Charting fields and spaces quantitatively: from multiple correspondence analysis to categorical principal components analysis

MCA as a technique is designed to uncover underlying relationships within quantitative data. More specifically, it looks for associations between categories of multiple variables, detecting, for example, that people who say X are also likely to say Y, but also that some people who say X and Y are likely to say A too while others say B instead. It does this by breaking down the total variance or inertia within the data into a series of axes – sometimes described as dimensions or factors – accounting for descending proportions (denoted by eigenvalues), the patterns of association and opposition between variable categories thus being translated into distances within a space. X and Y will be close together on one axis, but opposed to Z, while X, Y and Z might be close together on a second axis but A and B polarised. The analyst retains for interpretation only those first n axes that together account for a satisfactory proportion of total inertia, also paying attention to any substantial drop-off in inertia rates between axes.

MCA has been developed independently by different statistical traditions (DiFranco, 2016). The Leiden school of psychometry elaborated it under the label of ‘homogeneity analysis’ in the 1970s and 1980s, alongside PCA and other techniques, as a method of data reduction that can produce axes definable as scales for subsequent regression analysis (Gifi 1990). In France, MCA was spearheaded by Benzécri and evolved, in the work of Ludovic Lebart, Brigitte Le Roux and Henri Rouanet, into the broader programme of GDA, the core interest of which is the geometric properties of the space itself, that is, the distances and directions of deviation between variables/categories or cases (see esp. Lebart et al. 1984, 2006; Le Roux and Rouanet 2004, 2010; Le Roux 2014; Le Roux et al. 2020). An extra layer of analysis was enabled by the distinction between ‘active’ variables – variables used to construct the model – and ‘supplementary’ variables – variables not used to construct the space. This is because positions and dispersion along axes of supplementary categories can reveal correspondences and homologies between ‘outcomes’ and possible causal factors. Those advancing the GDA tradition have, moreover, established a number of statistical tests and guides for interpreting these correspondences. Lebart et al. (2006), for example, devised a test similar to the one-sample t-test to determine whether or not a category’s location on an axis is important (the congenial language of ‘atypicality’ is used for a similar test developed by Le Roux and Rouanet 2004), and a distance between factor coordinates is deemed notable when it is 0.4 or more units or standardised deviations (SDs) on an axis and large if it 1.0 or more (Le Roux et al. 2020). Univariate analysis of variance with an axis as the dependant variable, and the related eta-squared figure denoting explained variance on the axis (on a 0–1 scale), also allows one to adjudicate the extent to which a variable is associated with an axis given inter- and intra-category dispersion (Hjellbrekke 2019).¹

Bourdieu came into contact with Benzécri and Lebart in the 1970s and, in later years, worked directly with Le Roux and Rouanet (Bourdieu 2008). He believed MCA to be a good fit for his relational mode of thought centred around a conception of social structures in terms of ‘fields’ and ‘social spaces’ (Bourdieu 1984; Bourdieu and Wacquant 1992; Bourdieu et al. 1991). A field is an arena of social struggle between a set of agents over certain forms of power or ‘capital’, possession of different types and amounts of which constitute the structure of the field and the conditions of possibility for specific perceptions and practices. It is noticeable, in fact, that Bourdieu’s theorisation of fields as relational structures took on a specific form after his contact with Benzécri’s school in the 1970s: a more spatialised or geometric form, which harmonised with a structuralist vision organised around oppositions, directions and distances rather than interactions and which even tended to borrow operations and terms from the statistical methods such as ‘inertia’, ‘weight’ and so on. Conceptual development and methodological development went hand in hand, in other words, just as Gaston Bachelard, Bourdieu’s prime epistemological influence, would have it.

Examples of fields documented by Bourdieu and his colleagues using MCA include the academic field (Bourdieu 1988), the field of CEOs (Bourdieu 1996) and the field of publishing houses (Bourdieu 2008). The overall class structure of a society is also a field, though Bourdieu (1984) preferred to call this the ‘social space’, and is structured by possession of economic capital (money, assets), cultural capital (credentials, parental education) and social capital (connections, memberships). The primary axis of the social space was held to be total capital volume, while a secondary axis distinguished people on account of their capital composition, i.e. whether it is predominantly economic or cultural in constitution. This represents a break with unidimensional visions of stratification, whether measured via socio-economic scales or occupational schemas. Bourdieu did not map the French social space using MCA, however. Instead he mapped out the space of lifestyles: the space of goods, practices and tastes acting as symbols of class position. More accurately he mapped out two, one for the dominant class and one for the intermediate class. He could then explore the correspondences with social positions, or the homology with the social space, by projecting indicators of capitals, as supplementary variables, into the models of the lifestyle spaces, though he was working before the aforementioned tests and benchmarks were established.

