Simulation: an emergent perspective

Nigel Gilbert
Centre for Research in Social Simulation
Department of Sociology
University of Surrey
Guildford, GU2 5XH
United Kingdom

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The text of a lecture first given at the conference on New Technologies in the Social Sciences, 27--29th October, 1995, Bournemouth, UK and then at LAFORIA, Paris, 22nd January 1996.
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Abstract
Computer simulation is not just a new method to add to the social researcher's armoury, but a new way of thinking about society, and especially social processes. In this talk I shall try to justify this claim using a variety of examples of present day simulation studies taken from anthropology, social psychology and economics as well as sociology. The talk will identify some theoretical ideas that have been inspired by simulations and consider some methodological issues applicable not only to simulation but to social science in general.

The role of simulation
Let me begin by putting forward some propositions for you to consider: Simple patterns of repeated individual action can lead to extremely complex social institutions. It is impossible, in principle, to predict the outcomes of some social changes. Even when there are powerful processes tending to convert a population to a consensus view, minorities may persist.

Members' misperception and misbelief can be functional for groups and societies. These may seem to be rather peculiar propositions. First, they are all to some degree counter-intuitive. Secondly, they are couched in a rather odd vocabulary. They are concerned with processes, yet very little present-day sociology is about understanding processes. Even stranger, they use words like `functional'.

As you may know, there was a long debate in sociology starting around the Second World War about a form of explanation called functionalism. This argued that some forms of social organisation were functional for society. Most notorious were the assertions that it was functional for women to stay at home to look after the children, and that status and income differentials were functional to ensure that the best people took the most important jobs. Despite strong rearguard action, functionalist explanations are now extremely unfashionable and widely regarded with suspicion.

The legacy of functionalism
There are two problems with functionalism, in addition to a tendency for many of its most famous proponents to be white, American conservatives. The first is the problem of teleology, which means explaining the existence of something (an institution, a belief or whatever) by saying that it is functional for the survival of the society. The trouble with this is that it involves explaining a cause (the belief, for example) by means of its effect (its value for society). While it is perfectly reasonable to explain an effect by its cause (he fell over the cliff because he was pushed), an explanation the other way round is not logical. The second problem is that much functionalist sociology concerned itself only with synchronic analysis, that is analysis of things as they are now, as though from a single snapshot. This was partly in reaction to previous highly speculative `evolutionary' theories. For example, early 20th century anthropologists had proposed that some of the customs of patrilineal societies were leftovers from previous times when those societies were matrilineal. Unfortunately, these pre-literate societies had left no records about their earlier organisation, so this kind of evolutionary explanation was untestable.

Synchronic analysis
Synchronic analysis rules out the possibility of testing an important class of explanations, those based on process. If you want to understand why a person acts as she does, it is certainly possible to look around in the immediate environment for an explanation. But often an explanation needs to look also, or perhaps primarily, at events that occurred in the past and at how the present situation developed from previous circumstances. This was an approach to explanation which, on the whole, functionalists were not interested in, and their reluctance to explain in terms of processes through time is one that has left its mark even on present day sociology.

Consider, for instance, the two main methods of empirical analysis sociologists use today: statistical tools such as regression and its more complex variants, and the whole gamut of qualitative analysis of interviews and observational data which we can loosely characterise as `ethnography'. In the case of ethnography, it is rare for the analyst to have access to data about processes, that is, data about how things came to be as they are. If you interview people in some social setting, you will get a feel for their present ideas. You can of course ask them to recount their biographies or explain their careers, but the picture you will get will inevitably be influenced by their current circumstances and their current perceptions. For example, if you interview women doctors about their careers and their decisions about whether to have children, you will not include in your sample those women who decided not to qualify as doctors because they realised that it would be difficult to combine a medical career with bringing up a family. This is not a criticism of ethnography as a method; I am just saying that it is an almost inevitable consequence of this type of data collection that the analyst's attention will be shifted away from processes towards synchronic explanations.

As far as statistical analysis is concerned, until quite recently the only data that have been available have been from cross-sectional surveys, that is, from surveys of people at one moment in time. Gradually over the last ten years the inadequacies of this have been realised and increasing attention is being given to mounting panel studies. These are surveys in which the same people are asked the same or similar questions regularly over a period of years, so that it is possible to determine how the attitudes and circumstances of individuals have changed over time. In Britain, the best examples of these are the pioneering National Child Development Study, which is collecting data about all the people in Britain born during one week in 1953, and the British Household Panel Study, which is interviewing a random sample of households every two years or so and has now collected its third `wave' of data.

