1 Overview

In the previous chapter the numerous methodological and theoretical frameworks elucidated thus far were analysed as a whole in an attempt to develop a useful synthesis for the social science modeller. Bringing together elements from population biology, artificial life, and social science itself, we examined the multiple dimensions that must be addressed in a successful social simulation model.

In this chapter we will examine one particular example of such a successful model: Schelling’s residential segregation model. After describing the context in which this model was developed, we will analyse this relatively simple model under the constraints of each of the theoretical frameworks described thus far. Despite the abstractions inherent in Schelling’s construction, the model achieved a remarkable measure of recognition both inside and outside the social science community; our analysis will discuss how this ‘chequerboard model’ found such acceptance.

Using Schelling as a case study, we can further develop our fledgling modelling framework for the social sciences. In the quest to underwrite social simulation as a more rigorous form of social-scientific exploration, Schelling will provide a valuable examination of the issues facing modellers as this methodology grows in relevance throughout social science. After discussing the issues brought forward by this analysis, which brings together the frameworks and methodological proposals discussed thus far, we will move on to the last chapter of Part II and present a synthesis.

2 The Problem of Residential Segregation

2.1 Residential Segregation as a Social Phenomenon

2.1.1 The Importance of the Problem

One of the most puzzling aspects of the sociological study of residential segregation is the sizeable gap between the individual residential preferences of the majority of the population and the resultant neighbourhood structure. The General Social Survey of major US metropolitan areas asked black respondents whether they preferred to live in all-black, all-white, or half-black/half-white areas; 55.3% of those surveyed stated a preference for half-black/half-white neighbourhoods (Davis and Smith 1999). However, census data reveals that very small percentages of black individuals in major US metropolitan areas actually live in half-black/half-white neighbourhoods; the 1990 census indicates that for most major cities, less than 5% of black residents live in such mixed areas.

2.2 Theories Regarding Residential Segregation

The phenomenon of residential segregation is a complex one, involving interacting contributing factors at various levels of societal structure. A definitive statement of why residential segregation occurs still troubles researchers; the problem varies so widely across cultures, societies and ethnic groups that the specific factors at play are still elusive.

Freeman’s summary of residential segregation of African-Americans in major American metropolitan areas (Freeman 2000) provides one example of the difficulties facing social scientists in this area. As Freeman notes, African-Americans seem particularly prone to residential segregation; other minority populations tend to ‘spatially assimilate’ after a period of residential segregation, integrating with the majority population as educational and financial disparities decrease (Massey et al. 1985). African-American populations, however, do not display significant spatial assimilation, despite the decrease in socio-economic disparities evident from the available data; some posit that this may be due to unseen bias in local housing authorities, cultural cohesion keeping African-Americans in established minority communities, or decreased access to public services in low-income areas, but none of these possibilities can fully account for these unusual tendencies in the data.

3 The Chequerboard Model: Individual Motives in Segregation

3.1 The Rules and Justifications of the Model

Schelling’s ‘chequerboard model’ sought to make a singular point, as illustrated by the simplistic construction of the model. He argued that if the racial make-up of a given area was critical to an individual’s choice of housing, then even populations of individuals tolerant to mixed-race environments would end up segregating into single-race neighbourhoods (Schelling 1978). Schelling hoped to illustrate that large-scale factors such as socio-economic or educational disparities between ethnic populations could not explain the generally puzzling phenomenon of residential segregation; indeed, without a greater insight into the preferences and thought processes of individuals within a given population (their ‘micromotives’), some critical aspects of this social problem may elude the researcher.

Schelling illustrated this idea using a model constructed in a simple fashion, using a type of cellular automaton model (initially constructed using a physical chequerboard, hence the model’s nickname). He describes a world composed of square cells, filled with agents of one of two types. Each agent interacts only with its eight direct neighbouring cells, and there are no higher-level structures incorporated into the model. The agents are given a tolerance threshold: if the number of adjacent agents of its own type is less than that threshold, the agent will move to a nearby location on the grid where its tolerance requirements are fulfilled. Thus, the model incorporates a very simple rule set which allows each agent to display a singular micromotive which is taken to represent that agent’s level of racial tolerance. Schelling hoped to demonstrate the powerful influence of this simple micromotive on the resulting racial structure of the neighbourhood inhabited by the agents.

3.2 Results of the Model: Looking to the Individual

The results of Schelling’s model were surprising to social scientists at the time. The model showed that, for a wide range of tolerance thresholds, these initially integrated neighbourhoods of tolerant agents would ‘tip’ toward one group or another, leading the outnumbered group to leave and resulting in segregation (Schelling 1971). Given that residential segregation was widespread in American cities prior to the civil rights movement, even the rising tolerance following the additional rights granted to African-Americans was not sufficient to provoke a significant decrease in residential segregation, even by 1990 (Sander 1998).

