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The Dynamics and Evolution of Social Systems: New Foundations of a Mathematical Sociology

Jürgen Klüver
Dordrecht: Kluwer
Cloth: 0-792-36443-0

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Reviewed by
A. Maurits van der Veen
Department of Political Science, University of Pennsylvania, Philadelphia, USA.

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The central goal of this book is to provide insights into the formal (i.e. mathematical) modelling of social systems, using ideas from complexity theory and related approaches. The book provides a survey of different types of modelling approaches and their value to sociology and the social sciences more generally. It also raises a number of important issues for those concerned with the nature of the system parameters in their models. However, the material is not always presented as clearly as it might have been and the overall discussion is probably too theoretical to be of interest to those with a more passing concern in these issues. As a result, the audience that will find the book truly valuable is almost certainly very limited.

The meat of the book is in chapters three and four which run to 80 dense pages each. The introductory and concluding chapters are about 25-30 pages and thus rather more manageable. Chapter two provides the building blocks necessary to understand the material in the two core chapters. The role of the introductory chapter is to outline the research program followed in the book. Here Klüver defines sociology as the study of "the logic and consequences of social rule systems" (p. 1) and discusses how one might put this study on a more formal footing. Noting the shortcomings of traditional mathematical approaches, which tend to be unable to handle individual (or micro-level) rules and model macro-level patterns only, Klüver conceives of his task as follows:

  1. Elaborating a precise terminology for describing social systems
  2. Analysing formal systems and if necessary creating new tools to do so (in particular, as we shall see later, system-level parameters)
  3. Proving that social systems can be expressed as formal systems without losing their central features
  4. Showing that doing so provides new insights into social systems

The list immediately points to a basic problem with the book, as the audience for points 1 and 2 is likely to be rather different than that for points 3 and 4. The latter issues are of interest to sociologists open to the idea of computer-based modelling in their discipline who remain to be convinced that the approach is worthwhile. The former points, on the other hand, become salient only once one is already firmly convinced of the potential and value of such modelling. Trying to please both audiences ends up diluting the book's value to each.

Much of the discussion in the book is too abstract and dense to win many new converts (i.e. the target audience of points 3 and 4). This problem is aggravated by Klüver's attempt to be systematic and complete in his presentation. He argues that an approach to systems theory for sociology cannot just pick and choose concepts from complexity theory but must rather check for relevance "all essential concepts of extra-sociological systems" (p. 6). In some sense, then, the book is intended as a tour d' horizon of the entire field of complexity science. But Klüver himself admits that he does not do most of the topics justice. In fact, the material presented is often too general and abstract to be helpful to those with no background in computer modelling, yet too lengthy to sustain the interest of those already familiar with the basics.

Chapter two introduces the building blocks of a complexity-based approach to sociology. Central to this chapter is a discussion of how rule-based systems can self-organise (and adapt) to changing environments. Here Klüver provides an extensive discussion about the importance of rules and adaptation at multiple levels. If one conceives of a social system as containing a set of rules (with conditions), Klüver argues convincingly that the system can only truly be considered self-organised if it contains, in addition, some rules that govern how the basic set of rules can be modified over time. In other words, modelling a social system requires not just basic rules but also meta-rules. Although in theory the meta-rules need not be hierarchically superior to the basic rules (i.e. one could construct a system where some of the basic rules also operate on the meta-rules), in practice Klüver focuses on hierarchically organised rule systems.

The most interesting contribution of this chapter is an intriguing discussion of the relationship between different levels of rule systems and different types of learning, as defined by Bateson in his Steps to an Ecology of Mind (1972). Furthermore, types of rule systems and of learning are also connected to different types of attractors in the state space of a system. In the next chapter, Klüver makes one further connection, to classes of complexity in cellular automata. The presentation of these connections is more discursive than I would have preferred, leaving open the possibility that particular classifications of rule systems, learning, attractors and complexity simply happen to be conveniently comparable in specific instances. Nevertheless, the possibility that different levels of rule systems, learning types and complexity classes are equivalent (or at least systematically related) is very intriguing, and definitely deserves to be pursued further in a more formal fashion.

Chapter three deals with the dynamics of formal systems. The chapter introduces two types of systems in particular: cellular automata and boolean nets. As suggested earlier, the presentation of the models is at too high a level to be helpful for those unfamiliar with them. Moreover, the complete absence of any graphical representation of the models makes the discussion rather more difficult to follow even for those who are familiar with the basic ideas. This problem becomes particularly acute when Klüver introduces some of his own work. Indeed, although he is obviously quite enamoured of his models, variously noting that they bear "pretty" (pp. 130, 228) or even "beautiful" (p. 200) names, they are never described in sufficient detail to allow a full understanding of how they work.

