Exploring Bourdieu Using an Evolutionary Simulation Model

by

David Bradbury and Andrew Trigg*

* For correspondence:

Andrew Trigg

Faculty of Social Sciences

The Open University

Walton Hall

Milton Keynes MK7 6AA

Email: A.B.Trigg@open.ac.uk

Tel: 01908 654421

1. Introduction

The sociology of Pierre Bourdieu exhibits characteristics that are also found in evolutionary models of social behaviour. Evolutionary models simulate the reproduction of social structures, together with innovations in individual behaviour that shape these social structures. Key to such models is the simulation of feedback between changes in social structure and individual behaviour. In Bourdieu's Distinction (1984) groupings of social class provide the main focus of analysis, with social classes reproduced but the behaviour of individual members of these classes both structured and structure determining. The fragments of each social class undergo change and disruption depending upon the strategies of individual agents, which are in turn influenced by the class structures.

In formulating his analysis of individual trajectories, Bourdieu (1984) refers to the ‘evolution over time of the volume and structure of their capital’ (p.111) and reveals that ‘one sees the attraction of evolutionist models’ (p.163). The purpose of this paper is to further explore the interface between Bourdieu and evolutionary theory. Our particular focus is the genetic algorithm approach that is becoming widely used in evolutionary economics (see Birchenall et al, 1997). Adapting this approach involves the simulation of a population of individuals, with each holding a particular composition of capital. For ease of exposition Bourdieu’s comparison of cultural and economic capital is employed. The probable class trajectory of each individual depends upon the proportion and volume held of these two types of capital. Using the biological metaphor, the composition of capital acts as a fitness criteria for social mobility. The simulated class trajectory of the population, according to initial compositions of capital, feeds back via a modified social structure to individual stocks of capital.

As Maason et al (1995) have noted, a degree of caution is of course required when using biological metaphors. ‘The answer to the question of why metaphors cause irritation and excitement, may thus be summarized simply: as long as the perceived difference in meaning is slight, or serves the purpose to create additional insights, metaphors are judged to be good. As soon as the use of metaphors implies change of meaning, even change of the disciplinary identity, they are judged to be bad’ (Maason et al 1995, p.2). With respect to Bourdieu the intention is not to simplify or capture any particular essence of his work, but hopefully to add additional insights by relating it to a different area of research. In favour of this broad objective Geoff Hodgson, a leading proponent of evolutionary economics, has argued that by ‘providing a bridge between different discourses and contexts, metaphor can thus be both creative and constitutive’ (Hodgson, 1995, p.341).

There are two main ways in which the interface between Bourdieu and evolutionary modelling might be creative. First, although evolutionary economists have made some headway in examining the behaviour of firms, the literature on individual behaviour, and consumption in particular, is limited. Moreover, there is a recognition that Bourdieu has much to offer, but as Cowan et al (1997) have noted, Bourdieu’s theory ‘lacks the power of a quantitiative modeling framework which an evolutionary economic theory of consumption can bring’ (p. 717). By exploring the relationship between Bourdieu and quantitiative modelling a key objective is to make possible a translation of Bourdieu’s ideas into evolutionary economics. Second, there have been attempts in empirical sociology to formalise and quantify some of the insights provided by Bourdieu’s work. Inspired by Bourdieu’s own empirical work, there is a growing literature in which sociological theories are tested using different types of data (see, for example, Bennett et al, 1999; Peterson and Kern 1996) Our approach to modeling Bourdieu could help contribute to this sociological literature by exploring how concepts such as cultural and economic capital can be defined and quantified.

The first part of the paper examines some of the similarities between Bourdieu and evolutionary theory. A useful starting point is provided by the economic literature on evolutionary modelling. In the second part of the paper, an evolutionary simulation model is developed that represents some of the characteristics of Bourdieu’s sociology. To demonstrate the potential of this model in the third part some simple simulations of social mobility are reported.

