explanations, and attitudes about inequality among individuals in construal US1. Conversely, within the US2 construal, religion is negatively associated with perceptions of inequality, meaning that only people who perceive low levels of inequality think that religion is an important factor. In the Netherlands, interpretations of the role of religion are more consistent across different belief structures, with Dutch people generally endorsing all or none of the various explanations of inequality.

In summary, then, individuals can be distinguished by two different construals of inequality within these two countries. The comparison in the U.S. reveals that people differ mainly in how they relate the importance of hard work and religion to other perceptions and explanations of inequalities. In contrast, in the Netherlands, the main differences are people’s belief in meritocracy and the lesser or greater intensity of its negative association with their perception of different dimensions of inequality.

The comparison between countries underscores two key contrasts. First, Americans show a greater variety in the relationships between their perceptions, explanations, and attitudes about social inequalities as compared to the Dutch. The American public is effectively split into two groups, one whose explanations pointing at religion and hard work are detached from the other inequality beliefs, and one where these are all coherently integrated. In the Netherlands, people tend to either endorse or oppose explanations of inequality altogether, and this does not depend on the construal they adopt. Second, while people in the U.S. tend to support meritocratic principles no matter their perceptions, explanations, and attitudes about inequality, in the Netherlands positive attitudes toward meritocracy tend to be tightly linked to perceptions of low levels of inequality and negative views about diversity and equality.

4.2 Modeling Inequality Belief Systems Using EGA

Next, we perform Exploratory Graph Analysis (EGA) to model the between-item relationships of each construal as a belief system, adopting partial correlations to control for the rest of the variables and detecting communities to reveal their dimensionality. Figure 3 shows the four inequality belief systems as estimated by EGA.

Nodes of the network represent the selected survey variables. Network edges show the positive (blue) and negative (red) regularized partial correlations estimated from the data. The width of the edges indicates the strength of each association. Nodes are colored according to community membership. In all groups, the 16 beliefs about inequality form a fully connected network, with no isolated nodes. This means that all perceptions, explanations and attitudes about inequality are part of unified belief systems in both the U.S. and the Dutch population.

Fig. 3
figure 3

Item EGA networks for inequality belief systems—US & NL

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EGA refines the correlation matrices of Fig. 2 by plotting regularized partial correlation coefficients. The edges shown in the plot are thus indicative of the unique variance shared by each pair of survey items. Many Pearson’s correlations retrieved in the four subsamples were suppressed either as a consequence of the regularization procedure or because they were not present after controlling for every other attitudinal item.

The four inequality belief systems display two main similarities. First, the positive association between perceived income inequality and perceived wealth inequality is one of the strongest across all networks. Second, in both countries, belief systems are structured in three communities. The first one (red) usually encompasses perceptions of inequality and beliefs about the importance of different allocation criteria. A second cluster (blue) consists of items that pertain to both individual and structural factors shaping inequality, such as the importance of hard work and of coming from a wealthy family. The last dimension (green) brings together explanations of inequality related to identity aspects of people, such as the relevance of race, migration, religion, and sex. We might think of these clusters as communities of beliefs organized around views (red), factors (blue) and identities (green).

The four inequality belief systems also differ in two important ways. First, the belief systems of the US1 and NL1 groups are characterized by almost non-existent negative associations between beliefs about inequality. Conversely, the belief system of the other two groups features prominent negative associations. To reflect this first difference we resort to a dichotomy of uniform (US1 and NL1) versus contentious (US2 and NL2) belief systems. The second dimension of difference is that belief systems of the U.S. population are integrated, whereas those of the Dutch are compartimentalized. That is, the latter are both more sparse (a smaller number of detected associations) and more segregated (a smaller number of edges between nodes of their three different communities). Hence, we further distinguish belief systems as uniformly integrated (US1), contentiously integrated (US2), uniformly compartimentalized (NL1), and contentiously compartimentalized (NL2). In other words, although both countries have systems with fewer or more negative connections between beliefs, people in the United States display a more interconnected and integrated conception of inequality. Conversely, in the Netherlands, residents demonstrate a more compartmentalized understanding of inequality, marked by belief communities that are less interconnected.

Across these networks, EGA highlights numerous differences in the magnitude of edges. For instance, while in the contentiously integrated belief system, people strongly and negatively relate the importance of coming from a wealthy family with that of hard work, in the uniformly integrated system this association is weaker. Meanwhile, in the Netherlands, the relationship between the importance of race and immigration status for getting ahead attains a stronger positive strength, ranking among the most important in both networks. However, the contentiously compartimentalized belief system has the particularity that belief in meritocracy as a desirable allocation criterion is negatively related to most attitudes and perceptions of inequality.