Schelling’s model demonstrates that a mere improvement in individual preferences and a lack of housing discrimination (as outlawed by the Civil Rights Act of 1968) are not sufficient to eliminate residential segregation. In fact, largely tolerant ‘microbehaviours’ can still result in such problems, as long as social factors such as race remain a consideration in housing choice.

3.3 Problems of the Model: A Lack of Social Structure

Since Schelling’s original model formulation and the resultant interest of the social science community, many researchers have since attempted to update the model with more sophisticated computational techniques and a greater number of influential social factors within the model. While Schelling’s model was accepted as a remarkable illustration of a simple principle regarding the large-scale effects of individual housing preferences, some modellers sought to create a more ‘realistic’ Schelling-type model which could incorporate socio-economic factors as well (Sander et al. 2000; Clark 1991; Epstein and Axtell 1996). Given the accepted complexity of residential segregation as a social problem, and the new insight into the effects of individual preference illuminated by Schelling, models incorporating Schelling-style ‘micromotives’ and large-scale social factors were seen as a potential method for examining the interactions between these two levels of social structure, something that was very much lacking in Schelling’s original formulation.

4 Emergence by Any Other Name: Micromotives and Macrobehaviour

4.1 Schelling’s Justifications: A Valid View of Social Behaviour?

Interestingly, despite the general simplicity of Schelling’s model and the lack of a larger social context for the agents in the model, his discussion of micromotives quickly gathered momentum among social scientists. His contention that certain non-obvious conclusions regarding social behaviour may follow from studies that do not depend upon empirical observation was influential, leading other modellers to seek patterns of interaction in generalised social systems [other tipping models here].

In addition, Schelling’s description of critical thresholds that lead to these ‘tipping’ phenomenon led to an influx of sociological models exploring this possibility in relation to numerous large-scale social phenomena. Within political science, Laitin used tipping models to examine the critical points at which populations choose one language over another, as in the case of Ghana (Laitin 1994), and in the growing acceptance of the Kazakh native tongue over Russian in Kazakhstan (Laitin 1998). In general, then, Schelling’s justifications for his residential segregation model have been widely adapted throughout the social sciences; this simple method for examining critical points in societal interaction seems to have generated a great deal of related research in the years following his book’s publication.

Perhaps more importantly for the larger social science community, Schelling’s model also sparked additional interest in empirical studies over the years as social scientists wished to confirm his claims. The most prominent example of this model feeding back new ideas into the empirical domain was W.A.V. Clark’s study (Clark 1991). Clark used the most recent demographic surveys available at the time to examine elements of local racial preference in residential segregation in real communities; while the character of the results did differ from Schelling, the influence of local racial preferences was strong, confirming Schelling’s most important claim. This sort of empirical validation only lends further credence to Schelling’s methodology and its success.

4.2 Limiting the Domain: The Acceptance of Schelling’s Result

While Schelling’s model did not incorporate any semblance of large-scale social structure in its simple grid-world, this lack of detail may have contributed to the general acceptance of his model amongst the social-science community. While his work did provide a significant influence on later modelling work in the field and some empirical work, as noted above, his initial forays into the residential segregation problem were very limited in scope (Schelling 1971).

Schelling aimed to illuminate the role of individual behaviours in producing counter-intuitive results in large-scale social systems, and his simple residential tipping model produced just such a counter-intuitive result by demonstrating the inability of individual tolerance for racial mixing to eliminate segregation. In this way the initial chequerboard model provided a theoretical backdrop for the larger thesis of his later book-length examination Micro-Motives and Macro-behaviour (Schelling 1978). Rather than producing one large, complex model which illustrated the importance of these individual preferences in the behaviours of social systems, he produced a number of small-scale, simple models which illustrated the same point in a more easily digestable and analysable way. Perhaps then the lack of complexity on display was what made his models so influential; providing such a basic backdrop made replication and expansion of his result straightforward for the research community.

4.3 Taylor’s Sites of Sociality: One View of the Acceptance of Models

Computational modelling, as described earlier, is inherently a theory-dependent exercise. Modellers seek to simplify reality in order to examine specific behaviours within the system of interest, and those simplifications and abstractions often betray a theoretical bias. In addition to this difficulty, Taylor describes the concept of ‘sites of sociality’ within modelling communities (Taylor 2000). In Taylor’s view, these sites correspond to points at which social considerations within a scientific discipline begin to define parameters of a model, rather than considerations brought about by the subject matter of the model itself.