2. Bourdieu and Evolutionary Theory

Following Dosi and Nelson (1994) four building blocks of evolutionary theory can be identified:

1. A stable unit of analysis must be defined, comparable to genes in biology.
2. There must be an equivalent of organisms in biology that carry these genes
3. Mutation takes place in which new units of analysis (genes) are generated.
4. There is a competitive process in which some organisms are selected on the basis of fitness criteria.

Each of these building blocks of evolutionary theory can be closely related to Bourdieu. The first step in this translation is to suggest that in Bourdieu’s work individual capital can be viewed as analagous of the gene in biology. In the same way that particular gene structures can influence the evolution of an organism, a particular stock of capital may also influence the social mobility of an individual person. In Bourdieu individual people could be assumed to be the equivalent of biological organisms.

Bourdieu places particular importance upon cultural capital, which can defined as ‘an individual’s accumulated stock of knowledge about the products of artistic and intellectual traditions’ (Trigg 2001a, p.55). For Bourdieu (1984) the accumulation of cultural capital is ‘inscribed, as an objective demand, in membership of the bourgeoisie and in the qualifications giving access to its rights and duties’(p. 23).In relation to educational qualifications cultural capital is critical to each individual’s performance in the education system. School children from more privileged family backgrounds have relatively higher stocks of cultural capital that given them an advantage over the less privileged. Interesting for our purposes, Bourdieu sees the relationship between education and social mobility in evolutionary terms. He writes of the ‘evolution of the system of relations between the school system and the social classes…’ (Bourdieu and Passeron 1990, p.91).

Alongside cultural capital, Bourdieu places primary importance on the role of economic capital, which incorporates both the monetary wealth and income of individuals. The professions are defined by Bourdieu as the dominant group in society, being rich in both economic and cultural capital. ‘The distribution of the different classes (and class fractions) thus runs from those who are best provided with both economic and cultural capital to those who are most deprived in most respects’ (Bourdieu 1984, p. 114). Those at the other end of the spectrum are low in both economic and cultural capital. Importance is also placed on the role of social capital, which derives from social connections, but to keep our analysis simple we focus specifically on cultural and economic capital.

One of the main aims of Bourdieu is to examine the way in which social and economic inequalities are reproduced. Since educational performance is correlated with inherited cultural capital there is at tendency for children of parents with high cultural capital to become holders of high cultural capital. Economic capital also drives this process since those of high economic capital can purchase private education for their children. The structural inequalities in the distribution of economic and cultural capital are reproduced. Although the education system gives the outward appearance of being fair and meritocratic, it in fact it works as a mechanism for reinforcing the social hierarchy.

In analogy with biological processes there is a ‘degree of selection’ which is ‘objectively measured by the rate of elimination… from the education system’ (Bourdieu and Passeron 1990, 91). Borrowing from the language of population dynamics an ‘educational mortality rate’ is referred to in which dropping out of the education system is akin to the non-survival of biological organisms (ibid, p.73). The combination of each individual’s cultural and economic capital has the role of a fitness criterion for progression in the education system and throughout the social hierarchy.

In addition to providing the basis for reproduction of capital structures, these structures can also change in a way that is analogous to how genes mutate in biology. Central to this approach is the way in which Bourdieu views social classes as being made up of class fractions, each with their own particular social trajectories (see Trigg, 2001b). The middle class, for example, includes declining class fractions. It is not by chance ‘that the oldest classes or class fractions are also the classes in decline, such as farmers and industrial and commercial proprietors’ (Bourdieu 1984, p.108). Individuals in these class fractions resist change and this has a conservative impact on their tastes and values. It could be posited that their individual capital structure to some extent mutates - their economic and cultural capital declines due to structural changes in society as a whole but also because of the way in which they react and shape these structural changes. This reaction process is not smooth or predictable, but will have a random aspect to it that makes mutation possible.

