In the social sciences, multiple correspondence analysis (MCA) owes much of its fame to the work of the late Pierre Bourdieu (1930–2002). Now classic works like L’anatomie du gout (Bourdieu and de St. Martin 1976), Le patronat (Bourdieu and de St. Martin 1978), Distinction (Bourdieu 1984[1979]), Homo Academicus (Bourdieu 1984) and State Nobility (1996[1989]) all relied heavily on the use of either simple correspondence analysis (CA) or multiple correspondence analysis (MCA). By subjecting data on various forms of capital distributions to CA or MCA, field structures were objectified and the homology thesis, i.e. fields in the modern French society was structured in similar ways.

The problem of homology has been a returning question in the reception and the attempts of replicating Bourdieu’s work, both within and outside of France (see Robette & Roueff and Flemmen et al. in this volume). In this chapter, we’ll discuss how this hypothesis can be investigated statistically by turning to two variants of geometrical data analysis: MCA and class specific MCA (Le Roux and Rouanet 2010; Hjellbrekke 2018). In particular, class specific MCA (hereafter CSA) is a methodological innovation that allows us not only to explore the relation between the field of power and its subfields, but also to discuss how Bourdieu’s homology thesis may be scrutinized.

Social Space, Social Field, Field of Power and Subfield

Analytically, the term ‘social space’refers to a theoretically weighted synthesis of the main principles of stratification in any given society. In the disciplinary history of sociology it was Pitirim A. Sorokin who first associated the term with a synthesis of various forms of social stratification (Sorokin 1959 [1927]), but arguably, it is Pierre Bourdieu’s use of the term that has attracted most scholarly attention during the last decades. While Sorokin primarily used the term in order to demonstrate how various dimensions of stratification can be related analytically, Bourdieu used it in order to develop an alternative to Marxist class analyses. According to Bourdieu, the social space is structured by differences in volume and composition of capitals, and as these differences provide the basis for various forms of power and domination, one will find hierarchical divisions between dominating and dominated agents in the social space, and classes are identified on the basis of these hierarchical relations. But these are only classes ‘on paper’– i.e. sets of positions and relations between them that are more or less likely to produce real classes and class actions only under certain conditions. Constructing a social space according to this logic may support analyses of the basis of class formation, but it does not substitute analyses of real class behavior (Bourdieu 1992: 229–251).

Usually, this social space is constructed on the basis of indicators of three main types of capital: economic, cultural and social capital. The agents’positions in the space are located according to their capital volume and profile, and the position of each agent must therefore be interpreted relationally, i.e. in relation to the location of all other positions in the space (Bourdieu 1992: 229–251). Positions with relatively similar capital volumes and profiles will be located close to each other, while positions with different capital volumes and profiles will be located more distant from each other.

The same relational principles of interpretation apply to the social space as to what Bourdieu conceptualized as a ‘field’(see also Swartz in this edited volume). A field can also be perceived as a structured space of oppositions between a set of specific positions, and the structure of the field may be determined on the basis of the distribution of capitals between the agents that engage in the struggles over power in the specific field, whether it is the political field (Hjellbrekke and Osland 2010; Bourdieu 1991a: Part III), the journalistic field (Hovden 2008; Marchetti 2002), the religious field (Bourdieu 1991b), or the academic field (Bourdieu 1984). On the basis of capital volume and composition, hierarchical divisions between dominant and dominated agents may also be uncovered, both within field positions, between field positions in the same field, and between positions in different fields.

The concept ‘field of power’was developed as an alternative to ‘classical’sociological elite theories (Bourdieu and de St. Martin 1978, Bourdieu 1996). Analytically, the field of power is located in the area of the space where the overall volumes of capital are highest. It is conceptualized as a field in which agents in dominant positions of various fields are engaged in struggles over the power relations between, and the hierarchically ordering of the fields. And because different types of capital will be valued differently in different fields, the struggles in the field of power are also about the general value and distribution of different types of capital, and about the right to dictate what shall be the legitimate, i.e. dominating principles of domination.

Also, the relation between the field of power and its constituting fields may be characterized as a relation between a field and a subfield: The structural oppositions which permeate the struggles are not necessarily replicated in identical ways in the internal field struggles, e.g. in the bureaucratic or the political field. In an exhaustive field analysis this is rather something that must be explored empirically.