Thus, if a certain evolutionary theory has become dominant within a specific domain of population biology, for example, a model which ignores the conceits of that theory may not find acceptance among the community. Schelling’s modelling work served to add to current social theory in evidence at that time, but did not seek to overturn the dominant ideas of the field; perhaps, in Taylor’s view, this was a powerful method for gaining widespread acceptance in the social science community.

4.4 The Significance of Taylor: Communicability and Impact

Taylor’s description of sites of sociality within modelling communities brings an important point to bear. Even if a model is constructed in such a way that the modeller can justify its relevance to the broader empirical community, that community may be operating under a different understanding of what is important to display in a simulation, or the importance of simulations as a whole.

Once again, we may use Vickerstaff and Di Paolo’s model as an example (Vickerstaff and Di Paolo 2005). Their model was accepted and communicated in a very popular experimental biology journal, despite being entirely computational in nature. The editors of the journal still accepted the paper despite its lack of hard empirical data; the model’s relative simplicity kept it from being too alien a concept for the biological readership, and the data it presented was novel and relevant despite its origins. The ability to comprehend the model in a more substantive way is vital to its acceptance; if the model had been too complex and difficult to replicate, the results would have been less impactful and interesting for the target audience.

Also like Schelling, the nature of the model makes it very palatable to the experimental biology readership in a different manner: the model was adding to the discourse on a particular topic in biology, rather than attempting to make major alterations to the field. If an Alife researcher submitted a paper to an experimental journal that proclaimed an end to conventional insect biology as we know it, for example, then the editors are unlikely to be receptive. As with Schelling, this paper served to illuminate a new idea regarding an issue relevant to the community it addressed; the paper did not ignore the pre-existing conceits of the community, and the data it produced was of value to the theories established in that community by decades of difficult data collection and analysis.

Thus, Schelling and Vickerstaff and Di Paolo both show the importance of communicability in a model which seeks to engage the wider research community. Schelling had great impact due to the ease of communicating his model results, and the ease with which members of the social science community could replicate and engage with those results; similarly, Vickerstaff and Di Paolo achieved success by crafting a model which demonstrated relevant new ideas that could be communicated well to the biological community despite the differing methods of data collection. Moving forward, we will see how the simplicity of a model can not only assist communicability and impact for a given model, but also its tractability and ability to produce useful, analysable results.

5 Fitting Schelling to the Modelling Frameworks

5.1 Schelling and Silverman-Bullock: Backstory

Under Silverman and Bullock’s framework (Silverman and Bullock 2004), Schelling’s model succeeds due to the integration of a useful theoretical ‘backstory’ for the model. Schelling represents the chequerboard model as an example of one particular micromotive leading to one particular macrobehaviour, in this case residential segregation. In the context of this backstory, Schelling is able to present his model as a suitable example of the impact of these micromotives on one particularly thorny social problem.

By restricting his inquiry to this singular dimension, the model becomes more palatable to social scientists, as the significant abstractions made within the model facilitate the portrayal of this aspect of the phenomenon in question. This serves to emphasize Schelling’s original theoretical formulation by stripping away additional social factors from the model, rather than allowing multiple interacting social behaviours to dilute the evidence of a much greater role for individual preference in residential segregation.

5.2 Schelling and Levins-Silverman: Tractability

Under our clarified Levinsian framework from Chap. 4 (see Table 4.1), in which tractability forms the fourth critical dimension of a model alongside generality, realism and precision, Schelling’s model appears to fall into the L2 categorisation. The model sacrifices realism for generality and precision, producing an idealised system which attempts to illustrate the phenomenon of residential segregation in a broader context.

Meanwhile, tractability remains high due to the simplistic rules of the simulation as well as the general ease of analysis of the model’s results; for many social scientists, a simple visual examination of the resultant segregated neighbourhoods from a run of the simulation proves Schelling’s point fairly clearly. More in-depth examinations are also possible, as seen in Zhang’s assessment of the overall space of Schelling-type models (Zhang 2004); such assessments are rarely possible with more complex models, which involve much more numerous and complex parameters.

5.3 Schelling and Cederman: Avoiding Complexity

In Cederman’s framework (Cederman 2001, see Table 5.1), Schelling’s model is a C1 simulation, as it attempts to explain the emergence of a particular configuration by examining the traits of agents within the simulation. In this way the model avoids the thorny methodological difficulties inherent to C3 models, as well as the more complex (and hence potentially more intractable) agent properties of C2 models. While C3 models are perhaps more useful to the social science modeller, due to the possibility of producing agents that determine their own interactions within the simulation environment, constraints such as those imposed by Schelling help to maintain tractability. This tractability does however come at the expense of increased self-organisation within the model.