Other differences emerge at the community level, concerning the membership of three particular nodes. The perceived importance of coming from a wealthy family (e_weafam) and knowing the right people (e_people) tend to be a part of the factors community, but in the contentiously integrated belief system are part of the identities community. The other variation regards belief in meritocracy (a_merit), which is always part of the views cluster, except for the uniformly integrated system, where it belongs to the factors communityFootnote 5.

To explore the importance of nodes within these belief systems we additionally investigate node centrality. To this end, we compute strength centrality, which is a generalization of degree centrality for weighted network (Opsahl et al., 2010). For each node, strength centrality is calculated by summing the absolute values of a node’s ties. The results are shown in Figures 13 (NL) and 14 (US) in the Supplement.

In the Netherlands, the most central nodes in people’s belief systems are explanations of inequality pointing at race (e_race), and perceptions of income inequality (p_income). The least central ones are attitudes toward equality and diversity (a_equality, a_diversity). Comparing the centrality scores of the two belief systems in the Netherlands reveals minimal differences. The importance of just one node meaningfully differs between the two belief systems: attitudes toward meritocracy are rather peripheral in the uniformly compartmentalized (NL1) belief system, whereas this node is more important in the contentiously compartmentalized (NL2) network. Figure 3 shows that this pattern is mainly due to the embeddedness of attitudes toward meritocracy in the red cluster of the NL2 network, whereas this item weakly interacts with the rest of the nodes forming the views community of the NL1 belief system.

In belief systems in the U.S., perceptions of wealth inequality (p_wealth) and explanations pointing at the role of race (e_race) are the most central nodes. The least central nodes are attitudes toward diversity (a_diversity) and toward meritocracy (a_merit). The importance of all network nodes is highly similar across the two types of belief systems. The one exception is the node e_migra, which is quite more central in the contentiously integrated belief system (US1) as compared to the other (US2).

4.3 Sociodemographic Determinants of Inequality Belief Systems

In this section we estimate logistic regression models to explore the sociodemographic determinants of each inequality belief system. Table 2 shows the odds ratios for membership in the contentiously integrated (vs. the uniformly integrated) and in the contentiously compartimentalized (vs. the uniformly compartimentalized one) belief systems, respectively.

A first thing to note is the difference, between the two countries, in explained variance. The fairly exhaustive set of sociodemographic variables helps explain about 24% of variance in people’s inequality belief system in the U.S., whereas it can only explain about 8.6% of variation in Dutch people’s inequality belief systems. This means that, compared to the Dutch, the way that Americans relate their perceptions, explanations and attitudes about inequality tends to be more demographically segregated. Beliefs about inequality in the Netherlands vary just as much as in the U.S., but this variance is not easily explained by reference to sociodemographic factors.

Table 2 Logistic regression models on inequality belief system membership—US and NL
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As further illustration of this country-difference, the results in Table 2 show many more statistically significant associations between sociodemographic factors and people’s inequality belief system in the U.S. as compared to the Netherlands. Higher family income and right-wing political ideology are negatively associated with the US2 belief system. Conversely, age, educational level and identification with non-Catholic religions are positive predictors. Among these factors, political ideology is one of the most salient: the predicted probability of having a US2 belief system is around 81% (73–87% with 95% CI) for strong Democrats (0), and only 13% (8–19% with 95% CI) for strong Republicans (10).

In the Netherlands, only a few sociodemographic factors are statistically associated with a person’s inequality belief system, namely gender, household income and political ideology. Concretely, being male, having a low household income and having a leftist political ideology are associated with an NL2 inequality belief system. Once again, political ideology stands out: the odds of having an NL2 belief system is about 76% ([64%, 85%] 95% CI) for people who identify as far left, and only 18% ([11%, 28%] 95% CI) for those on the political right-wing.

Thus, the possession of different inequality belief systems, i.e., different structures of relationships between beliefs about inequality, tends to have a more marked demographic pattern in the U.S. than in the Netherlands. While among Americans, age, education, household income, political ideology and religion are associated with significant differences in belief system membership, among the Dutch these differences are only present with respect to political ideology and, to a lesser extent, family income.

4.4 The Association Between Inequality Belief Systems and Support for Redistribution

In the fourth and final step of the analysis, we test the implications of our inequality belief systems framework by examining if and how the structure of people’s beliefs about inequality has an independent association with support for redistribution, net of the content of those beliefs.