There are, however, no easy and straightforward ways to analyze the relation between structures in the field of power and its subfields empirically, which duly respect the fundamental relational logic that underpins the field constructions. The field of power and its subfields must be constructed on the basis of distributions of the same types of capital, but when analyzing and interpreting the results of an analysis of a subfield, one must bear in mind that the subfield is always already situated in the structures of a more global field. An adequate analysis of a subfield must take this relation into account.

The purpose of this chapter is to explore how this may be done in an analysis of the Norwegian field of power and three of its subfields – the subfields of politicians, higher civil servants, and business leaders.

The Construction of a Field of Power

The field of power was constructed on the basis of data from The Leadership Survey which was part of the Norwegian Study of Power and Democracy (1998–2003) commissioned by the Norwegian Government. The survey was distributed to an ‘area selected sample’of 1710 individuals in ten different sectors (see Gulbrandsen et al. 2002). The data were not produced with the ambition of constructing a field in the Bourdieusian sense, but contained variables which made it possible to do so, and 30 variables were chosen for constructing a field of power (see Hjellbrekke et al. 2007). The active variables were grouped into five main categories: economic capital, inherited and personal cultural capital, inherited and personal social capital (Table 4.1).

Table 4.1 Active variables, construction of a field of power
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Briefly summarized, MCA revealed a space with three main dimensions, summing up to 75% of the variance (Benzécri’s modified rates).

  • Axis 1 was interpreted as an economic capital axis, contrasting high and low volumes of economic capital.

  • Axis 2 was interpreted as a seniority and social mobility axis, separating high and low volumes of both inherited cultural and social capital, and also as describing an opposition between high volumes of educational capital and high volumes of political capital.

  • Axis 3 was interpreted as a capital structure axis, where high volumes of inherited social capital and low volumes of personal educational capital are contrasted to high volumes of both personal educational and inherited economic capital.

When the variable on sectorial belonging was projected into this space as a supplementary variable, a tripolar opposition between positions in business, in politics, in research and in the church was revealed in factorial plane 1–2. The sectors’positions in the space are shown in Fig. 4.1.

Fig. 4.1
figure 1

Sectorial Positions in the Field of Power

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Horizontally, along axis 1, there is a clear opposition between the business positions and all the other positions. Whereas all the business positions are located to the right in the plane, almost all the others are located to the left. However, when the full set of 48 positions was projected as a supplementary variable into this space, there were also clear indications of sector internal oppositions. For instance, the positions of leaders of public companies and of cooperatives, with career trajectories that also depend on the accumulation of political capital and on political consecration, are located much closer to the political positions in the field (see Hjellbrekke et al. 2007; Hjellbrekke and Korsnes 2016).

Vertically, along axis 2, we find a clear-cut opposition between religious positions and positions in higher education and research (upper left quadrant) and the political positions (lower left quadrant). With respect to social mobility, positions in politics seem more ‘readily’available for newcomers in the field than positions in academia or in the church. But at the same time, the axis might also describe an internal capital hierarchy in the political field. Whereas the mean positions for the state secretaries are located near the barycenter, the position of the MPs is located at the bottom of the quadrant.

Axis 3 (not shown, see Hjellbrekke et al. 2007) reveals an opposition between judicial and military positions on one side of the axis, and a figuration of positions in politics, including trade unions and professional organizations, NGOs and public and private cultural institutions on the other side of the axis.

However, this analysis is still not able to tell us what capital oppositions prevail internally in a subfield, e.g. in the political field, the administrative field, or the academic field. Are these field-internal structures much the same as those in the global construction of the space, or do other types of capital generate field-internal lines of divisions, among politicians, civil servants, or among business leaders, which we find in analyses of the divisions in the global field of power? In Bourdieusian terms, this is a question about structural homologies between the oppositions in the field of power and the various subfields, and in order to explore such structural homologies we shall apply CSA (Le Roux 2014: 264–69).