By way of contrast, for Bourdieu a class fraction that is not in decline is the so called new middle class. Bourdieu (1984) refers to a ‘creative redefinition’ of capital structures that is ‘found particularly in the most ill-defined and professionaly unstructured occupations in the newest sectors of cultural and artistic production (radio, TV, marketing, advertising, social science research and so on)..’ (p.151). Members of the new middle class innovate in how in their tastes and values, defining new and unpredictable capital structures. One of the challenges of Bourdieu’s approach is to work out how such innovations relate to the overall reproduction of the social hierarchy.

3. An evolutionary simulation model

An introduction to the Genetic Algorithm (GA)

The last few years have seen an upsurge in interest in the use of computational modelling techniques in the social sciences. The GA has been and continues to be an important part of this process. This has been a result of the increasing popularity of such techniques in both the academic literature and in commercial applications, as well as the increasing power and declining cost of computational hardware – more bytes per buck.

In broad terms the GA can best be described as a system that modifies internal parameters so as to better specify some problem. This process is cyclical in nature. It is based on the Darwinian model of evolution. It is this process of adaptation which gives rise to the behaviour that the social scientist is interested in. The behaviours of adaptive systems can best be described as emergent properties of that system, which are not coded directly in any way, but rather are a result of the various parameters set by the user. GAs are particularly suited to problems concerned with learning, search and optimisation. Although there are many different varieties of GA, the following can be considered a list of properties that any algorithm must have if it is to be considered a GA:

• The process starts with a series of individuals
• Each individual consists of a series consisting of binary values. This series is analogous to the DNA string that encodes the characteristics of lifeforms. Just as the string as a whole can be thought of as a DNA string each individual "bit" can be thought of as being analogous to an individual gene.
• Each bit of the binary string represents the presence (when it’s = 1) or otherwise (when it’s = 0) of a particular characteristic.
• The "DNA" of an individual represents its attempt to solve a particular problem.
• Each individual then attempts to solve the problem domain. The result of this attempt is represented as a score referred to as its fitness.
• The higher an individual’s fitness the better it did at solving the problem.
• The population is then replaced by a new generation, created by breeding from the existing population.
• The "breeding" process is performed by selecting two existing individuals and crossing over their DNA. This cycle is then repeated either a fixed number of cycles or until a certain fitness level is achieved.

Naturally there are several variations to the general scheme described above, most notably in the algorithm that is used to select the parents of the new generation. Broadly speaking the probability of a particular solution being selected increases as its fitness increases.

Modelling Social Activity Using a Genetic Algorithm

Our model uses a modified version of the GA. Whereas most Genetic Algorithms use a single fitness landscape, our model looks at a group of individuals attempting to improve their position in the social structure. Their ability to do this however is limited (or not) by the quantities of economic and cultural capital that they have at their disposal. Therefore each individual has its own fitness landscape

A model of social behaviour corresponding to Bourdieus’ theories should have the following characteristics:

• Those at the bottom of the social hierarchy look to improve their lot and should therefore seek to "mate" with those whose lifestyle they aspire to.
• Those at the top of the social hierarchy look to stay where they are and seek to "mate" with those individuals with lifestyles similar to their own.
• Over time this desire to imitate should lead to clusters, which can be seen to represent different social classes.

A First Experiment

In order to demonstrate these assertions it was decided to run a "stripped down" simulation where individuals cannot mutate their DNA and the fitness function is stationary. This environment consisted of one hundred individuals with a DNA consisting of twenty genes, ten each for economic and cultural capital. The fitness function consists of a vector, which contains values that show the effect of the total fitness of possessing a particular piece of capital. Each member of the population started with a randomly generated DNA string. Each simulation was run for twenty cycles. Figures 1 and 2 below show the resulting clustering behaviour when the fitness function has a bias of 2 (See the appendix for further details).

Figure 1: Population Clusters after One Generation

Figure 2: Population Cluster after Twenty Generations

The above diagrams show clear clustering over time. Interestingly there are far more individuals clustered together in the lower social classes than the upper social classes.