After a period of relative neglect, MCA has, over the last 15 years, started to penetrate mainstream sociology. Scholars interested in testing or updating Bourdieu’s ideas, mostly but not exclusively across Europe, have started to adopt it (see Robson and Sanders 2009; Grenfell and Lebaron 2013; Blasius et al. 2020). For the most part this has been mediated by the continued influence of Le Roux and Rouanet, meaning the majority – there are some exceptions – implement the specifically French GDA-style approach to MCA. Especially prominent have been studies of national social spaces (e.g. Prieur et al. 2008, Rosenlund 2009, Flemmen et al. 2018; Atkinson 2022a) and lifestyle spaces (Bennett et al., 2008; Le Roux et al. 2008; Blasius and Muchlichen, 2010; Flemmen et al. 2019; Coulangeon and Duval 2015; Schmitz 2017; Hanquinet and Savage 2018; Atkinson 2017, 2021, 2022b; Atkinson and Marzec 2023), but another strand of work has also examined the space of political attitudes and its relationship with class (Harrits et al. 2010; Flemmen 2014; Flemmen and Haakestad, 2018; Barth and Schmitz 2018; Jarness et al. 2019; Atkinson, 2017). The logic in the last case, building on arguments and sketchy analyses by Bourdieu (1984) himself, is that political attitudes form a relational system symbolising class ethos in a similar manner to lifestyles. MCA offers an alternative to the common use of factor analysis in the study of political attitudes, as in the work of Ronald Inglehart (1977, 1990, 1997; Norris and Inglehart 2019) for example, and the usual finding is that political attitudes fall along two axes: one distinguishing ‘old’ left/right-wing views on economic matters (e.g. income redistribution, collective ownership, industrial relations) and another distinguishing ‘new’ liberal/traditional-authoritarian views on ‘moral’ or non-material matters (e.g. homosexuality, immigration, defence). Summarising crudely, high/low cultural capital corresponds with the liberalism/authoritarian axis and high/low economic capital corresponds with the right/left-wing economics dimension, but this means that capital volume and capital composition are associated with different shades, combinations and polarisations of views.

At stake in many of these Bourdieu-inspired studies is not just the relative importance of social class but the status of capital composition as a principle of social, cultural and political differentiation. This is important from a theoretical point of view because it relates to whether and to what extent class structures are multidimensional – and thus how well they are approximated by catch-all hierarchal measures like occupational schemes – and if Bourdieu’s thesis might overplay the cultural/economic polarisation because of a Francocentric overestimation of the importance of intellectuals (e.g. Lamont 1992; Savage 2010, 2021). Some analyses using MCA have, indeed, questioned it. Several studies of lifestyles, for example, have suggested capital composition is subordinate to age or gender in polarising tastes and practice, if it appears at all (e.g. Bennett et al., 2008; Le Roux et al. 2008; Börjesson, 2015). In these cases, the conclusions rest on the specific selection of variables for analysis, and when alternative variables are used – arguably more suited to testing the capital composition thesis – Bourdieu’s model is more or less confirmed and updated, including in the very same national cases where it is apparently absent (see e.g. Flemmen et al. 2019; Atkinson 2017, 2021).

In other cases, however, the capital composition principle is questioned because the MCA model suggests a unidimensional solution. More precisely, the categories and cases on the plane of the first two axes are arranged in a parabolic U-curve known as the horseshoe or Guttman effect, indicating strong intercorrelation between the active variables. In practical terms, the first axis usually opposes high/low-style responses to questions while the second axis opposes extreme/middle responses. If the space in question is a model of the social space – as in Lemel and Katz-Gerro (2015), Doolan and Tonkovic (2021) or Marzec (2019), for example – then the first axis distinguishes those with high/low capital while the second axis distinguishes those with high and low capital from those with middling levels of capital.