As a visual starting point, Fig. 4 shows, for each inequality belief system, the distribution of responses to the statement that “it is the government’s responsibility to reduce income differences between high-income earners and low-income earners”, ranging from strongly disagree (1) to strongly agree (7). As the figure shows, people in the uniformly integrated and in the uniformly compartimentalized belief systems report moderate support for redistribution (means of 4.19 and 4.37, respectively). In contrast, the other part of the population, characterized as having a contentiously integrated or contentiously compartimentalized belief system, expresses high levels of agreement with income redistribution (means of 5.84 and 5.78, respectively).

Fig. 4
figure 4

Support for redistribution by inequality belief systems—US & NL

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To tease out the statistical relationship between belief systems and support for redistribution in the U.S. and the Netherlands, we estimate stepwise linear regression models. Model 1 includes only a measure of a person’s inequality belief system (CCA group). As such, the coefficient reports the association between belief system and support for redistribution, mirroring the histogram visualized in Fig. 4. Model 2 includes measures of the content of a person’s beliefs about inequality (EGA indexes for views, factors, and identities), in addition the sociodemographic controls. This model addresses the more conventional question of how beliefs about inequality are related to redistributive attitudes. Model 3, finally, incorporates all variables included in models 1 and 2. Doing so allows us to gauge the independent relationship between inequality belief system and support for redistribution, controlling both for people’s beliefs and their sociodemographic correlates.

Table 3 Linear regression models on support for redistribution—US
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Table 4 Linear regression models on support for redistribution—NL
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Tables 3 and 4 report the results for the U.S. and the Netherlands, respectively. The first models (M1-US and M1-NL) show that, in both countries, the structure of a person’s inequality beliefs explains a significant part of the variance in support for redistribution: 20% in the U.S. and 23% in the Netherlands.

Another way to think of the link between belief systems and redistributive values is as follows: in the U.S., individuals with a contentiously integrated inequality belief system express more support for redistribution by 1.65 points (on a 7-point scale) than whose with a uniformly integrated one, while in the Netherlands different belief systems are associated with a 1.41 point gap in redistributive support.

Despite these similarities between the two countries, when we take into account also the content of people’s inequality beliefs and sociodemographic factors, we start to see some sharp differences. In the United States, incorporating beliefs and demographics renders non-signifcant the relationship between belief system and redistributive support. In other words, the statistical relationship between the two can be fully attributed to differences in inequality beliefs as well as the sociodemographic factors we explored in Sect. 4.3.

In the Netherlands, by contrast, even when we control for a wide range of sociodemographic factors and the content of beliefs about inequality, the structure of the latter still contributes significantly to our understanding of their redistributive support. Net of controls and beliefs about inequality, the second inequality belief system in the Netherlands is associated with stronger support for redistribution by 0.87 points on the 7-point scale, which is statistically significant with a 99% of confidence. Another way to describe the importance of incorporating belief systems into the analysis of redistributive attitudes is that it contributes about 7.3% of explained variance (comparing the R2 reported in models M2-NL and M3-NL).

In summary, while in the U.S., content clearly trumps structure, in the Netherlands, both the content and structure of people’s inequality beliefs provide important analytical tools for understanding a person’s support for redistribution.

5 Conclusion

Our aim in this paper has been to develop and empirically apply a framework for studying the structure of people’s inequality belief systems.

To untangle the different relationship between inequality beliefs, we started by isolating the typical construals of these concepts in each country. In contrast to most research using CCA or RCA (e.g. Daenekindt et al., 2017; Evd et al., 2022; DiMaggio et al., 2018; DiMaggio & Goldberg, 2018), we find two, not three, ways of organizing perceptions, explanations, and attitudes about inequality in each country. These different belief structures are held by groups of comparable sizes (53.1% of respondents adopting US1; 52.7% holding NL1). We compare the construals within and between countries. Construals in the U.S. differ mainly in how they relate the importance of hard work and religion to other perceptions and explanations of inequalities. In the Netherlands, the key difference between the two construals concerns people’s belief in meritocracy and the strength of its negative association with their perceptions of inequality.

The between-country comparison reveals that Americans vary more strongly in the kinds of connections they make between perceptions, explanations, and attitudes about inequality. Also, unlike the Dutch, the U.S. public tends to see no conflict between supporting meritocratic principles and believing in equality or diversity. This is an important finding, which we interpret in light of cultural differences between the U.S. and the Netherlands. Admittedly, both countries have similar levels of wealth, ethnic and racial inequalities (Mijs et al., 2023). However, a key difference between these unequal societies is that the Dutch public tends to be aware of such inequalities (Duyvendak, 2011; Lechner, 2012), while the American public explains it away by drawing on a meritocratic ideology that paints inequalities as the deserved outcomes of fair competition (Kluegel & Smith, 1986; McCall, 2013).