Subfields in the Field of Power: Field Homologies and Class Specific Multiple Correspondence Analysis (CSA)

A subfield may be perceived as a subspace constituted by a certain group or a subsample within the frames established through the construction of the global space. The characteristics of the dimensions in this subspace depend upon the internal oppositions in the group that is analyzed. To reveal these dimensions, the most straightforward procedure would be to conduct an analysis of only the subsample, without taking the global space as a point of reference, neither analytically nor statistically. This, however, would imply separating these individuals from the structures of the global space, and not to analyze their internal oppositions within this structure. If their relations to the other individuals and positions in this space shall be taken into account, this is not a feasible solution.

By way of a class specific MCA, this problem can be overcome, as the distance between two individuals, say Hillary and Donald, is defined by the positions they have on all the axes in the global space. These axes which are used as variables in the CSA, will again be determined by all individuals in this space, and not just those in the subgroup. A CSA can be compared to running a non-normed PCA (Principal Component Analysis), or a PCA on the covariance matrix, on this subset of individuals, where the individuals’factorial coordinates are the values on the active variables. The distances between the individuals are thus defined in the original space, but we search for new axes within the given nested subcloud. In this way, one can analyze statistically whether or not the individuals in the given subgroup are similar to, or different from the individuals in the reference group. In our case, this reference group is constituted by all the individuals in the above outlined elite sample, i.e. the global cloud. Each subcloud belongs to the same space as the global cloud, making direct comparisons between the results from different subclouds statistically legitimate (Le Roux 2014: 264–69 and 391–394, Bonnet et al. 2015: 120–29).

Briefly summed up, the more the distributions for the individuals in the subsample are close or similar to those of the individuals in the global sample across the active set of variables, the more similar will the results from the CSA be to the results from the MCA, both in terms of dimensionality and in terms of the interpretation of the individual axes. Conversely, the more the distributions in the subsample differ from the ones in the global sample, the more will also the results from the CSA differ from those obtained in the global MCA, not only when it comes to how the axes are to be interpreted, but in most cases also in terms of the dimensionality of the solution.

Table 4.2 shows the eigenvalues of the original MCA (N = 1710), of the CSA of the politicians (n = 190), of the higher civil servants (n = 197) and of the business leaders (n = 390), three subgroups whose mean points are located in different sectors of the factorial plane shown in Fig. 4.1.

Table 4.2 Axes 1–5, MCA and CSA
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As Table 4.2 indicates, the oppositions revealed in the CSAs of the three subsamples are not identical to the ones structuring the global space. Firstly, the eigenvalues, and also the dimensionality, differ between the three CSAs. Whereas four dimensions should be retained for interpretation in the MCA space, there are three dimensions to interpret among the civil servants and in the business elite, but only two among the politicians. There might, however, be a secondary factorial plane to interpret among the latter, i.e. a plane constituted by lower order axes (axes 3 and 4).

Secondly, the strength of axis 1 varies from subsample to subsample. Among the politicians and the business leaders, axis 1 is clearly the most important axis. This is not at all as clear among the civil servants. The differences between axes 2 and 3 are also systematically smaller in the CSAs than in the original MCA space. The oppositions in the subsamples might therefore not be as clear cut as in the global sample.

Table 4.2 does not, however, tell us anything about how similar or dissimilar the axes found in the CSAs are to those we have found to structure in the global field of power. To what degree is this the case? And to what degree do field-specific types of capital generate field-specific structural oppositions? In other words: are the axes from the various CSAs oriented through the respective sub-clouds in similar ways? The cosines for the angle between the ‘old’and the ‘new’axes which can be interpreted in the same way as correlation coefficients, give us a first indication on this; the respective values are given in Table 4.3 Footnote 1:

Table 4.3 Cosines, axes from specific MCA and CSA
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The closer the cosine or the correlation is to +1 or −1, the sharper is the angle between an old and a new axis, and the more similar is also the given axis from the CSA to the axis from the MCA. The closer the cosine is to 0, the closer to orthogonal are also the axes, and the more different are also the orientations of the given axes through the cloud. If the value of the cosine = 0.0, the axis from the CSA will be at an angle of 90 degrees to the axis from the MCA. From Table 4.3, we find that both among the politicians and the civil servants the new axes 1 display clear similarities to the old axis 2, i.e. the mobility and seniority axes. In other words, in both of these subfields, the most distinct opposition is found between ‘inheritors’and ‘newcomers’. But as we know from Table 4.2, this opposition is stronger, or more dominant, in the political subfield than in the administrative subfield. This said, the structural correspondence is not perfect. A cosine of .75 indicates that the angle between the new first axis and the old axis 2 is approx. 40 degrees. This might in turn indicate that there are two different versions of the mobility or seniority oppositions at work in the subsamples. Furthermore, as far as can be judged from the cosines, the new axes 2 in the CSAs are also different. The field internal structures are thus also different.

