Introduction: conceptualizing ideology as a belief system
For much of the 19th century, the concept of ideology was often treated pejoratively, especially under the influence of Marxist critiques (Jost, Reference Jost2006). Its scientific prominence further declined during the Cold War and post-ideological debates of the late 20th century. However, recent work in political science (Kalmoe, Reference Kalmoe2020) and political psychology (Jost, Reference Jost2006; Jost et al., Reference Jost, Federico and Napier2009) has renewed interest in ideology as a legitimate object of scientific inquiry.
A common thread across classic and contemporary scholarship is the view of ideology as an interconnected system of beliefs. Adorno (Reference Adorno1950, p. 2), for instance, defines ideology as an “organization of opinions, attitudes, and values.” Other definitions describe it as a “set of idea-elements that are bound together, that belong to one another in a non-random fashion” (Gerring, Reference Gerring1997, p. 980), an “organization of beliefs and attitudes” (Rokeach, Reference Rokeach1968, p. 123), or an “interrelated set of attitudes and values” (Tedin, Reference Tedin1987, p. 65). This structural view remains salient in political psychology, where recent handbooks explicitly adopt a network perspective on political attitudes (Bakker and Lelkes, Reference Bakker, Lelkes, Osborne and Sibley2022; Federico and Malka, Reference Federico, Malka, Huddy, Sears, Levy and Jerit2023). This view suggests political beliefs directly influence each other.
Despite the network conceptualization, most empirical research has relied on (often unidimensional) latent variable models. For instance, the left-right self-placement item has long dominated the measurement of ideology in public opinion studies (Bakker and Lelkes, Reference Bakker, Lelkes, Osborne and Sibley2022), assuming economic and cultural preferences align along a single continuum. Importantly, this approach treats attitudes as mere manifestations of a latent ideological trait, excluding direct influence between political beliefs.
Two developments challenge this framework. First, comparative studies increasingly suggest that political attitudes are better represented as bidimensional (Federico, Reference Federico2019) and that the association between economic and cultural dimensions varies depending on national context and elite cues (Malka et al., Reference Malka, Lelkes and Soto2019). Second, scholars have adopted network models to study political attitudes (Brandt et al., Reference Brandt, Sibley and Osborne2019). This new approach allows for a direct relationship between beliefs, permitting scholars to reduce the mismatch between networked definitions of ideology and its latent-based empirical examination (Brandt and Sleegers, Reference Brandt and Sleegers2021).
Together, these developments prompted a return to the classic work of Converse (Reference Converse2006[1964]), who first proposed conceptualizing ideology as a belief system. Converse argued that political sophistication enhances belief constraint (the degree to which attitudes correlate), meaning that only politically knowledgeable individuals hold coherent attitudes. However, belief systems may also differ in their underlying structure (Baldassarri and Goldberg, Reference Baldassarri and Goldberg2014), that is, in how individuals organize their support for political issues. Based on this, I contend that belief constraint is a bidimensional construct. Before measuring attitudinal tightness (i.e. how strongly attitudes are connected), it is indeed necessary to ask whether belief systems display consensus, that is, whether individuals agree on “what goes with what” (Alexandre et al., Reference Alexandre, Gonthier and Guerra2021).
In bipolar systems, parties tend to send clear and consistent cues, bundling issues along a sharp ideological divide. This entails parties clearly signaling to the public which attitudes should co-occur. In this case, belief systems are likely to differ mainly in connectedness, based on how politically sophisticated individuals are (Converse, Reference Converse2006; Boutyline and Vaisey, Reference Boutyline and Vaisey2017). However, in multiparty systems, party cues tend to be more complex, inconsistent, or even contradictory. Rather than providing a single ideological map, elites in such systems offer multiple, competing cue structures, presenting voters with different ways of linking political issues. This might reduce belief consensus by fostering variation not only in the strength of attitudinal connections, but also in their direction and configuration.
The Italian multiparty system represents the perfect setting to investigate how citizens structure their political beliefs. The country features pronounced ideological fragmentation, with its main parties (Partito Democratico -PD, Fratelli d'Italia -FdI, Lega -L, and Movimento 5 Stelle -M5S) offering distinct and, at times, contradictory configurations of cultural and economic positions. FdI and L, both right-wing populist parties (Baldini et al., Reference Baldini, Tronconi and Angelucci2022), fuse cultural conservatism (opposing immigration and extensions of civil rights) with market-oriented economic policies, such as support for flat taxation and skepticism toward redistribution. In contrast, the PD combines a socially liberal agenda (supporting LGBTQ+ rights, abortion, and end-of-life choices), with moderate pro-European, redistributive economic stances. The M5S disrupts, or at least communicatively rejects (Benasaglio Berlucchi, Reference Benasaglio Berlucchi2022), the conventional left-right alignment. Once anti-establishment (Chiaramonte et al., Reference Chiaramonte, Emanuele, Maggini and Paparo2018), the party now embraces progressive stances on cultural issues but retains a distinctively protectionist, anti-globalization economic agenda. It supports redistributive welfare (e.g. basic income), opposes free trade deals like Comprehensive Economic and Trade Agreement (CETA), and emphasizes national sovereignty in economic policy. This positioning is heterodox in the Italian context, as it combines cultural progressivism with economic nationalism, two dimensions traditionally championed by different parties. Italy's partisan landscape thus creates ideal conditions for studying the coherence and segmentation of belief systems under conditions of elite-driven attitudinal cross-pressures.