6 Lessons from Schelling

6.1 Frameworks: Varying in Usefulness

Having tied Schelling’s work into each of our previously-discussed modelling frameworks, a certain trend becomes apparent in the placement of Schelling’s model within each theoretical construction. The simplicity of Schelling’s model places it toward the extreme ends of each framework: it has an easily-defined theoretical backstory; lies well within the range of tractability under Silverman and Bullock; and falls firmly within the C1 category described by Cederman.

While Cederman’s categorisation may help us to understand the aims and goals of a Schelling-type model, such ideas are already apparent due to the theoretical backstory underlying the model (which in turn places the model in good stead according our modified Levinsian framework). The pragmatic considerations of the model itself, as in whether it is amenable to analysis, are more important in driving our declaration of Schelling as a useful model. After all, a very ambitious and completely incomprehensible model could quite easily fall into Cederman’s C3 category; however, its impenetrable nature would be exposed to much greater criticism under the more pragmatic views of Levins and our revision of Levins presented in Chap. 4.

6.2 Tractability: A Useful Constraint

As described earlier, Schelling’s model benefits in several ways from its notably simple construction. Referring back to our revised Levinsian framework, the general concern of tractability is mollified by the model’s inherent simplicity. Given that the model can produce a visual demonstration of a segregation phenomenon, the job of the analyst is made much easier; the qualitative resemblance of that result to an overview of a segregated, real-world neigbourhood already lends credence to the results implied by Schelling’s model.

Perhaps more interestingly, the abstract nature of the model also makes further analysis less enticing for those seeking harder statistics. While the model does represent agents moving in space in reaction to stimuli, they do so as abstract units during time and space intervals that bear no set relation to real-world time and space. Fundamentally, the model seeks only to demonstrate the effects of these agents’ micromotives, and the effects of those micromotives on the question of interest; in that sense an in-depth analysis of the speed of segregation through the model’s space and similar measures, while interesting, are not necessary for Schelling to illustrate the importance of individual motives in residential segregation. As will become evident in the following section, Schelling’s ideas regarding modelling methodology drove him to construct his model in this way to maintain both tractability and transparency.

6.3 Backstory: Providing a Basis

Silverman and Bullock’s concept of the importance of a theoretical ‘backstory’ for any modelling enterprise (Silverman and Bullock 2004) seems supported by the success of Schelling’s work. His approach to modelling social micromotives derived from a theoretical backstory which takes in several important points:

1) Within a given research discipline, there are non-obvious analytical truths which may be discovered by means which do not include standard empirical observation (specifically mathematical or computational modelling in this case).

In the case of Schelling’s residential segregation model, the non-obvious result of the interaction of his tolerant agents is that even high tolerance levels still lead to segregation; one should note in this case that Schelling’s result was not only non-obvious in the context of the model, but was also non-obvious to those who studied the segregation phenomenon empirically.

2) The search for general models of phenomena can lead to the important discovery of general patterns of behaviour which then become evident in examples across disciplines.

Schelling uses ‘critical mass’ models as an example (tipping models being a sub-class of these), arguing that they have proven to be useful in ‘epidemiology, fashion, survival and extinction of species, language systems, racial integration, jay-walking, panic behaviour, and political movements’ (Schelling 1978, p. 89). The explosion of interest in tipping models following Schelling’s success with residential segregation indicates that such inter-disciplinary usefulness may indeed be a crucial element to the success of his model.

3) Modellers should seek to demonstrate phenomena in a simple, transparent way. As he states, a model ‘can be a precise and economical statement of a set of relationships that are sufficient to produce the phenomena in question, or, a model can be an actual biological, mechanical, or social system that embodies the relationships in an especially transparent way, producing the phenomena as an obvious consequence of these relationships’ (Schelling 1978, p. 87).

Schelling’s own models conform to this ideal, utilising very simple agents governed by very simple rules to illustrate the importance of individual behaviours in social systems. Zhang’s analysis of Schelling-type models using recent advances in statistical mechanics shows one of the benefits of this transparency in a modelling project (Zhang 2004).

6.4 Artificiality: When it Matters

The importance of artificiality within a simulation methodology as espoused by Silverman and Bullock (2004) is especially crucial to an evaluation of Schelling-type models. Schelling himself posits that models can illuminate important patterns in a system of interest without requiring recourse to empirical observation (Schelling 1978); in this fashion his work suggests Silverman and Bullock’s Artificial1 and Artificial2 distinction as a sensible path for models to take. However, he further clarifies this idea by proposing that such models must remain transparent and easily analysable, displaying a clear interaction which leads to the appropriate results in the system of interest; an overly-complex Artificial1 model, in his view, cannot provide that clear link between the forces at play within the model and the resultant interesting behaviour.