This may be explained by the fact that historically the careers and trajectories that lead to top positions in politics and in the civil service have not been identical, and the qualifications and capital assets needed for entering the two fields have differed. Even though the educational heterogeneity increased in the civil service in the decades from 1976 to 1996, in 1996, 27% did not hold the equivalent of a master degree or higher (see Christensen et al. 2001). The educational level has been lower among the politicians, and even though there are good reasons to ask whether or not the Norwegian MPs constitute a social elite (Hellevik 1969), the hurdles a politician must pass on his or her way to a top position are different from those a civil servant must pass on his or her way to the top of the administrative hierarchy.

Table 4.4 Points with contributions >1/K, axes 1 and 2. CSA, Higher Civil Servants. Contributions to axes
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Table 4.5 Points with contributions >1/K axes 1 and 2. CSA, Politicians
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Table 4.6 Points with contributions >1/K, axes 1 and 2. CSA, CEOs in Business
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The structural oppositions in the business elite, however, prove to be other than in the political and in the administrative elite. Of the three CSAs presented in Table 4.3, the resultsfrom the CSA of the business elite is closest to the results from the global analysis. Firstly, the new axis 1 displays a clear similarity to axis 1 in the global analysis. We have therefore reasons to expect that the dominant opposition among the business leaders is an opposition linked to economic capital assets, i.e. to the dominant form of capital in this subfield. Secondly, the cosine between axis 2 in the Business CSA and axis 2 in the global analysis is .6415, i.e. an angle of 50 degrees between the two axes. Whereas, to a certain degree, axis 2 in the CSA describes an ‘inheritors’vs. ‘newcomers’opposition, this opposition does not have the exact same orientation as it does in the global cloud. Most likely, also in this case, we’ll find field specific variations over the more general principle. Finally, in the subset of business leaders, axis 3 describes an opposition not found in the MCA space. It might therefore describe an opposition that is specific to the business elite.

In order to get a more precise idea of the field specific oppositions, the contributions from the individual categories to the most important axes must be examined in greater detail. This is done in Tables 4.4, 4.5 and 4.6 and in Figs. 4.2, 4.3 and 4.4, where only categories with contributions above the average contribution, i.e. > 1/K, are included.

Fig. 4.2
figure 2

CSA, higher civil servants. Categories with contributions >1/K to axis 1 in bold, to axis 2 in italics and to both axis 1 and 2 in bold and italics. (Legend: FM = Father/Mother, P = Partner, F = Father)

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Fig. 4.3
figure 3

CSA, politicians. Categories with contributions >1/K to axis 1 in bold, to axis 2 in italics, and to both axis 1 and 2 in bold and italics. (Legend: FM = Father/Mother, P = Partner, F = Father)

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Fig. 4.4
figure 4

CSA, business executives. Categories with contributions >1/K to axis 1 in bold, to axis 2 in italics and to both axis 1 and 2 in bold and italics. (Legend: FM = Father/Mother, P = Partner, F = Father)

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Starting with the higher civil servants, axis 1 is not only skewed; the contributions from points on the right hand side are far higher than from those on the left hand side. It is also strongly dominated by an opposition between high and low inherited social capital, two categories stand out with a combined contribution of 25.8% having a father or mother who at a national level has served at the board of either a trade union or a managerial association. In this way, the dominant opposition between insiders and outsiders is more clearly linked to having or not having had parents with board memberships in key organisations and associations in the Norwegian tri-partite system of industrial relations. Among the higher civil servants, the parental opposition in a central arena for concertation manifests itself in the next generation as a structural opposition between newcomers and inheritors to powerful positions in the Norwegian state apparatus.