Drawing on a post-electoral Italian survey, I test four hypotheses: (H1) political attitudes in Italy are bidimensional; (H2) the adoption of network models to political attitudes is empirically justified; (H3) belief system structures vary across the population; and (H4) this variation is better explained by political orientation than by sociodemographic factors or political interest. The article contributes to a growing body of research conceptualizing political ideology as a network of interconnected beliefs.
Theory
I begin reviewing the classical foundations of belief system literature. I then address the bidimensionality of political attitudes and the shift from latent to network-based conceptualizations. Finally, I build on this literature to propose my typology of belief constraint.
Belief systems and their constraint
Noting the ambiguous and contested nature of ideology in philosophy, Converse (Reference Converse2006, p. 3) urged political scientists to study the structure of political attitudes under the label of belief system, which he defined as “a configuration of ideas and attitudes in which the elements are bound together by some form of constraint or functional interdependence.” This influential definition highlights that belief systems are understood as networks of mutually influencing beliefs. Hence, recent scholarship has emphasized the conceptual overlap between belief systems and ideology (Bakker and Lelkes, Reference Bakker, Lelkes, Osborne and Sibley2022; Federico and Malka, Reference Federico, Malka, Huddy, Sears, Levy and Jerit2023). Federico (Reference Federico2019), for instance, explicitly equates ideologies as belief systems, that are socially shared arrangements of political identities, attitudes, and values. Thus, despite emerging from different disciplinary traditions, ideologies, and belief systems are now widely seen as overlapping concepts.
Most empirical research on belief systems has focused on the concept of constraint: the degree to which political attitudes are internally consistent and coherently organized. Constraint has important consequences. Individuals with highly constrained beliefs consistently associate related policy positions, enabling them to form coherent political choices. In contrast, low constraint indicates inconsistent and potentially uncoherent associations. This fragmentation matters for democratic representation: as Barbet (Reference Barbet2020) shows, individuals with weakly structured attitudes often struggle to identify parties that align with their views. Lacking a sense of political representation, they may disengage from electoral politics and abstain from voting. Operationalizing constraint as the mean absolute correlation among political attitudes, Converse (Reference Converse2006) famously showed that most citizens possess poorly structured beliefs, while coherence was notably higher among politically sophisticated individuals. This insight forms the basis of the theory of social constraint, which attributes attitudinal consistency to exposure to elite discourse (Zaller, Reference Zaller1992; Converse, Reference Converse2006). Under this framework, elites act as cognitive authorities, offering structured political narratives that engaged citizens are more likely to receive and internalize (Keskintürk, Reference Keskintürk2022).
In sum, belief systems and ideologies are defined as networks of political beliefs. Their organization has been mainly linked to political sophistication. Yet, political context matters, and this is especially clear when examining the dimensionality of political attitudes.
The dimensionality of political attitudes
Early research in political science and psychology often treated political attitudes as unidimensional. This view explains the widespread use of the single-item left-right scale (Bakker and Lelkes, Reference Bakker, Lelkes, Osborne and Sibley2022). However, a growing body of work now challenges this assumption. Although political scientists and psychologists differ in how they conceptualize ideological dimensions (Federico and Malka, Reference Federico, Malka, Huddy, Sears, Levy and Jerit2023), both fields increasingly acknowledge that political attitudes are structured along at least two axes. Political scientists have moved toward issue-based measures of ideology (Hillygus, Reference Hillygus2011), distinguishing between economic and cultural domains. Political psychologists often rely on the Social Dominance Orientation (SDO; Pratto et al., Reference Pratto, Sidanius, Stallworth and Malle1994) and Right-Wing Authoritarianism (RWA; Altemeyer, Reference Altemeyer1988) scales, which tap into preferences for group-based hierarchy and social conformity, respectively. These constructs are interpreted as reflecting deeper psychological orientations: preferences for inequality versus equality, and for security versus openness to change (Duckitt and Sibley, Reference Duckitt and Sibley2009). Regardless of differences in labels, these two traditions map onto parallel dimensions, as equality versus hierarchy, and openness versus tradition closely mirror the economic and cultural split observed in political science (Federico, Reference Federico2019; Federico and Malka, Reference Federico, Malka, Huddy, Sears, Levy and Jerit2023).
Crucially, the relationship between economic and cultural dimensions is not consistent across contexts. One contribution used data from 99 countries, finding that a positive correlation between economic and cultural conservatism is uncommon (Malka et al., Reference Malka, Lelkes and Soto2019). In most countries, the correlation is weak or absent. In others, particularly in post-communist societies, it is negative. This pattern can be explained through the lens of the theory of social constraint, as in these contexts, political elites often pair social conservatism with economic liberalism, creating ideological configurations that deviate from the conventional left-right schema.