Further, Schelling’s two-part definition of models goes on to describe the potential for using an actual biological or social system in a limited context to illustrate similar points (Schelling 1978); this statement implies that Artificial2 models, which would be a man-made incidence of these natural behaviours, may be able to provide that simplicity and transparency that empirical observation of such complex systems cannot provide. In one sense, then, Schelling appears to dismiss the question of artificiality in preference to the modellers motivations: in order to display the effect of micromotives or emergent behaviour, the model must display a clear relationship between the resultant behaviour and the contributing factors alleged to create that behaviour, and whether that model then embodies Artificial1 or Artificial2 is not necessarily of any consequence.

6.5 The Practical Advantages of Simplicity

Schelling also demonstrates the practical usefulness of creating a simple model of a phenomenon. So far we have seen how this simplicity allows us to avoid some of the methodological pitfalls that can trouble those who choose to utilise agent-based models, and likewise it is easy to demonstrate how this same property can help the modeller in more pragmatic ways.

Firstly, such simplicity not only allows for higher tractability, but also much simpler implementation. In the case of Schelling’s model, numerous implementations of the model exist in a large variety of programming languages. Writing the code for such a simulation is almost trivial compared to more complex simulations; indeed, some pre-packaged simulation codebases such as RePast (designed for the social scientist) can be utilised to produce a Schelling-type model in only a few lines. Beyond simply the time savings of these ease of implementation, the simple construction of Schelling’s model vastly reduces the amount of time spent tweaking a simulation’s parameters. In more complex simulations, such as an evolutionary model, parameters such as mutation rates can have unexpected impacts on the simulation results, and finding appropriate values for those parameters can be time-consuming.

Secondly, starting from such a simple base allows for much greater extendability. With the Schelling model being so easily implemented in code, extending some elements of that model becomes very easy for the researcher. For example, alterations in the number of agent types, the complexity of the agents themselves, or the set of rules governing the agents are easy to create. In addition, the simple nature of the initial model means it is also easy to change one aspect of the model and see clearly the results of that change; in a more complex formulation, changing one element of the simulation may produce unexpected changes, and complex elements in other areas of the simulation could be affected in ways that produce unanticipated results.

Finally, the modeller benefits from potentially a much larger impact of the simulation when it is simple to implement. For example, we saw previously how Zhang was able to probe the properties of the entire space of Schelling-type models (Zhang 2004). If Schelling’s model were too complex, this would be an impossible task. Instead, due to its simplicity, dozens of interested researchers could implement Schelling’s model for themselves with little effort, see the results for themselves, and then modify the model or introduce new ideas almost immediately. Such ease of replication and modification almost certainly helped Schelling to reach such a high level of impact from his initial model; the simplicity of the model essentially lowers the barrier of entry for interested parties to join the discussion.

7 Schelling vs Doran and Axelrod

7.1 Doran’s View: Supportive of Schelling?

Doran’s views of agent-based models in social science (Doran 2000) proposes that such models can provide a means to generate new ‘world histories,’ or artificial explorations of versions of human society that may have come into being given different circumstances. While Schelling’s model could be construed as an ‘artificial society’ of the simplest order, the model is oriented less toward reaching grand conclusions about the structure of society as a whole and more toward a demonstration of the low-level factors in a society which may produce one particular phenomenon.

With this in mind, Doran’s further concerns about the undefined role of agents in social simulation also seem of particular import. Doran argues that agents in social simulation should be defined on a computational basis to allow those agents to develop emergent behaviour in the same way as other aspects of the simulation. Schelling’s model incorporates agents in a most abstract way; each individual in the model makes only a single decision at any given time-step, based on only a single rule. Given this simplicity, could we argue that these agents are sufficiently advanced to bring us a greater understanding of the residential segregation problem? If not, how might Doran’s view inform a more rigorous version of Schelling’s original vision?

While Schelling’s model is indeed oriented toward a specific social problem in an intensely simplified form, in a sense he is providing a minimal ‘artificial society’ as Doran describes this methodology. Schelling is able to create alternate ‘world histories’ for the limited two-dimensional space inhabited by his simple agents; he can quite easily run and re-run his simulation with different tolerance values for the agents, and examine the resulting patterns of settlement following each change. For example, he could determine the result of populating a world with completely tolerant agents, completely intolerant agents, and all variations in between.