The central opposition on axis 2 is one between high volumes of personal and inherited cultural capital. It can also be interpreted as an axis of endogamy. Popular origins, having partners with low educational levels, relatively high volumes of personal social capital and experience from politics and/or justice stand in a clear opposition to categories indicating high volumes of both personal and inherited cultural capital. These oppositions are displayed in Fig. 4.2.

In Fig. 4.2, axis 1, the horizontal axis, describes an opposition between high and low volumes of inherited cultural capital and partly also inherited social capital. Even though the contributions to the axis are strongly skewed, the axis is ‘balanced’in that the contributions stem from these two main types of capital. The axis can therefore be interpreted as a general volume axis for these two types of capital; a volume axis that is specific to the higher administrative field.

Figure 4.2 confirms that axis 2 must be interpreted as a volume axis with respect to educational capital, and also an endogamy axis. Higher civil servants without the highest educations, with popular origins and also partners with lower educations will more often be found in the upper quadrants of Fig. 4.2. Civil servants with the opposite properties are more often located in the two lower quadrants.

When we turn to the political subfield, the results (Table 4.5) seem at first clearly different. Firstly, one single category, having ‘Diploma’as one’s highest education, has a contribution of 35.3% to axis 1. However, categories indicating higher own educations do not have a contribution over the threshold. Instead, the category of low own education stands in opposition to categories indicating high volumes of inherited social capital and partly also inherited cultural capital. It is therefore a nearby conclusion that in the political field, axis 1 describes an opposition between a group that constitutes a ‘political nobility’, i.e. a group of individuals with a ‘right of inheritance’to the positions once held by their parents, and a group of ‘newcomers’with far less ‘exclusive’backgrounds and with far more restricted capital profiles. The latters’potential for capital conversion is probably lower than that of the inheritors, and their dependency on the political field is therefore also higher (see Denord et al. 2011).

In contrast, axis 2 is not only far better balanced, in that no single category stands out with an extremely high contribution. It is also more of a capital composition axis, discriminating relatively high volumes of cultural capital (left side) from high volumes of inherited social capital (right side). Low volumes of economic capital are also contrasted to relatively high volumes of economic capital (Capital Income Low vs. Capital Income High).

The structures in the political subfield are shown in Fig. 4.3: whereas axis 1 is clearly defined by an opposition between politicians with the lowest educations and the others, i.e. a version of the ‘newcomers’vs. ‘inheritors’opposition (see also Lie Andersen 2014), axis 2 is a more complex-structure axis.

The dominant oppositions in the administrative and in the political field are therefore not identical. But even so, in both cases, the CSA has revealed an opposition linked to social mobility that structures these two subfields within the field of power. Whereas the axes from the CSAs describe oppositions between different forms of capital, the general, structuring principle is the same; one between ‘newcomers’and ‘inheritors’.

And the same overall principle of division is found to structure the oppositions among the business executives, although in yet another and also slightly more complex version. Table 4.6 shows the contributions to axes 1 and 2 in the CSA of the CEOs in the business sector.

Firstly, and as could be expected, axis 1 describes an opposition between high and low volumes of economic capital. But this opposition is also one between inheritors and newcomers in terms of volume of field-specific ‘inherited social capital’, e.g. having parents that were board members in private companies and/or managerial associations. Furthermore, having or not having held key positions in the field, e.g. being a ‘gatekeeper’as member of an election committee or being member of a general assembly, two key indicators on field specific ‘consecration’and on personal social capital, is also polarised along the same axis. Whereas ‘outsiders’are systematically located to the right, the ‘insiders’are located to the left in Fig. 4.4. As the axis is also separating between high and low volumes of economic capital, it can therefore be interpreted as a general volume axis, where the ‘haves’are contrasted to the ‘have not so muchs’.

But the opposition between inheritors and newcomers is not structured uni-dimensionally, which can be seen clearly from Fig. 4.4.

Also, axis 2 can be interpreted as an axis describing an opposition between a group of ‘double’inheritors, located in the two upper quadrants, and the most powerful newcomers in the lower left quadrant. Categories indicating high volumes of inherited social and of both personal and inherited cultural capital are located in the upper quadrants, and experience from organisations – both managerial associations and trade unions – are located on the lower left side. Thus, one may partly interpret the axis as describing an opposition between personal social capital and inherited social and cultural capital. The homogamy pattern is also distinct: executives with partners with high educations are more often found in the upper quadrants and executives with lower educations and partners with low educations more often found in the lower quadrants.