The contingency of the association between these two dimensions challenges the universality of the left-right scheme and underscores the role of elite discourse in shaping belief systems.
Network models: connectedness and heterogeneity
Although Converse described belief systems as networks, his empirical work relied on zero-order bivariate correlations. Methodological advances have allowed researchers to model political attitudes as interconnected systems using network approaches to multivariate data. This section reviews two key strands of this literature: (1) Belief network analysis (BNA) and partial correlation networks, and (2) correlational and relational class analysis (CCA, RCA). These approaches differ from the latent variable perspective, which assumes that political attitudes are caused by an underlying ideological trait. Indeed, network models are open to the possibility that attitudes are mutually reinforcing elements that interact directly with one another (Borsboom et al., Reference Borsboom, Deserno, Rhemtulla, Epskamp, Fried, McNally, Robinaugh, Perugini, Dalege, Costantini, Isvoranu, Wysocki, van Borkulo, van Bork and Waldorp2021).
The first major advancement in the field was BNA, which represents survey items as nodes in a weighted network, with edges corresponding to absolute correlation coefficients. Studies using BNA confirm that political sophistication enhances belief constraint, as politically knowledgeable individuals display stronger inter-attitudinal correlations (Baldassarri and Goldberg, Reference Baldassarri and Goldberg2014; Boutyline and Vaisey, Reference Boutyline and Vaisey2017). Comparative work supports corollaries of the theory of social constraint, as in polarized political contexts (Gonthier and Guerra, Reference Gonthier and Guerra2023), and in highly institutionalized party systems, there is higher interdependence of political beliefs. Crucially, BNA edges represent zero-order correlations, risking spurious links. Partial correlation methodologies developed in network psychometrics (Borsboom et al., Reference Borsboom, Deserno, Rhemtulla, Epskamp, Fried, McNally, Robinaugh, Perugini, Dalege, Costantini, Isvoranu, Wysocki, van Borkulo, van Bork and Waldorp2021) mitigate these limitations by isolating the unique variance shared between each pair of attitudes (Brandt et al., Reference Brandt, Sibley and Osborne2019). Research using these models shows that symbolic beliefs, such as partisanship, are structurally central (Brandt et al., Reference Brandt, Sibley and Osborne2019; Fishman and Davis, Reference Fishman and Davis2022). They also confirm that political interest (Dalege et al., Reference Dalege, Borsboom, Van Harreveld, Waldorp and Van Der Maas2017, Reference Dalege, Borsboom, Van Harreveld and Van Der Maas2019; Fishman and Davis, Reference Fishman and Davis2022) and ideological extremity (Bentall et al., Reference Bentall, Zavlis, Hyland, McBride, Bennett and Hartman2023) enhance the connectivity of the networks.
A second key insight emerges from studies of CCA (Boutyline, Reference Boutyline2017) or RCA (Goldberg, Reference Goldberg2011). These techniques group individuals based on the correlational structure of their attitudes. Research has shown that the structure of belief systems can dramatically change across population strata. In the U.S., Baldassarri and Goldberg (Reference Baldassarri and Goldberg2014) identified three belief types: Ideologues, whose attitudes align along the left-right axis; Alternatives, who combine progressive and conservative positions; and Agnostics, whose beliefs are weakly and unsystematically correlated. Van Noord et al. (Reference Van Noord, Turner-Zwinkels, Kesberg, Brandt, Easterbrook, Kuppens and Spruyt2024) found that while some Europeans organize their beliefs along traditional economic and cultural dimensions, others structure them around alternative axes. A similar finding emerges from another research, suggesting only those most interested in politics associate their economic and cultural attitudes in accordance with the liberal-conservative continuum (Alexandre et al., Reference Alexandre, Gonthier and Guerra2021). This structural heterogeneity extends beyond political attitudes. Cultural beliefs vary across individuals, with some organizing them along a single axis and others displaying fragmented or multidimensional patterns (Daenekindt et al., Reference Daenekindt, De Koster and Van Der Waal2017). Economic attitudes also diverge: individuals link profit-seeking, redistribution, and state intervention in distinct ways (DiMaggio and Goldberg, Reference DiMaggio and Goldberg2018), and meritocratic beliefs can align either positively or negatively with support for equality and diversity (Bertero et al., Reference Bertero, Franetovic and Mijs2024).
While studies using BNA and partial correlation networks support Converse's original insight (showing that the connectedness of belief systems varies with political sophistication), research adopting CCA and RCA highlights important variation in belief system structure that Converse's theory may overlook. Taken together with findings on the context-dependence of ideological dimensionality, this suggests that political belief systems vary both in internal coherence and in form. In the next section, I integrate these perspectives into a unified framework for understanding belief constraint.