Future research

The promising results from this initial experiment point towards some interesting future experiments:

• The trajectories of individuals: Do individuals move from one social class to another or do they stay where they are?
• The Effects of Mutation: Do mutations of DNA change the behaviour of the model significantly i.e. do clusters still form?
• Non stationary fitness functions: Does a non-stationary fitness function cause social upheavals and the collapse of hitherto stable clusters?
• More types of capital: With economic and cultural capital only, the evolution of the society can be seen as a series of journeys in two dimensional space, what types of richer behaviour occur when more types of capital are introduced, can the bias function be extended to include such a society?
• Different ways of calculating total fitness: In this simulation the total fitness is calculated by adding economic and cultural capital together. Are different types of capital equivalent however and if some are more important than others how can this be represented when calculating the overall fitness of an entity?

Appendix: A Modified Fitness Function for a Genetic Algorithm

Most existing genetic algorithm models simply assume that each individual entity in a population has free access to other individuals. This results in the population as a whole moving towards a global equilibrium representing an optimum (or near optimum) solution best suited to their environment. This scenario does not represent the way in which societies behave

Let I₁, I₂, … I_n represent a population of individuals each with a stock of economic and cultural capital (represented by E₁, E₂, … E_n and C₁, C₂, … C_n respectively). The mean fitness derived from this population for each type of capital m_e and m_n respectively is used to decide if an individuals stock of capital is high or low. A typical individual I_m has a high level of a particular type of capital K if K_m > m_k

And low otherwise.

This splitting of individuals into groups according to high and low capital-owning categories are used when a new generation of individuals is to be produced. As well as the fitness of an individual, the probability that an individual will be selected as a parent can be written as f(b,f) where b is a bias value > 1 and f is the fitness function. The value of the bias depends on how many types of capital the two individuals have in the same category (i.e. high or low). For a given bias value b the modifier is shown in the table below:

It is this bias function which causes individuals with low total capital to aspire to get higher capital (but have only a limited success in doing so) and individuals with high capital to seek out those with a similar social standing.

References

Bennett, T., Emmison, M. and J. Frow (1999), Accounting for tastes: Australian everyday cultures. Cambridge, Cambridge University Press.

Birchenall, C., Kastrinos, N. and Metcalfe, S. (1997). Genetic algorithms in evolutionary modelling. Journal of Evolutionary Economics 7: 375-393.

Bourdieu, P. (1984). Distinction: a social critique of the judgement of taste. London: Routledge (original in French, 1979).

Bourdieu, P. and Passeron, J-C. (1990). Reproduction in Education, Society and Culture, 2^nd edition. London: Sage.

Cowan, R., Cowan, W. and Swann, P. (1997). A model of demand with interactions among consumers. International Journal of Industrial Organization 15: 711-732.

Dosi, G. and Nelson, R. (1994). An introduction to evolutionary theories in economics, Journal of Evolutionary Economics 4: 153-72.

Hodgson, G.M. (1995). Biological and physical metaphors in economics. In Maason, S., Mendelsohn, E. and Weingart, P. (eds.) Biology as Society, Society as Biology: Metaphors, pp. 339-356. Dordecht: Kluwer

Maasen, S., Mendelsohn, E. and Weingart, P. (1995). Metapors: is there a bridge over troubled waters? In Maason, S., Mendelsohn, E. and Weingart, P. (eds.) Biology as Society, Society as Biology: Metaphors, pp. 1-10. Dordecht: Kluwer.

Peterson, R.A. and Kern, R.M. (1996) Changing highbrow taste: from snob to omnivore. American Sociological Review 61: 900-907.

Trigg, A.B. (2001a) Consumer dependeny. In Himmelweit, S.F.., Simonetti, R. and Trigg, A.B. (eds.), Microeconomics: Neoclassical and Institutionalist Perspectives on Economic Behaviour. London: Thompson Learning (forthcoming).

Trigg, A.B. (2001b) Veblen, Borudieu and conspicuous consumption, Journal of Economic Issues, March (forthcoming).