Together with the increasing availability of such longitudinal data has come the development of new statistical methods of analysis. For example, event history analysis aims to show how the characteristics of an individual can be used to explain the timing of that person's life events. Given some data from a panel study on when people enter and leave unemployment, we might use event history analysis to explain the duration of a period of unemployment in terms of a person's education, previous spans of unemployment, age and similar variables.

An event history

Individualistic explanation
Even these new methods of statistical analysis, however, leave something to be desired. First, they are individualistic forms of explanation. If we use event history analysis to explain length of unemployment, we do so in terms of each individual's own characteristics: their own education, their age, their past history of employment and so on. The only way in which the society enters into the explanation is as a substrate in which there is a rate of unemployment and an education system and so on, but these characteristics of the society are taken as givens and are not themselves explained.

Secondly, explanations provided by techniques such as event history analysis fail to suggest the processes which generate the observed relationships. An analysis of unemployment might show that expected length of a span of unemployment is related to the unemployed person's previous employment history. It could provide a beta coefficient to measure the strength of this relationship, but what it could not do is provide an explanation of why the relationship holds: just what is it about previous unemployment that tends to lengthen the duration of current unemployment? Not only does it not offer an answer to this question, but it also fails to offer any clues about where we should look to discover more about the processes involved.

So far, I have been rather critical about current forms of explanation. Of course it is easier to be critical than it is to suggest remedies, so it behoves me to propose how we might do better. Before I do that, however, let me summarise the argument so far. I have suggested that sociologists have under-emphasised the importance of process and the passage of time. And where they have attempted to analyse longitudinal data, they have treated societies and social groups as the aggregate of individuals, rather than engaged in truly sociological analyses. Now I would like to turn to explaining an approach which might help to overcome these problems: the construction of models of social processes.

Computational models
One powerful way of explaining things is in terms of models. Some philosophers of science maintain that all scientific explanation depends on building models. For example, to understand the atom, late nineteenth century physicists visualised electrons and protons and so on and even drew pictures of atoms as miniature solar systems. Similarly, biologists constructed models of living cells as chemical factories. More recently, scientists have tended to construct mathematical models rather than graphical ones, but the principle is much the same. Model building is not just confined to the natural sciences. Economists build models of economic systems and psychologists build cognitive models of brain functions. Explicit models of social phenomena have not been so common, but with the advent of powerful computers, computer models of social systems have become possible. The models are designed to be `run' as processes within a computer, simulating the processes thought to exist in the social world.

I shall now review the main types of simulation which social scientists around the world are currently developing. This will give you some idea of the scope of simulation. At the same time, I will indicate some of the ways in which simulation can go beyond the limitations of the methods that I criticised at the beginning of this paper.

Micro-simulation
One of the earliest and probably the best known kind of simulation in sociology is called `micro-simulation' (Harding 1990). It was developed for investigating the consequences of social policy changes on populations. It has been used to great effect to predict the financial effects of pension changes on future generations and for investigating the implications of welfare benefit and tax changes on households. At present most fiscal projections are made by rather simple extrapolations of trends into the future. Crudely, one takes a graph of, say, state expenditure on pensions and continues the line for a few more years. Micro-simulation aims to provide much more reliable estimates.

The basic idea is simple: collect data about a random sample of a few thousand households at one moment in time from, for example, the Family Expenditure Survey, then simulate the effect of the passage of a year on each of the households in turn. For example, all the members of the household will get one year older. This means that some of the children may leave school and join the labour market; some of the older members may leave the labour market and retire. Some women may give birth to children and some people may die during the year. Each of these life course events is simulated with a specified probability, the probability varying according to the situation of each person. Thus a women aged between 16 and 25 may have a certain probability of becoming pregnant, while a man will have a zero probability of doing so. After simulating demographic changes during the year, consequential changes to income and expenditure are made (for instance, people who retire lose their salary but gain a pension). More complex models may also simulate the break-up and formation of households. Once the effects of one year have been modelled, the simulation advances to the next year, building on the results of the first year's simulation.