The Guttman effect is not necessarily a statistical artefact, but neither is it especially interesting. The usual response is to seek to go beyond it and find other dimensions of greater sociological interest (Hjellbrekke 2019: 96). This can be done by focussing on a third axis (e.g. Harrits et al. 2010; Marzec 2019), aggregating variable categories (e.g. Meuleman and Savage 2013) or employing forms of fuzzy coding such as ‘doubling’ (Greenacre 2017). Sometimes, however, the effect can account for so much inertia in the model as to make interpreting a third axis hard to justify from a statistical point of view, or it can persist even after extensive recoding, which can itself become distortive or reduce differentiating power in the model (or produce artificial models in the case of doubling). The effect can be especially intractable if the variables analysed are Likert scale items. After all, the Guttman effect efficiently reveals that the variables selected for analysis follow an ordinal structure – there is a known low-to-high rank order to responses – rather than a strictly multiple nominal structure (Le Roux and Rouanet 2004: 220-1). In this case some researchers would turn to a different method designed to handle ordinal variables: CatPCA.

CatPCA, also known as nonlinear PCA (NLPCA), was developed by the Leiden School and, in technical terms, operates in precisely the same way as MCA and linear PCA (Di Franco 2016): it constructs a space defined by axes of varying contribution to total model inertia that can then be subjected to follow-on tests of supplementary variables in the style of GDA. The difference is that CatPCA can handle any and all types of data simultaneously – continuous and categorical data – and, crucially, one can specify beforehand if categorical variables follow an ordinal or simple/multiple nominal structure. If a variable is set to follow an ordinal structure, then the low-to-high structure is assumed and the variable is constrained to follow a vector through the centre of the space, thus erasing the possibility of it forming a horseshoe.² This is accomplished via optimal scaling. Categorises are quantified, i.e. assigned numerical values on a scale, in such a way as to maximise explained inertia in the model. One can then inspect transformation plots for each variable, plotting category quantifications in a line graph, to adjudicate whether a variable is indeed best treated as nominal or ordinal, to see where the key points of differentiation within the variable are and to check model stability (see Atkinson 2020). CatPCA as a method is therefore much more flexible than either MCA or linear PCA and allows an efficient escape from the Guttman effect. The downsides are that it is not as simple since the optimisation phase requires the analyst to iteratively inspect, determine and justify the best measurement level of each variable, and that resultant models are sensitive to such decisions. There is also the risk that a horseshoe effect is erased without acknowledgment of its existence or strength if variables are assumed to be, and set as, ordinal from the outset. That is as undesirable as being unable to move past the effect. Starting from the multiple nominal level of categorical measurement, perhaps with a straightforward MCA, is thus prudent before proceeding to explore other options.

There are a few minor operational differences between MCA and CatPCA. One is that axis retention in CatPCA is based on slightly different criteria and takes place only after examination of solutions of varying pre-set dimensionality. These criteria include the Kaiser principle (eigenvalue > 1), very good total variance accounted for on each variable (> 0.4 according to Comrey 1973) and satisfactory explained inertia in the model (e.g. >50%), as well as the usual considerations of sociological interpretability and parsimony. Models can be rotated, in the style of linear PCA, to modify differences and axis inertia, but many working in the French GDA tradition criticise rotation on the grounds that it introduces artificial distortion and produces a less proximate model of reality (Rosenlund 2009: 154) and it is not advocated. After all, the point of rotation is often to maximise axis orthogonality for subsequent regression analysis while the focus of GDA is on the base dimensions, distances and directions of deviance. For this reason, Cronbach’s alpha is of little interest. A risk of the French approach, though, is that one can sometimes be left with axes that represent skewed proxies for hypothesised or theoretically meaningful axes, which then effects the capacity to perform subsequent tests satisfactorily.³

Another difference between the methods is that, in judging the importance of a variable to an axis in CatPCA, one pays attention to the factor loading, or the correlation of the variable with the axis, with anything greater than +/-0.4 being considered important. However, one can calculate from this the relative contribution of the variable to the axis variance and highlight above-average (‘explicative’) contributions, matching the common logic of MCA.⁴ Finally, centroid coordinates of variable categories in CatPCA are mean scores on axes rather than factor coordinates. Lebart et al’s (2006) test values for notability can still be calculated, but instead of SDs one can use independent (Student’s) t-tests to determine whether the distances between points are important or not, so long as this is understood as a benchmark for assessing the notability of distances rather than a tool of hypothesis testing.⁵ This can be paired with Cohen’s d to estimate the ‘effect size’ in a manner comparable to SDs: anything between 0.2 and 0.5 is considered small (but not negligible), anything between 0.5 and 0.8 is typically considered a ‘medium’ effect and anything over 0.8 is considered ‘large’, though of course these are points on a scale rather than fixed categorical thresholds (Cohen 1988: s.2.2.3).