Extending converse: a typology of belief constraint
Measuring constraint at the aggregate level entails assuming that belief systems are homogeneous across individuals, differing only in the strength of attitudinal associations rather than in their fundamental organization. However, the literature on the dimensionality of political attitudes and on the heterogeneity of belief systems suggests population-level measures of belief constraint might obscure structural variations in how different groups conceptualize political issues.
If all individuals were exposed to consistent partisan cues, variation in belief systems would be limited to differences in how strongly individuals internalize these associations. In bipolar systems, parties likely provide opposing cues (e.g. one party supports two policies, while the other opposes both). Therefore, citizens likely exhibit similar belief structures, as both groups would display a positive correlation between the two issues. However, in multiparty systems, individuals are often exposed to conflicting elite signals (Macdonald et al., Reference Macdonald, Listhaug and Rabinowitz1991; Adams et al., Reference Adams, Weschle and Wlezien2021), where different parties might promote divergent issue alignments (Arndt, Reference Arndt2016). This can generate not only variation in the strength of associations but also in their direction. Additionally, in fragmented political systems, parties emphasize issues selectively, based on what they are perceived to “own” (Petrocik, Reference Petrocik1996) and on the priorities of their target voters (Wagner and Meyer, Reference Wagner and Meyer2014). By giving different salience to political issues, parties might influence whether attitudinal connections emerge at all in the belief systems of their voters.
To illustrate these differences, Figure 1 uses simulated data to present a typology of belief constraint along two dimensions: tightness (the strength of associations between attitudes) and consensus Footnote 1 (the extent to which voters of different parties structure beliefs similarly). The bottom-left panel depicts high tightness and high consensus, where attitudes are strongly interconnected, and the correlation is consistent across voters. The bottom-right panel shows low tightness but high consensus, where attitudes are organized similarly across electorates but with a weaker magnitude. In contrast, the top-left panel illustrates high tightness but low consensus: within each partisan group, attitudes are strongly linked, yet voters reach no consensus on how the support for these two issues should be organized. Finally, the top-right panel shows low tightness and consensus, where the correlation of the two issues is low, and where this association is moderated by party choice. The top panels show that low consensus might bias aggregated measures of belief consistency.
A typology of belief constraint.
Research hypotheses
Building on the existing literature and on my extension of Converse's ideas, I test four hypotheses. Issue-based research distinguishes between economic and cultural preferences, while psychological models identify distinct orientations toward equality and tradition. Thus, a growing body of comparative research shows that political ideology is not unidimensional.
H1: Political attitudes in Italy are bi-dimensional
Latent models assume political attitudes reflect a single underlying construct, such as ideology, and treat correlations between attitudes as spurious byproducts of the latent trait (Borsboom et al., Reference Borsboom, Deserno, Rhemtulla, Epskamp, Fried, McNally, Robinaugh, Perugini, Dalege, Costantini, Isvoranu, Wysocki, van Borkulo, van Bork and Waldorp2021). In contrast, network approaches conceptualize attitudes as directly interacting and mutually reinforcing elements. Rather than viewing ideology as an unobservable variable, network approaches conceptualize it as the system emerging from the interconnections between beliefs. Therefore, I empirically evaluate the fit of the two frameworks to understand if the adoption of network models is justifiable.
H2: A network model adequately captures the observed covariance structure among political attitudes
While most prior research has emphasized the tightness of belief systems (how strongly political attitudes correlate), recent research shows that belief systems may also differ in structure across individuals (Baldassarri and Goldberg, Reference Baldassarri and Goldberg2014). Therefore, citizens may reach no consensus on how political attitudes should be organized.
H3: Belief systems show low consensus; their structures vary across the population
In bipolar systems, parties provide clear, consistent cues, aligning issues along a single ideological divide. Here, belief system variation mainly reflects how strongly individuals internalize these signals, which is mainly a function of political sophistication. In multiparty systems like Italy, however, partisan cues are more fragmented and inconsistent. Parties offer competing bundles: PD combines social liberalism with pro-globalization policies, FdI and L link cultural conservatism with market liberalism, while M5S promotes economic protectionism with progressive cultural stances. Given this fragmented cue structure, I expect belief system types to be shaped primarily by political orientations, rather than by sociodemographic traits or political sophistication.
H4: Belief system structures are more strongly shaped by political orientations (ideology and vote) than by sociodemographic characteristics or political interest
Method
Data and variables
I use the fifth wave of the ResPOnsE open dataset, an Italian survey based on quota sampling for residence, gender, and age group (Vezzoni et al., Reference Vezzoni, Ladini, Molteni, Dotti Sani, Biolcati, Chiesi, Maraffi, Guglielmi, Pedrazzani and Segatti2020). Data collection occurred through a CAWI questionnaire. Earlier waves focused on the COVID-19 pandemic, but the fifth wave was fielded one month after the 2022 general elections and includes a thematic section on political attitudes.