With regard to Doran’s concerns regarding the roles of agents in social simulation, Schelling’s model suffers more under scrutiny. Despite the simplicity of the model itself, the agents are built to a pre-defined role: each agent is assumed to be searching for a place to settle, with its preference for a destination hinging upon the appearance of its neighbours. This presumes that individuals in a society would prefer to remain settled, rather than move continuously, and that all individuals will display a primary preference based upon the characteristics of its neighbours; both of these assumptions have been placed into the model by Schelling’s own conceptual model, rather than having those agent properties emerge from the simulation itself.

One could imagine constructing a Luhmannian scenario in which agents are given only the most base properties: perhaps a means of communication, an ability to form preferences based on interactions, and the ability to react to its neighbours. Might these agents, based upon interactions with neighbours of different characteristics, form preferences independent of the experimenter’s expectations? If so, then these preferences would emerge from the simulation along with the resultant agent configurations in the simulated world, making the agents more independent of the experimenter’s biases, though of course never entirely independent of bias. Such a set-up would certainly alleviate Doran’s concerns about pre-defined agents and theoretical biases, but whether the results would be more or less useful to the community than Schelling’s original is still debatable.

7.2 Schelling vs Axelrod: Heuristic Modelling

Robert Axelrod and Leigh Tesfatsion’s introduction to agent-based modelling for social scientists, discussed in the previous chapter, describes four main goals of social simulation models: empirical understanding, normative understanding, heuristics, and methodological advancement (Axelrod and Tesfatsion 2005). Schelling’s model seems to fall most readily into the heuristic category, seeking as it does a fundamental insight into the mechanisms underlying the phenomenon of residential segregation.

Axelrod’s view, unlike Doran’s, stops short of examining specific methodological difficulties in social simulation modelling. Instead, he develops these four general classifications of model types, placing agent-based modelling into a framework oriented more toward empirical study. Given that three of Axelrod’s four categories are directly concerned with empirical uses of agent-based models, this framework offers little guidance as to the appropriate use of models like Schelling’s.

Of course, as indicated by the discussion of Axelrod’s categorisations in the previous chapter, our analysis thus far has indicated a number of theoretical difficulties with this empirical approach to social simulation. With this in mind the fact that Schelling lies outside the prominent focus of Axelrod’s approach is not particularly surprising. Along with Doran, Luhmann, and Silverman and Bryden (Silverman and Bryden 2007), Schelling’s model is more appropriate in the context of a more general and abstracted modelling perspective, one which seeks general understanding of social phenomena rather than data relating to specific aspects of society.

8 Schelling and Social Simulation: General Criticisms

8.1 Lack of ‘Real’ Data

While Schelling thus far has held up well under the scrutiny of several major theoretical frameworks regarding simulation models, there are still concerns levelled generally at social simulation which must be addressed. The first, and potentially the most troublesome, is the lack of ‘real’ data attributed to models within social science, and the resultant disconnection between these simulations and empirical social science.

Schelling quite clearly falls afoul of this methodological sticking point. There is no aspect of the chequerboard model which is based upon empirical data: the chequerboard itself is designed arbitrarily, with no real-world context or comparison; the agents are given a tolerance threshold by the experimenter, not one based upon any empirical study; and there is no representation of the nuances of human residential areas, such as buildings, other residents, or other interacting social factors that may effect the residential segregation phenomenon. In other words, Schelling’s model is very much an abstraction with no real basis in empirical social science.

However, given the context of Schelling’s work, the abstraction is entirely justifiable. Had Schelling proposed to understand residential segregation in one particular circumstance, then produced such an abstract model, then he would have been reaching for conclusions far beyond the scope of the model itself. His question instead was much more broad: can we illustrate the effect of individual ‘micromotives’ on an otherwise difficult-to-explain social phenomena? His model answers this question without the need for specific ties to empirical data-sets, and indeed ‘real’ data would most likely dilute the strength of his result in this context.

8.2 Difficulties of Social Theory

Revisiting Kluver and Stoica once more, we recall their assertion that social theory does not benefit from being easily divisible into interacting hierarchical structures as in other fields, such as biology (Klüver et al. 2003). Given that a social system will encompass potentially millions of individuals, each interacting on multiple levels, while higher-level social structures impose differing varieties of social order, the end behaviour of a society through all of these factors can be exceedingly complex. This inherent difficulty in social science makes the prospect of empirically-based simulation seem ever more distant.

However, Schelling once more illuminates the benefits of a more abstract approach to examining social systems. Schelling’s model suffers little from the problem of interacting social structures, as the model itself involves only a set of agents interacting in a single space: there are no social structures; no imposed social order in the system; and only a single type of interaction between agents. The model thus escapes this difficulty by quite simply eliminating any social structures; without these multiple interacting structures to confound analysis, the model’s result remains clear.