CatPCA is employed readily within political science and sometimes within sociology (e.g. Maire 2021). It is not, however, currently considered part of the French GDA toolkit, even though linear PCA is. It is absent, for example, from the major texts of the tradition, including Le Roux and Rouanet (2004), Lebart et al. (2006) and, more recently, Husson et al. (2017). The disconnect is even perpetuated by software differences: SPAD, a French software package for conducting MCA and other GDA methods recommended by Le Roux and Rouanet (2010) and Hjellbrekke (2019), does not currently contain a module on CatPCA. CatPCA, on the other hand, is available in, among other software packages, R, Stata and SPSS, the last of these containing an MCA module designed by the Leiden School but explicitly warned against by Le Roux and Rouanet (2010).⁶

As a consequence, CatPCA is not typically deployed by the Bourdieu-inspired wishing to construct and explore statistical models of fields or spaces. An exception is Joye et al. (2020), whose mission to broaden the methodological mindset of Bourdieusians and encourage experiments and comparisons with different spatialising techniques is similar to that expressed here (see also Rosenlund 2009), though their focus is only on concordance of solutions and they do not explore geometric properties of the spaces. Most, however, stick resolutely to MCA, and where the horseshoe effect occurs it is sometimes – as in Lemel and Katz-Gerro (2015) or Doolan and Tonkovic (2021) – simply reported as an approximation of social reality. That is not inadmissible – the effect does demonstrate the importance of the middle/extremes opposition – but it is problematic to then leap from the model to reality and conclude that any other dimensions of difference are irrelevant or sociologically marginal. It may simply be that the MCA model is telling us that all/most of the variables follow an ordinal structure and should be treated as such. After all, MCA was designed for multiple nominal variables and is ideal for variables such as favourite restaurant, industry of occupation or political party of choice. These can even be mixed with ordinal variables without much disturbance – a Guttman effect may appear on a lower-order axis, for example (as, indeed, it did for Bourdieu, [1984], Bennett et al. [2008] and Atkinson [2022a]), if at all – but the more ordinal variables there are, to the limit point of having exclusively ordinal variables, the more the chances of obtaining a Guttman effect in the principal plane increase. Perhaps for this reason, Rosenlund (2015) expressly recommended including a multiple nominal measure of occupation or industry when constructing models of social spaces with MCA, since many measures of capital like education level or income do often follow ordinal structures, though if there are no such variables available in the dataset at hand then that advice founders. So why not turn to CatCPA instead? Possibly because MCA is considered exhaustive, in the minds of many of those inspired by Bourdieu, of statistical methods of constructing and exploring spaces, whether because of lack of familiarity with other methods or aversion to techniques associated with very different traditions. Yet there may be more than one way to skin the proverbial cat. There may even be better ways to flay the feline.

Elsewhere I have suggested the utility of using CatPCA for constructing models of national social spaces when MCA struggles to get beyond horseshoes (Atkinson 2020, 2022c), but here I want to demonstrate its usefulness in relation to studying the space of political attitudes. As a case study I will take the recent analysis of British attitudes produced by Lindell and Ibrahim (2020). This case has been selected because of Lindell and Ibrahim’s commitment to Bourdieu-style MCA, the boldness of their conclusions, the stark contrast with previous findings, including in the same national case (Atkinson 2017), the public availability of their chosen data source and the welcome openness of the authors to further studies on the dimensionality of political attitudes. It is not a comment on the facility of the authors with either MCA or British politics or on the quality of their work.