At the end of each simulated year, aggregate statistics about the sample, such as the proportions in and out of the labour force or the total expenditure on benefits, can be calculated and grossed up to predict what would be the case for the whole population. In this way, forecasts about changes years ahead at the level of a whole society can be made that are based on simulations of the behaviour of individual households.

Micro-simulation can be a simple and relatively unsophisticated form of simulation, aimed principally at providing answers to matters of social policy. As such it is at the applied end of the spectrum of social research. It suffers from some of the same points of criticism as I have levelled at more conventional methods. For example, it treats each household as an isolated entity. In practice, proponents concentrate almost exclusively on prediction, what the situation will be like in, say, twenty years time, rather than on explanation, why it should be like that. Nevertheless, micro-simulation is interesting because it shows how behaviour at one level --- national taxataion and benefit expenditure --- can be modelled by a simulation of households at lower level of analysis. As we shall see in subsequent examples, the relationships between levels of analysis, individual, organisation and societal, are a matter of central concern in social simulation. Some more advanced micro-simulation programs are now modelling not only households but also the business sector and are beginning to use simulated changes at the aggregate national level to influence behaviour modelled at the individual level, for example, the effect of national unemployment rates on the probability of individuals securing employment.

Cellular automata
I mentioned that the micro-simulation approach treats the units of analysis, households, as isolated individuals. Work based on a different approach, cellular automata, suggests one way of going beyond this to model interaction between people. One of the first and simplest cellular automata models was called the Game of Life by its inventor, John Conway, in 1970. Imagine a rectangular grid of cells. Each cell can either be `alive' or `dead'. Time proceeds in discrete steps. At the end of each step, a living cell remains alive only if it has two or three living neighbouring cells. Otherwise it will die, either of loneliness or of overcrowding. A dead cell starts to live if there are exactly three living cells around it. The strange thing about this arrangement is that while the two rules which determine whether an individual cell is alive or dead are very simple, the effect at the macro level, that is at the level of the grid as a whole, can be very complex, with different starting configurations of live and dead cells giving sequences of patterns arising and evolving, sometimes remaining stable and sometimes dying away. The form of these dynamic patterns is impossible to predict analytically; the only way of discovering the patterns is to simulate. The patterns are said to `emerge' from the life and death of the individual cells.

Cellular automata have been used to investigate the properties of physical materials (e.g. magnets), engineering problems (e.g. fluids in pipes) and have been of great interest to mathematicians. Now they are beginning to be used for investigating social phenomena. Of course, a cell in a grid is not a complete simulation of a person. Rather CA models are used to investigate the abstract properties of interacting agents. In some of these models, as in the Game of Life, the cells remain fixed on the grid. In others, the cells are allowed to move over the grid like pieces on a draughts board, again dependent on the results of applying simple rules about the state of neighbouring cells.

A famous and early example is the study by Schelling in 1971 of ethnic segregation(Schelling 1969, 1971). Segregation into distinct geographical neighbourhoods was and is still often considered to be a product of direct discrimination (estate agents dissuading black people from moving into white areas, for instance) or of the effects of economic constraints (e.g. poor black families only being able to afford housing in deprived areas). But by investigating the properties of a cellular automata, Schelling pointed out that if families, both black and white, prefer to live in neighbourhoods in which their own ethnic group is a majority, and they are able to move to the nearest location which satisfies this desire, complete segregation will inevitably emerge. This is the case even if none of the families actually wanted complete segregation. An unintended outcome emerges from the effect of many individual decisions.

Modelling dynamic social impact
Latané has put the cellular automata model in good effect in exploring the implications of his theory of dynamic social impact. Social impact is defined quite generally as a change in a person's subjective feelings, motives, emotions or beliefs as a result of the actions of other individuals. Latané (1981) proposed that social impact is proportional to the product of the strength (e.g. status, persuasiveness, attractiveness, etc.), immediacy (closeness in space or time, for example) and number of people influencing an individual. The principle seems absurdly simple, yet it has been shown to hold in a wide variety of situations. But as I have formulated the principle, it is a static and individualised theory. The interesting question is, assuming that it is true, what happens if we have a population of people, all influencing each other?