This also makes it nearly impossible to understand or assess independently how the outcomes of these models are likely to be affected by the system parameters of greatest interest to Klüver as presented in the discussion. These parameters include those that determine the space of a model's transition function (its complexity, the frequency with which different regions of the space are visited), the variability of the model's rules, the rate of variation of these rules and so on. Often Klüver gives us precise numbers for the parameter values he uses in his models, but given how abstract his description of those models is, these precise numbers are rarely meaningful to the reader.

More seriously, I am not convinced that those precise numbers (or even the parameters themselves) are at all generalisable to a wider class of models. In fact, although Klüver discusses several of his own models, they are all based on a single underlying model of social stratification. The only other basic model covered in some detail is the familiar non co-operative game with a 2 x 2 payoff matrix.

Even a cursory glance at the literature in agent-based modelling shows that a large corpus of very different models already exists. I am in full agreement with Klüver that it would be of immense interest to find out whether the broader system parameters of these models can all be formalised so as to make them more comparable. In other words, are there ways to compare the rate at which rules or strategies are allowed to change across models? Can we formalise representations of the search space for rules or strategies in a non-model-specific fashion? However, Klüver applies the parameters he proposes only to his own basic model. As a result, it is impossible to tell whether those parameters, let alone their specific values, ought to be of any interest to those using other basic models. Klüver does indicate that he has experimented with different models in studying some parameters (e.g. p. 149) but no specifics are given. Since all the different 'models' discussed in the book appear to be based on the same basic approach to social stratification, one suspects that these different models were simply additional variations on the same theme.

In chapter four, Klüver's focus turns to the parameters that affect whether systems stagnate and how they can break out of stagnation and/or overcome crises. This is obviously an issue of directed search within a specific search space and I missed a discussion of different search algorithms that would have seemed appropriate here. Genetic algorithms are discussed, and classifier systems are mentioned, but I would have liked to see a more formal treatment of their strengths and weaknesses at exploring different kinds of search spaces. Simulated annealing, another potentially valuable model, is not get considered at all.

Nor is there much discussion of the nature of search spaces themselves and how they might differ for different models. Yet this is obviously a crucial issue. Some of the best work in this respect is that based on Kauffman's NK landscape model (1993), which Klüver is apparently familiar with but does not draw on in his own discussion. Others have argued that social systems are characterised by high K values, which makes searches in their space particularly difficult. Klüver's discussion, however, is once more rather model-specific. Moreover, since the model has never been fully described, it remains impossible for the interested reader to decide for him- or herself the nature of the model's search space.

Another crucial feature of any social system is, of course, its interaction topology: which agents interact with which other agents, how do social connections vary over time and so on. The latter part of chapter four is concerned with some of these issues. Although the nature of a system's interaction topology must have important implications for the values and effects of the system parameters, Klüver treats them largely as separate issues, and most of the system parameters introduced earlier in the book disappear once topologies are introduced. Some of the most interesting recent work on interaction topologies (and their implications for network behaviour) is that inspired by Duncan Watts' PhD work (and subsequent book) on "small worlds" (1999). Oddly, although Klüver cites Milgram's original small world experiment in the 1960s, he does not seem to be familiar with Watts' work. This is a pity, since it would have been interesting to read more about the implications of different network typologies for his model outcomes.

As should be evident by now, I found this an intriguing but also a frustrating book. The questions of interest to Klüver are undeniably important ones and he does a fine job of laying out some of the potentially relevant models and findings in complexity theory. Moreover, the book introduces some very promising ideas, especially concerning the possible equivalence between different formalisations of social system behaviour (learning, rule systems, etc.) and of system complexity (attractors, search spaces) and concerning the generalisability of certain system parameters of different models. Unfortunately, the treatment of these ideas is rather unsatisfactory.

On the back cover of the book, the publishers define its target audience as "researchers and graduate students in the fields of theoretical sociology and social and general systems theory and other interested scientists" and emphasise that "no specialised knowledge of mathematics and/or computer science is required." Strictly speaking, the latter is true. Yet if one has no experience with the computer-based modelling of social systems this is definitely not the book to start with. On the other hand, for those really interested in some of the intriguing questions raised in the book, I would recommend some of the non-sociological texts that treat these questions more formally, such as Kauffman's Origins of Order, or Watts' aforementioned Small Worlds. Klüver's book is most likely to be of interest to those who have done a little computer-based modelling and would like a suggestive overview of some of the possible questions and issues they are likely to encounter as the proceed in this field.

* References

BATESON G. 1972. Steps to an Ecology of Mind. Chandler, San Francisco, CA.

KAUFFMAN S. A. 1993. The Origins of Order: Self-Organisation and Selection in Evolution. Oxford University Press, New York, NY.

WATTS D. 1999. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton, NJ.

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© Copyright Journal of Artificial Societies and Social Simulation, 2002