Lindell and Ibrahim use the following five-point Likert scale variables denoting left/right politics and liberal/authoritarian attitudes from the 2016 sweep of the European Social Survey (ESS) to construct an MCA model of the post-Brexit space of political attitudes and examine the relationship with class and other factors:

Their model suggested that left/right and liberal/authoritarian attitudes are strongly correlated along the first axis and cross-cut on the second axis only by intensity of opinion – in other words, they uncover a Guttman effect (cf. Majima and Savage, 2008). The authors stated that, when faced with this result, they tried recoding the five-point scales into three-point scales but produced the same outcome, opting to retain the five-point scales apparently because of greater proximity to reality. They declined to discuss the third axis, even though it had an inertia rate comparable to the second dimension and substantially higher than the fourth dimension (representing drop-off), because it is described as a ‘variant’ of the first axis. Ultimately, they concluded, intensity of opinion is a real and powerful feature of British political attitudes crowding out any other secondary polarisations. Scrutinizing supplementary variables, they conclude with surprise – since it contradicts established patterns – that class is relatively unimportant for shaping political attitudes and, on top of that, any effects of capital composition are entirely absent. They suggest this may reflect the social realities of contemporary Britain as opposed to Bourdieu’s France.

One can raise questions about whether the active variables are really the best to tap into the different dimensions of political attitudes, and the use of five-point scales with low-frequency extremity categories risks model instability, i.e. attributing small-n categories disproportionate power in determining axes (Hjellbrekke 2019). We will put those issues to one side, however. More problematic is the reliance on basic unidimensional indicators of class position, especially the UK National-Statistics Socio-Economic Classification of occupations (NS-SeC). This is an insufficient proxy for any posited multidimensionality of the social space and an alternative classification of occupations designed to approximate capital volume and capital composition, and validated via MCA, will be used instead (Fig. 1) (Atkinson 2017, 2022c; Atkinson and Rosenlund 2014).

I have taken the liberty of obtaining the 2016 ESS dataset and replicating Lindell and Ibrahim’s analysis as closely as possible. The results obtained from the replication were not exactly the same as theirs, which might have something to do with the unspecified ‘missing values’ in Lindell and Ibrahim’s analysis (missing values were treated as passive in my analysis rather than excluded). Still, relative frequencies and the general distribution of categories in the plane of Axes 1 and 2 are almost identical (Fig. 2). Inclusion of the Bourdieusian class scheme already reveals a stronger relationship with political attitudes than originally supposed: coordinates of different class fractions are more dispersed, important according to tests and notably distanced from others in terms of SDs (Fig. 3, Table 1). We learn that the cultural dominant class fraction is most left-liberal and that technicians, skilled workers and lower managers/proprietors (LMPs) are most right-authoritarian, but also that caring/sales workers and cultural intermediaries are associated with less ‘intense’ opinions.

The third axis is not, in fact, merely a variant of the first. It operates to split the liberal-left pole of Axis 1 into a liberal/pro-EU quadrant (bottom right) and an economically egalitarian quadrant (top right) and to split the authoritarian-right pole into a mild version (bottom left, at the same pole as liberalism on Axis 3) and a more extreme version (top left, at the same pole as economic egalitarianism) (Fig. 4). This is not all that far from what has been found in other studies. However, the modified inertia rates in the present model, using Benzécri’s (1992) formula to correct for underestimation, are different from Lindell and Ibrahim’s: in this version, the first axis bears a rate of 68% and the second a rate of 23%, followed by just 4% on the third. In this instance, then, there is certainly a good argument for forgetting about the third axis. Many of the small-n extremity categories also have relatively powerful contributions on one or more axis, attributing a lot of structuring power to relatively few people and confirming earlier reservations about stability. Aggregating all the variables into three categories remedies this but has the effect of producing a first axis with a modified inertia rate of 84%, making the model truly unidimensional (the second dimension still, as Lindell and Ibrahim found, produces a parabolic curve).⁷

We can accept, then, that the MCA reveals that intensity of opinion matters in structuring political attitudes. To say that any other principles of difference are sociologically marginal or irrelevant, however, is too hasty and possibly to mistreat the data on the basis of what they are telling us in the MCA. Lindell and Ibrahim quote Benzécri to the effect that the model should fit the data, not the other way around, but if the data are clearly revealed to be ordinal, then should we not construct a model fitting that structure? We are not hiding or downplaying the middle/extreme opposition – far from it, since I have also argued for its importance on similar grounds (Atkinson 2017) – but it is worth exploring other methods specifically designed to look beyond the extreme/middle divide, i.e. CatPCA. MCA is then a necessary preliminary to CatPCA: it establishes the ordinal nature of responses, and that intensity of opinion (or some other middle/extreme divide) matters, and if third axes or moderate recoding are off the table then we move on to other methods to explore salient polarisations obscured by the first method.