Not having access to more detailed data on individual positions in the political field (e.g. party leader, MP, mayor etc.) or on exact positions in the hierarchies in the civil service or on what companies the business executives lead, we cannot analyze whether or not these oppositions also manifest themselves in, and correlate with other hierarchies. Even so, oppositions regarding capital volume and capital composition will in many cases also be indicators on power and dominance relations both within and between various fractions of the power elite.

Field Analysis, GDA and Field Homologies

When we conduct specific field analyses of these three subgroups of the field of power, we observe that the oppositions in the subfields are not identical with those we find in the global field of power. This is not surprising, as there are many reasons to believe that the relations of power and domination one finds, e.g. in the political field, are quite different from those one will find e.g. in the economic field. Nevertheless, we claim that there are clear tendencies of homology in the oppositions in the global field and the subfields. In our understanding, the homology thesis does not imply that the relations of power and domination in different social spaces and fields are identical, but structured according to the same basic social logic. This means that in the global field, as well as in the subfields, one should expect that the oppositions between the positions, and the relations of power and domination between them, are related to inequalities in the volume and composition of the same basic types of capital. And this is clearly the case. Moreover, structural oppositions specific to the Norwegian field of power seem to repeat themselves in various, non-identical ways across the subfields – this applies in particular to oppositions relating to social mobility and field seniority, between ‘newcomers’and ‘inheritors’. This further strengthens the homology argument, and the purpose of doing field analysis of subfields – which CSA makes possible to do statistically – is exactly to demonstrate that oppositions in the field of power must be understood as oppositions between subfields that are inter and intra-relationally structured by similar, but non-identical oppositions of relations of power and domination.

The same argument pertains to comparative studies of fields of power. In Bourdieu’s analyses of the French field of power, the homology thesis refers to a structural coincidence between capital oppositions in the field of Grandes écoles and the French field of power (Bourdieu 1996). The analyses also reveal that agents with high volumes of inherited cultural capital are less often oriented towards the economic pole of the field of power, while agents in dominating sectors of the field are less preoccupied with intellectual and cultural ‘temptations’(Bourdieu 1989: 234–235). To assume, in line with an empiricist interpretation of the homology thesis, that this will automatically also be the case in states that have not institutionalized a system of higher education similar to the French one, is quite absurd for obvious reasons. Nevertheless, a field theoretical research program may have more universally relevance, e.g. in elite studies, as long as it is not assumed to imply that fields of power always display the same structure, comprise the same positions, and must be constructed on the basis of exactly the same capital indicators, and that the relations between the types of capital must be identical. Such an assumption would imply a de-contextualization of the object of research, and make the analysis a-historical. And it would amount to a preconstruction of the research object of the sort Bourdieu repeatedly warned social scientists against (Bourdieu et al. 1968).

The same empiricist interpretation of the homology thesis, and the analytical weaknesses that follow from this, can be found in studies of relations between structures of class inequalities and differences in life styles that relate to Bourdieu’s Distinction (Bourdieu 1979). Concerning the very simplistic positions one can find in the debate about this issue (see Jarness 2013, 2015; Hjellbrekke et al. 2015), it is also necessary to point out that relations between structures of class inequalities and differences in life styles may be very similar across contexts, even if the objects or the variables that constitute the differences may vary a lot. The implication of the homology thesis is that more or less consistent sets of preferences in taste correspond to oppositions between the location of different positions in the capital structures that make up the structures in different social spaces; not that these preferences and oppositions are the same across contexts and time.Footnote 2

Capital structures may be perceived as universal principles of structuration of both class and life styles, but they are combined in ways that may result in national as well as field specific variations and variants, when it comes to field structures, field trajectories, and structuring of the habitus of persons that are placed in similar, but never identical positions. A comparative approach is necessary in order to reveal such variations, but must take into account the distinction between universal and societal-specific factors, and between the epistemological and ontological status of the research object. If not, one runs the risk of confusing empirical and theoretical generalizations, e.g. by generalizing Bourdieu’s findings in France to other countries, and pretend to test the homology thesis by mechanically moving around constructions of social space (Hjellbrekke and Korsnes 2013).