Table 1 presents the six attitudes analyzed in this study. Descriptive statistics appear in Table S1 (Supplement). All items are recoded so that higher values indicate greater support for the issue. These variables cover a range of topics often associated with economic and cultural domains, and align closely with prior research on the dimensionality of political ideology (Malka et al., Reference Malka, Lelkes and Soto2019). Items include opinions on euthanasia, same-sex marriage, abortion, income redistribution, and economic globalization, as well as immigration.
Label and survey questions
Variables and labels. The polarity of asterisked items is inverted, so that high scores indicate support.
Sociodemographic variables are sex, age, education, household income, and political interest, the only available proxy for political sophistication. Two categorical variables capture political orientations. Left-right self-placement (0–10) is recoded into four groups: left (0–3), center (4–6), right (7–10), and non-placement. Vote choice is coded into five categories reflecting Italy's major political formations running for the 2022 elections: (1) right-wing coalition (Forza Italia, L, FdI, Noi Moderati), (2) left-wing coalition (PD, Verdi-Sinistra, +Europa, Impegno Civico), (3) M5S, (4) other minor parties, and (5) non-voters (abstention and null votes). This operationalization reduces missingness and preserves analytic coverage.
Given the number of variables included in the analysis, relying on listwise deletion would reduce the sample size from 2,253 to 1,714 respondents. This reduction risks introducing bias. To avoid this, missing data were addressed using multiple imputation by chained equations (van Buuren and Groothuis-Oudshoorn, Reference van Buuren and Groothuis-Oudshoorn2011). Full details on the imputation model and diagnostics are reported below Table S1 (Supplement), which shows variables’ descriptives before and after the procedure. Notably, the sample appears highly polarized along the left-right spectrum and, when compared to actual vote shares in the 2022 Italian elections, it skews toward left-wing parties. All analyses are based on the imputed datasetFootnote 2 (n = 2,253).
Analytical strategy
The analyses feature four steps, each designed to test one of my hypotheses. To evaluate whether Italian political attitudes are structured along two distinct ideological dimensions (H1), I employ exploratory graph analysis (EGA; Golino et al., Reference Golino, Epskamp and Voracek2017), a network psychometric method designed to assess the dimensionality of multivariate data. EGA begins by estimating a Gaussian Graphical Model (Epskamp et al., Reference Epskamp, Waldorp, Mõttus and Borsboom2018), where each item is rendered as a node in a weighted, signed network. Every edge represents a partial correlation: the unique variance shared between two items, controlling for all others. Edges are selected using a regularization approach, the graphical LASSO, which penalizes the complexity of the model by shrinking weak partial correlations toward zero, resulting in a sparse and interpretable network structure (Friedman et al., Reference Friedman, Hastie and Tibshirani2008). EGA then applies the Walktrap community detection algorithm (Pons and Latapy, Reference Pons and Latapy2005) to identify clusters of tightly connected nodes. The number of communities informs the dimensionality of the data. I also bootstrap the sample to evaluate if EGA results are robust.
EGA offers key advantages over factor analysis. It operates on partial rather than zero-order correlations, improving its sensitivity by reducing the risk of spurious associations. It also requires no rotation method. Simulation studies show that EGA outperforms the traditional techniques in recovering dimensionality (Golino et al., Reference Golino, Shi, Christensen, Garrido, Nieto, Sadana, Thiyagarajan and Martinez-Molina2020). Above all, EGA is not constrained by a latent variable framework. While the number of communities mirrors the number of latent factors when data stem from a factor model (Christensen and Golino, Reference Christensen and Golino2021), EGA also accommodates alternative data-generating processes. This flexibility makes it particularly suitable for belief system research, which conceptualizes attitudes not merely as indicators of ideology, but as directly interacting elements (Brandt and Sleegers, Reference Brandt and Sleegers2021). Given the novelty of EGA, I complement it with a confirmatory factor analysis (CFA) that specifies the measurement model derived from EGA's community structure. This two-step strategy enables direct comparison between one-factor and two-factor models using standard fit indices (CFI, TLI, RMSEA, SRMR)Footnote 3 and chi-square difference tests. Converging support (EGA finding two communities, and CFA showing superior fit for the two-factor model) would confirm H1.
To evaluate whether the adoption of network models is empirically justified (H2), I examine the fit of the EGA network structure. Moreover, I compare the fit of the best fitting CFA with that of the EGA network, with the procedure proposed by Kan et al. (Reference Kan, De Jonge, Van Der Maas, Levine and Epskamp2020) and recently refined by Du et al. (Reference Du, Skjerdingstad, Freichel, Ebrahimi, Hoekstra and Epskamp2025). Both models are estimated from the same observed covariance matrix using the psychonetrics R package (Epskamp et al., Reference Epskamp, Rhemtulla and Borsboom2017), which enables direct comparisons via an extension of the structural equation modeling framework. The procedure also involves comparing each model's fit to that of a saturated model, which serves as a benchmark. The saturated model is characterized by zero degrees of freedom, as it perfectly reproduces the observed covariance matrix. This comparison contrasts two theoretical perspectives: the CFA treats attitudes as indicators under the assumption of local independence, while the network model allows attitudes to directly interact. However, the aim of these analyses is not to assert the superiority of one modeling framework over another, as a better-fitting network model does not necessarily indicate that it represents the true data-generating process.