As a second step, we have modeled the four construals of inequality as distinct belief systems. This was achieved by applying EGA—a partial correlation-based methodology—to the four correlational structures. As shown in past research (Franetovic & Bertero, 2023), perceptions, explanations and attitudes toward inequality form integrated cognitive structures. In the U.S., people’s inequality belief systems show a higher number of connections than in the Netherlands. Different dimensions of perceptions, explanations and attitudes about inequality are distinct yet closely connected, giving belief systems an integrated character. In contrast, in the Netherlands, different dimensions of inequality beliefs are compartmentalized in communities of beliefs that are only loosely connected. One belief system we describe as uniform, marked mainly by positive connections between the various nodes and communities of the network, meaning that people tend to link and associate various aspects of social inequality in their society. The other belief system has a more marked presence of negative relationships between nodes, and especially within network dimensions. We describe this belief system as contentious, meaning that people who understand inequality in this way sharply distinguish and delineate between various forms of social inequality. To highlight one such contentious connection, Dutch people with this belief system draw a strong line between their belief in meritocracy and their perception of income and wealth inequalities and of equal opportunities. Conversely, for people with a uniform belief system, these beliefs can go hand-in-hand.

Third, we have explored the sociodemographic correlates of the two belief systems. In so doing, we draw on the ‘usual suspects’ of variables studied in past research on beliefs about inequality, which includes sex, age, race/ethnicity, education, employment status, religion and political ideology, among others. Doing so allows us to explain about 24% of variance in the U.S. (i.e., who holds which belief system), yet these variables only account for about 8% of variance in the Netherlands. That is, for the American sample, belief systems correlate with more or less the same factors that research associates with the content of people’s beliefs, whereas belief systems in the Netherlands are almost orthogonal to these factors. In sum, beliefs about inequality are more socially patterned in the U.S. than in the Netherlands.

Finally, we have demonstrated the empirical import of analyzing belief system by exploring their association with people’s support for income redistribution—a key variable in scholarship on the politics of inequality. We observe notable differences between the two countries, echoing the findings from our sociodemographic analysis. In the U.S., belief systems have as much explanatory power in predicting people’s redistributive attitudes as in the Netherlands, yet content trumps structure: in the U.S., a person’s belief system has no predictive power on their redistributive support over and above the content of their beliefs. In contrast, in the Netherlands, the structure of a person’s belief system is a wholly separate dimension from the content of their beliefs. As such, belief systems have an independent effect on people’s political attitudes, net of the particularities of their beliefs. To quantify the analytical benefit of studying beliefs alongside belief systems, our regression model—that incorporates measures of both structure and contents—is able to explain 55–61% of variance in people’s support for income redistribution in the two countries.

Our contribution is not without its limitations. Notably, we relied on a single measure of support for income redistribution as the sole variable gauging political attitudes. Including a wider range of questions about responses to social inequality, political or otherwise, would allow for a deeper analysis of the consequences of inequality belief systems for the politics of inequality. For instance, a better mapping of belief systems may aid the design of more effective government and nonprofit campaigning as well as targeted information provision to tackle misperceptions about inequality.

We hope that this theoretical, methodological and empirical application on inequality belief systems will open up new opportunities to explore how people conceptualize inequality. We believe the field to be particularly promising because of the large amount and high quality of data available from long-standing international surveys on distributive justice, such as the International Social Survey Programme’s Social Inequality module, which now spans five waves and includes a wide ranging and growing set of countries.

Future research could investigate the variety of inequality belief systems across different nations and how these conceptions are shaped by institutional frameworks, welfare regimes, and cultural repertoires (Mijs et al., 2016). Another interesting avenue for future research regards the association between political ideology and the structure of inequality belief systems.Footnote 6 Our results show that contentious belief systems are most commonly held by Democrats in the US, and by left-wing supporters in the Netherlands. Future studies might exploit these insights to study how political leaning influences the structure of beliefs about inequality, beyond their content. Moreover, longitudinal studies that track changes in belief systems over time could provide important insights into the dynamics of belief change. Such research could reveal whether external shocks, such as economic crises, political upheavals or demographic transformations, influence not only what people believe, but also how they structure their understanding of inequality.