Running a CatPCA on exactly the same data, with the variables set as ordinal, certainly provides a very different view. Three axes are extracted on the basis of the criteria set out earlier (Table 2).⁸ The first of these, judging from factor loadings and relative contributions of variables, is the same opposition of right/authoritarian and left/liberal that emerged in the MCA, confirming that this is indeed the key dimension of difference structuring British politics. We do see, however, that attitudes toward classic materialist issues of redistribution and welfare are less important to the axis than views on immigration, Europe, sexuality and fossil fuels, suggesting the liberal/anti-liberal polarity is the primary structuring feature of political attitudes in the sample. The second axis bears an opposition between those who are right-wing on material matters but liberal on ‘new’ politics – especially immigration – and those who are left-wing on old politics but anti-migration. Looking at vector coordinates in the plane of axes one and two (Fig. 5), we see four distinct quadrants: left-wing (top left), right-wing (bottom right), liberal (bottom left) and anti-liberal (top right). This structure approximates what has been found in previous Bourdieu-inspired studies, including in the UK (Harrits et al. 2010; Flemmen and Haakestad, 2018; Jarness et al. 2019; Atkinson 2017).⁹ The third axis, for its part, is structured around an opposition between those who are against government redistribution (and who self-identify as right-wing), but nonetheless in favour of benefits to get people working even if it means higher taxes, and those of the opposite view, who also oppose taxing fossil fuels.

Focusing on the plane of Axes 1 and 2, projection of indicators of capital and class position as supplementary variables reveals a very different picture from what emerged in Lindell and Ibrahim’s paper (Fig. 6).¹⁰ First, education level, or institutionalised cultural capital, follows a roughly south-westerly trajectory: lower cultural capital is associated with authoritarian views and higher cultural capital is associated with liberal views. Coordinates for all the presented categories are important on one or both axes, according to test values, with the exception of GNVQs/5 + GCSEs (these are mid-level secondary qualifications), which sit close to the centre of the space (Table 3). Tertiary education is, however, more strongly associated with Axis 1 than Axis 2, as indicated by not just coordinates but the relative size of test values, suggesting that its holders are typically more liberal-left than liberal-right in ethos. This is in contrast to holders of A levels – higher-level secondary qualifications – who are, by the same metrics, strongly associated with Axis 2 but situated more centrally on Axis 1. Student’s t-tests suggest that, on Axis 2, the distances between, on the one hand, the mean for those with A levels and, on the other hand, the means for those with PhDs (t = 2.59, df = 173, p < 0.01), Masters degrees (t = 2.47, df = 278, p < 0.05) and undergraduate degrees (t = 3.74, df = 424, p < 0.001) are important, even if effect sizes are in the small-to-medium range (d = 0.44, 0.28, 0.37 respectively).

Mother’s education – as an indicator of ‘inherited’ cultural capital – is also strongly related to the axes. In this instance, though, the relationship with the first axis is much stronger than with the second axis: test values are noticeably larger on Axis 1 and the F statistic and eta-squared figure are three times those for Axis 2. The distance between mean points for mothers with no education and degree educated mothers is significant on axis 2 (t = 5.92, df = 1072, p < 0.001) but the relationship is much stronger on axis 1 (t = 9.74, df = 1072, p < 0.001). This is reflected in the respective Cohen’s d figures: on Axis 2 it is 0.49 – a medium effect – but on axis 1 it is 0.88, and thus comfortably large.

Confirming the patterns so far, but alluding to homology with the broader structure of the British social space, is the distribution of the categories of the Bourdieusian class scheme. There are, for sure, some categories clustering around the barycentre, which suggests a tendency toward ‘the middle ground’ among those class fractions – this is what the MCA detected – but more categories possess coordinates in the space that roughly approximate the expected structure of the homology from previous research (esp. Atkinson 2017): the cultural dominant are associated with liberal/centre-left views, business executives with liberal-right views and the white-collar workers in between; manual workers, skilled workers and technicians tend toward authoritarian views but are differentiated by their gravitation toward left or right-wing views on material politics; and the LMPs are associated above all with right-wing views on materialist politics.