H3 predicts that it is possible to detect differences in the full sample structure of the belief systems. Building on the concept of consensus, I expect to find structural differences, beyond simple differences in connectedness. I use CCA (Boutyline, Reference Boutyline2017) to partition the sample based on the correlation patterns among respondents’ attitudes. Individuals are grouped together if their responses are linearly dependent, that is, if one individual's response vector can be obtained from another's through scaling, shifting, or inverting the values across items. For example, CCA would assign a progressive and a conservative individual to the same class if both respond consistently across all issues (one giving the maximum score and the other the minimum) since their answers produce the same correlational pattern: a uniformly strong and positive correlation profile. CCA determines the number of classes inductively by applying modularity maximization to the network of respondent-level correlations, identifying the partitioning that best captures structural similarities in how individuals organize their attitudes. I proceed by visualizing the correlational network for each group and computing belief system tightness using the bootstrapped mean absolute inter-item correlation (Boutyline and Vaisey, Reference Boutyline and Vaisey2017; Keskintürk, Reference Keskintürk2022). To formally assess whether belief structures differ across classes, I estimate a multi-group SEM comparing a model with freely estimated covariance structures across CCA groups to one where these structures are constrained to be equal. A significantly better fit for the unconstrained model would indicate low consensus.
A key advantage of CCA over other clustering techniques, such as Latent Class Analysis, is that it does not group individuals based on attitudinal means. Each class typically retains high variance in attitude scores and is not, by construction, aligned with specific political identities (Baldassarri and Goldberg, Reference Baldassarri and Goldberg2014). This enables an analysis of individual-level predictors of belief system type, assessing whether CCA-class membership is better predicted by political orientations or sociodemographics (H4). I estimate four regressions: M1 includes only sociodemographics and political interest; M2 adds left-right self-placement, whereas M3 adds vote choice; M4 includes both. Of note, I do not expect CCA to recover a class for each Italian political coalition. Rather, these analyses compare model fit (AIC and BIC) to test whether political factors (M2, M3, and M4) or sociodemographics (M1) better account for belief system structure.
Results
I assess the dimensionality of political attitudes with EGA and CFA. Figure 2 displays the EGA network, where edges represent regularized partial correlations (blue for positive, red for negative), and node layout follows a force-directed algorithm. The figure represents the average belief system structure found in the sample. Most associations are positive; the strongest occur between euthanasia, same-sex marriage, and abortion. The only negative partial correlation is between support for globalization and redistribution. EGA's community detection algorithm identifies two clusters. The first includes cultural attitudes: abortion, same-sex marriage, and euthanasia, which form a tightly connected triad. The second includes economic attitudes (globalization and redistribution) and immigration. Immigration occupies a pivotal position in the network, bridging between cultural and economic clusters.
EGA results.
The dimensionality structure is highly stable: bootstrap results replicate node membership in 99% of samples (Figure S1). CFA prefers the two-dimensional solution. The two-factor model shows improved fit relative to the one-factor model across all indices (CFI = 0.83 vs. 0.77; RMSEA = 0.15 vs. 0.16; SRMR = 0.08 vs. 0.09; Table S2). However, both models fall short of conventional fit thresholds. This is likely due to the negative correlation between globalization and redistribution, which poses difficulties for a latent variable framework. Nonetheless, the combined evidence from EGA and CFA supports H1: political attitudes in Italy are best represented as bidimensional, with distinct cultural and economic clusters.
To test whether the adoption of network models to study Italian political belief systems is empirically justified (H2), I investigate the fit statistics of the EGA network. Moreover, I follow the confirmatory model comparison framework proposed by Kan et al. (Reference Kan, De Jonge, Van Der Maas, Levine and Epskamp2020) by comparing three models: the two-factor CFA, the EGA partial correlation network, and a saturated model serving as the benchmark.
As shown in Table 2, the network model fits the data extremely well. Relative to the CFA model, it yields lower AIC (42,297 vs. 42,684), lower BIC (42,389 vs. 42,793), and a dramatically smaller RMSEA (0.02 vs. 0.15). This value indicates excellent model fit, although a sharp reduction in RMSEA is expected, as recent work has suggested a stricter RMSEA cutoff (0.03) for network models (Du et al., Reference Du, Skjerdingstad, Freichel, Ebrahimi, Hoekstra and Epskamp2025). A chi-square difference test confirms this improvement is statistically significant (Δχ2 = 380.90, P < 0.001). Importantly, the network model does not differ significantly from the saturated model (Δχ2 = 10.94, P = 0.053), indicating that it captures the covariance structure nearly as well as a fully parameterized benchmark. This reinforces the suitability of partial correlation network models for representing the structure of political attitudes. Given that the item on globalization correlates negatively with redistribution, which is another economic variable, I conduct a robustness check excluding it. This improves the fit of the CFA model (Table S4) but does not lower the adequacy of the network model, which retains excellent fit. Together, these findings support the view that political attitudes in Italy can be modeled as a network of interrelated beliefs.