8.3 Schelling and the Luhmannian Perspective

With the abstraction and simplicity of Schelling’s model allowing it to escape from the methodological traps common to most social simulation endeavours, we are left with an interesting perspective on our earlier proposed method for developing fundamental social theory. Similar to Schelling’s tipping model, the Luhmannian modelling perspective would construct an agent-based model bearing as few assumptions as possible, allowing the resultant configurations of agents and model properties to emerge of their own accord.

In essence, Schelling’s model takes the Luhmannian approach and boils it down to an exploration of a single aspect of human society. While Luhmann asks what drives humanity to develop social order (Luhmann 1995), Schelling restricts his domain to only residential segregation, asking whether individual motives can drive agents to separate themselves from one another. While Luhmann condenses the whole of human interaction down to social developments linked to an iterated process based on our ‘expectation-expectations,’ Schelling similarly condenses the puzzling behaviour of human segregation down to a series of simple individual decision-making steps.

Schelling’s success, then, gives the Luhmannian approach a further emphasis. While the investigation of the overall origins and development of the human social order is certainly a much more complex endeavour than that of investigating a single social phenomenon a la Schelling, this residential segregation model provides an insight into the benefits of the process. Schelling wrote of the importance of demonstrating the relationships between model properties transparently (Schelling 1978), and with a Luhmannian model the same approach is necessary.

8.4 Ramifications for Social Simulation and Theory

Having established the importance of Schelling’s perspective, and the links between his modelling paradigm and our proposed means for developing fundamental social theory, a further re-evaluation of Schelling’s impact on social simulation is required. We have seen the import of this model’s simplicity and transparency, and even how its inherent abstraction enables the model to draw intriguing conclusions within the larger context of general social theory. Does this imply that the empirically-based approach of Cederman, Axelrod and others is a scientific dead-end?

Perhaps not: certainly as the field of geographic information systems (GIS) continues to advance, and real-time data collection within social science becomes more wide-spread and rigorous, then the introduction of real and current data into social simulation becomes an interesting possibility. This after all is a central criticism of social simulation of this type: real data is hard to come by, and that data which is available is often limited in scope or out of date. When this obstacle disappears, then simulations more closely linked to data produced by real human society becomes more viable.

However, the other fundamental concerns related to social simulation still remain. Doran’s concerns regarding the lack of definition of the roles of agents in social simulation (Doran 2000) remain important, and as integration with real data becomes vital to a simulation that concern becomes ever more central. The question of how to develop cognitive agents with an appropriate set of constraints and assumptions to produce parsimonious results is not one that will be answered quickly.

Similarly, the inherent abstraction of social processes and structures necessary in a computer simulation could be problematic in a simulation designed to produce empirically-relevant results. Axelrod and Tesfatsion (2005) proposes social simulations that may inform public policy (his ‘normative understanding’ category of social simulations), and while this is an enticing prospect, we have already seen the troubling pitfalls the researcher can encounter in this approach (see Chaps. 4 and 5).

This reinforces the importance of Schelling’s model as deconstructed in the preceding analysis. While initially appearing simplistic, the theoretical implications of Schelling’s work are rather more complex. The importance of this model in social science despite its simplicity, complete abstraction, and lack of empirical data shows the potential of social simulation to stimulate social theory-building. Schelling’s model stimulated the field to view the importance of individual ‘micromotives’ in a new fashion; a more sweeping model portraying the emergence of a social order in a similar way could have an equally stimulating effect on social theory.

9 The Final Hurdle: Social Explanation

9.1 Schelling’s Model and the Explanation Problem

As described in Chap. 5, there is some debate over the explanatory power of computer simulation within the social sciences. While the predominant idea within such endeavours is that of emergence, or the development of higher-level organisation in a system given interacting lower-level components, some theorists argue that social systems do not produce higher-level organisation in this way (Sawyer 2002, 2003, 2004).

Sawyer’s development of the idea of non-reductive individualism, in which certain properties of a society cannot be reduced to the actions of individual actors in that society, does pose a fundamental problem for agent-based modellers. If agent-based models proceed on the assumption that individual-level interactions can produce the higher-level functions of a social order purely through those interactions, then such models may be missing a vital piece of the explanatory puzzle within social science. In this respect individual-based models need a theoretical underpinning in which emergence is a valid means for the development of high-level social structures.

Schelling’s model focuses entirely on the actions of individual agents, and the impact of their individual residential preferences on the racial make-up of a given neighbourhood. In this sense the model does seek to demonstrate the emergence of a higher-level configuration from the actions of individuals, which according to this view of social explanation is problematic.