Fit comparison
Comparison of fit statistics across saturated, EGA, and latent variable model.
H3 posits that there is low consensus on how Italian political attitudes should be structured. I use CCA, which partitions individuals based on similarities in the inter-attitude correlation patterns. The algorithm identifies three distinct classes, whose belief system is shown in the top panel of Figure 3. The bootstrapped distributions of belief tightness (the average absolute correlation) of each class are plotted in the bottom panel. Full correlation matrices are available in Figure S2.
Consensus and tightness of Italians’ belief systems.
Class 1 (N = 517) exhibits the most coherent belief system, with consistently strong and positive correlations across all attitudes (tightness ≈ 0.45). Following Baldassarri and Goldberg (Reference Baldassarri and Goldberg2014), this group can be described as Ideologues: individuals whose attitudes are tightly integrated and align with the left-right organization. Class 2 (N = 852) shows a structurally distinct pattern: globalization is negatively associated with redistribution and immigration, as well as with two cultural attitudes (same-sex marriage and euthanasia). This class displays moderate tightness (≈ 0.35). These individuals adhere to a coherent belief system, but one that deviates from conventional left-right ideological alignments. I label this group Alternatives, a term used by Baldassarri and Goldberg to describe individuals whose beliefs are internally consistent but follow a cross-cutting or unconventional logic. Class 3 (N = 876) is the largest and least ideologically structured. Their belief system presents weak associations (tightness ≈ 0.25) and negative links between most economic items. I term this class Fragmented, to highlight their disjointed, loosely connected attitudes.
To formally test H3, I estimated a multi-group SEM based on the CCA-derived classes and compared it to a pooled (single-group) model. As shown in Table S5, the multi-group model provided a significantly better fit (Δχ2 = 123.87, P < 0.001), along with substantially lower AIC and BIC values. This confirms that Italians do not share a single, unified belief system structure.
Figure 4 displays the distribution of responses for each item by class. Red dots mark overall means, while black dots with confidence intervals (CIs) indicate within-class means. This plot informs us about how attitudinal levels vary across belief system types, introducing results for H4. The distributions reveal substantial heterogeneity within each class, although none of the items are truncated or polarized at the extremes. This confirms CCA retains meaningful variance, avoiding to simply divide respondents into “high” versus “low” agreement groups. Ideologues (Class 1) express above-average support for redistribution, globalization, and immigration, suggesting a concentration of economically progressive profiles. Alternatives (Class 2) are generally aligned with the national average on all issues, but exhibit pronounced opposition to globalization. Finally, Fragmented individuals (Class 3) tend to score lower on immigration and redistribution, pointing toward a conservative attitudinal profile. Importantly, these class-specific distributions reflect variation in levels of agreement, not in the structure of associations. For instance, the Ideologue class includes both progressive and conservative respondents; what unites them is not their stance on each issue, but the consistency of their responses across them. Similarly, the Alternatives may support all issues except globalization, or oppose all except globalization: their internal pattern remains coherent.
Item means and distribution by CCA class.
To examine the individual-level predictors of belief system type (H4), I estimate a series of multinomial logit models predicting CCA class membership. M1 includes only sociodemographic variables and political interest. As shown in Table S6, these predictors explain very little variance in belief system type (McFadden's R 2 = 0.005). Among them, only political interest is statistically significant: it decreases the odds of belonging to the Fragmented class (OR = 0.82, 95% CI [0.71–0.94]), as it is related to membership in the Ideologues class. Figure 5 visualizes these predictions. All other sociodemographics (education, income, sex, and age) are not significantly associated with class membership.
Predicted probability of belief system membership by political interest (M1).
M2 adds ideological self-placement. As shown in Table S7, this model significantly improves explanatory power (R 2 = 0.029). M3 includes vote choice instead of ideology, achieving a similar improvement (R 2 = 0.022; Table S8). I visualize predictions from these models in Figure S3. Taken together, these models show that right-wing identifiers and voters are significantly more likely to belong to the Fragmented class, whereas supporters of the M5S and of the left-wing coalition are more likely to be Alternatives. The predicted probabilities of being an ideologue are always the lowest across models. Notably, these values are the highest among left-wing identifiers (M2) and voters (M3). Finally, individuals who refuse to locate on the left-right scale (M2) or abstain (M3) show lower odds of being Ideologues.
I test H4 through Table 3, which compares models’ performances using AIC and BIC. Results confirm that political variables offer substantial gains in explanatory power over sociodemographics. While M1 (sociodemographics + political interest) has the weakest fit, adding ideological self-placement (M2) substantially improves performance (ΔAIC = −105.70). M3, which includes vote choice instead, performs worse than M2, suggesting that left-right is a stronger predictor of belief system type than party preference. The best-fitting model is M4 (Table S9), which considers all political predictors and background variables (AIC = 4710.30; BIC = 4858.93). Taken together, these results support H4.
Model comparison
AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), and DF (Degrees of Freedoms) of the four models.
Discussion and conclusions
This study examined the structure of political ideology in Italy by conceptualizing it as a belief system: a network of interconnected political attitudes. Using both a latent and a network-based framework, I found that Italian political beliefs were best represented as bidimensional, distinguishing between economic and cultural domains. Moreover, EGA, a partial correlation network model, fits attitudinal data extremely well. I then applied CCA and multi-group SEM to demonstrate that Italians exhibited low belief consensus, holding structurally distinct belief systems. Finally, I showed that holding a certain type of belief system was more strongly predicted by ideological self-placement and vote choice than by sociodemographic characteristics or political interest.
This article engages with two strands of literature. First, I contribute to ongoing debates on the dimensionality and conceptualization of political ideology. In line with prior work (Malka et al., Reference Malka, Lelkes and Soto2019), I found evidence of two distinct ideological dimensions. Notably, immigration attitudes clustered with economic beliefs and served as a bridge between economic and cultural domains. Although the item specifically concerned extending citizenship to migrants born in Italy, its association with economic rather than cultural issues may reflect the longstanding framing by Italian right-wing parties, which emphasized immigration's economic costs (Bulli and Soare, Reference Bulli and Soare2018). Moreover, these results echo studies showing that the dimensional structure of ideology varies across individuals (Alexandre et al., Reference Alexandre, Gonthier and Guerra2021; Van Noord et al., Reference Van Noord, Turner-Zwinkels, Kesberg, Brandt, Easterbrook, Kuppens and Spruyt2024). My findings build on this by showing that network models offer a flexible and empirically adequate way to represent associations among political attitudes. Importantly, this does not imply that latent variable models should be dismissed. Rather, network models complement traditional approaches by relaxing the assumption of local independence, which treats inter-item correlations as spurious. Conceptually, the two frameworks differ in how they understand ideology: latent models treat ideology as an underlying, unobservable cause that gives rise to manifest attitudes; network models, by contrast, treat ideology as isomorphic to the structure of observed attitudes.
Second, I advance research on belief system heterogeneity. Consistent with Baldassarri and Goldberg (Reference Baldassarri and Goldberg2014), I identified three distinct types of belief systems in Italy: Ideologues, who aligned with the classic left-right schema; alternatives, whose beliefs showed a negative association between globalization and other attitudes; and Fragmented individuals, whose networks were weakly structured and loosely connected. Their U.S.-based contribution has found that social background characteristics and political sophistication importantly predicted belief system structure. In Italy, political orientations (left-right self-placement and vote choice) were stronger predictors instead. This result supported my extension of Converse's theory: in fragmented multiparty systems with inconsistent partisan signals, belief systems are primarily shaped by the heterogeneities of party cues. Italians, specifically, disagree on how globalization relates to other issues: some link it to social and economic progressivism, others to conservatism. This ambivalence reflects the conflicting signals sent by the major Italian parties: while the PD defends globalization as compatible with progressive values like international cooperation and environmental regulation, the M5S mixes left-wing economic justice rhetoric with sovereigntist skepticism, and right-wing parties frame it as a cultural threat to national identity, yet endorsing pro-business policies.
This study has two main limitations. First, despite using CCA to avoid modeling the belief system as a population-level construct, the analysis remained rooted in aggregate data. Therefore, as noted by Brandt and Sleegers (Reference Brandt and Sleegers2021), the output of the network models I used represents more sociopolitical cleavages rather than the individual-level structures of belief systems. This is at least partially at odds with the original theoretical framing of belief systems as individual-level constructs (Converse, Reference Converse2006). Future research should explore methodological tools like conceptual similarity judgments to address this gap (Brandt, Reference Brandt2022). Second, this study adopted a bottom-up approach that emphasized elite messaging and cue structures. While theoretically grounded, this perspective should be complemented with research on the psychological and dispositional foundations of ideology (Bakker and Lelkes, Reference Bakker, Lelkes, Osborne and Sibley2022), to better integrate top-down and bottom-up mechanisms of belief system formation.
Funding
This research received no specific grant from any public or private funding agency.
Data
This study relies on publicly available survey data, accessible at the following link: https://dataverse.unimi.it/dataset.xhtml?persistentId=doi:10.13130/RD_UNIMI/IJDSVS. The R Markdown files reproducing the analyses reported in this Article and in the Supplement, are available at the project's Dataverse repository: https://doi.org/10.7910/DVN/RDEXKC. For a fully reproducible workflow that can locally generate all figures and tables please refer to the project's GitHub repository: https://github.com/arturobertero/Beyond_Constraint.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/ipo.2025.10080.
Acknowledgements
Analyzing data and writing a single-author paper are lonely enterprises, but thinking is not. I am grateful to all those with whom I have discussed this project, listed in alphabetical order: Giuliano Bobba, Moreno Mancosu, Raffaele Vacca, Federico Vegetti, and Cristiano Vezzoni. I also thank the anonymous reviewers for their constructive comments.
Competing interests
The author declares none.
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