However, Macy and Miller’s take on this social explanation problem (Macy and Willer 2002) would allow for Schelling-type models, as the model focuses purely on a situation for which there is no central coordination of the behaviour in question. The agents in Schelling’s chequerboard world do act individually, but the results he sought were not a higher-level social organisation or function, but instead merely a particular configuration of those individuals at the end of a simulation run. Even in Sawyer’s less forgiving view, Schelling’s simulation does not strive to explain a larger-scale structure that might be dubbed irreducible.

9.2 Implications for Luhmannian Social Explanation

Our earlier discussions of Niklas Luhmann’s ideas regarding the development of the human social order presented a means for applying these ideas to agent-based models designed to examine the fundamentals of society. By applying Luhmannian ideas of extremely basic social interactions that lead to the formation of a higher social structure, a modeller may be able to remove the theoretical assumptions often grafted into a model through the design of restrictive constraints on agents within that model.

However, our examinations of the difficulty of social explanation remain problematic for a Luhmannian approach. If certain high-level aspects of human society depend on functions which are irreducible to the properties of individuals within that society, then even the most cleverly-designed agent-based model would be unable to provide a complete explanation for the functioning of society. This places a fundamental limit on the explanatory power of the Luhmannian approach, barring us explaining the social order in its entirety.

Perhaps Sawyer’s comparisons with non-reductive materialism within the philosophy of mind may provide a solution (Sawyer 2004). As he notes, ‘the science of mind is autonomous from the science of neurons,’ alluding to the disconnect between psychology and neuroscience (Sawyer 2002). Indeed, within the study of mind there are conscious and unconscious phenomena which are irreducible in any straightforward way to the functioning of the underlying neurons; after all, psychologists still struggle to explain how neuronal firings lead to the subjective experience of individual consciousness.

However, very few psychologists still adhere to the concept of dualism: the idea that conscious experience is a separate entity from the physical brain itself. Sawyer clearly does not, as is evident from his discussion of non-reductive materialism. In that case, while we may not be able to draw a direct relation between conscious phenomena and brain activity, the relation nonetheless exists; neurons are the cause of conscious phenomena, merely in a way we cannot understand straightforwardly.

In the same sense, individuals will be the fundamental cause of large-scale social phenomena, whether those phenomena display clearly evident relationships or not. If we accept that a sufficiently advanced and appropriately constructed computer may be able to achieve consciousness, then surely a similarly advanced social simulation could allow sophisticated structures to emerge as well? In either case, the functioning of those individual units would be very difficult to relate to the emerging high-level phenomena but developing artificial (and hence de-constructable) models of both these processes could provide a unique insight.

Thus, Sawyer may very well be correct, and understanding the relation between high-level social structures or institutions to individuals in society may be difficult, or even impossible. But this is not to say that individuals, even in a model, could not produce such phenomena; nor that study of such models would not produce any insight. The Luhmannian modelling perspective aims to discover the roots of human society, and if those individual roots produce irreducibly complex behaviour, those models have surely functioned quite well indeed.

10 Summary and Conclusions

In this chapter we have examined one particular example of social simulation, Schelling’s chequerboard model, in light of the various theoretical concerns raised thus far. Schelling’s model was a marked success in the social sciences, producing an endless stream of related works as the idea of social phenomena emerging from the actions of individuals grew in the social sciences as it did in artificial life.

The simplicity and transparency of the model allowed it to have a stronger impact than many more complex models. Along with being easily reproducible, Schelling’s results were restricted to a very specific question: can individual housing preferences drive the mysterious process of residential segregation? The answer, demonstrated by the starkly-separated patterns of white and black squares so prominent in the literature, appeared to be yes.

This approach, while falling within the remit of the theoretical frameworks laid out by other social simulators, also provides an insight into new paths for producing social theory. While the use of social simulations for empirical study is enticing, and potentially both useful and lucrative, the methodological and theoretical difficulties involved in such an approach are many and complex. In contrast, a simple model with few inherent assumptions can offer a more basic and general description of the origin of various social phenomena.

Schelling’s model also provides a view into the potential benefits of the proposed Luhmannian modelling approach for the social sciences. Like Luhmann, Schelling’s model took very basic interactions as a basis for producing more complex social behaviour; Luhmann takes a very similar approach, but on a much larger canvas. In this respect Schelling shows that the Luhmannian approach could allow social theorists to develop ideas regarding the social order that may have large ramifications for social science as a whole.

Of course, the problem of social explanation still looms as large for Luhmann as it does for Cederman or Axelrod. The debate over emergent phenomena in social science is unlikely to subside, and as such the results of such simulations may always be disputed on some level. However, even if we accept that some aspects of a Luhmannian simulation may not provide complete explanatory power, the results could still be revolutionary for social theory.