We can investigate this using simulation (Latané 1996). Imagine that we have a population of some hundreds or thousands of people, and we know that their values on three different and independent issues. Suppose also that to begin with, 60 per cent of the population follow the majority view and the remaining 40 per cent have the contrary view, but these attitudes are distributed among the individuals entirely at random. Furthermore, the people vary in how influential they are, but again at random. We can set up a cellular automata model with each cell representing a person and with state change rules that implement the principle of dynamic social impact, so that if the sum of the influences on a particular person in one direction exceeds the sum of the influences in the other direction, that person flips their attitude correspondingly. We can then watch what happens as people influence their neighbours, and are in turn influenced by their neighbours.

Surprisingly, the minority survives, though with a reduced percentage of adherents, rather than being overwhelmed by the combined influence of the majority view. While individuals continually change their affiliation as a result of social impact, overall there remains a minority of more or less constant size. Secondly, the distribution of attitudes changes from the initial random distribution to being spatially clustered. That is, people with similar attitudes are grouped together, influencing each other to stay in line. It is the clustering that protects the minorities from extinction, because it is only cells on the edges of clusters that are exposed strongly to the other attitude. Thirdly, although changes of attitude on the three attributes are modelled at the individual level as being entirely independent, the three attributes become correlated at the level of the population. This is becuase as the simulation proceeds, clusters of like minded people develop. These clusters are different for each of the three attributes, but because a person in one cluster is somewhat more likely than random chance to be in another cluster (or vice versa), at the population level there will apparently be a correlation between the attitudes.

While this may at first appear to be a rather boring statistical result related to spatial auto-correlation, it has some thought-provoking sociological implications. We often call a set of correlated attitudes or beliefs an ideology and assume that ideologies arise as a coherent group of beliefs from social movements. But here we have modelled the emergence of a prototype ideology literally from nothing. What if the cluster of attitudes we might call a class ideology arises not from people's relationship to the mode of production but from their spatial clustering?

I should make it clear that the results I have been summarising are robust. That is, it doesn't matter what the initial random starting configuration of attitudes is, nor the distribution of strengths, nor the number of people in the simulation, nor the number of attitudes modelled; the clustering and the survival of minorities occur every time. Those features of the simulation which are essential, and without which interesting behaviour does not occur are: people must be located in social space so that they have more influence on near neighbours than on distant strangers; attitudes must be on a discrete rather than a continuous scale (this introduces non-linearity into the system, an idea I shall return to later); and the distribution of strengths in the population must not be uniform (the strong individuals protect the borders of minority clusters).

Models based on Artifical Intelligence
The result of this kind of simulation can be fascinating to watch, but it requires a lot of theoretical imagination to move from patterns of cells on a grid to conclusions about societies. This is partly because the individuals are modelled as such very simple units. Another strand of recent simulation research has favoured using rather more complex models in which individuals are simulated using `agents' based on techniques derived from Artificial Intelligence (AI).

A model of budgeting
Edmund Chattoe and I have recently been building a simulation of how people divide their income between major categories of expenditure such as rent, food and leisure (Chattoe and Gilbert 1995). Existing economic theories about consumption behaviour are based on rational choice but tend to be poor at predicting actual expenditure, partly because they have difficulty in incorporating factors such as social influences, personal rules of thumb and the fact that consumption decisions are made over time. What we have done is to build a simulation which incorporates rules about what to buy derived from interviews with actual consumers. Because we assume that most people most of the time make budgetary decisions from habit (for example, buying a pack of toilet roll every three weeks), we sought to interview people who would be more likely to be budgeting explicitly. Eventually, we will be interviewing the recently retired, many of whom will have had a major change in their economic circumstances and will therefore have had to adjust their purchasing. But to begin with, we chose to interview postgraduate students whom we expected would have some difficulty making ends meet.

The respondents were asked to give details of their major sources of income and outgoings using their own categories. They explained how they dealt with regular outgoings like rent, how they would deal with unexpected expenses and which categories they regarded as fixed or negotiable. Their replies were formalised as a set of rules which drove a simulation. One of our conclusions was the importance of planning for consumption. The respondents were able to project their likely expenditure ahead and appeared to use this to decide whether they had to economise. The effect of such projections could be examined by running the simulation both with and without modelling the ability to project. Without projection, the simulation showed that people would rapidly get into dire trouble. With projection and the same stream of income and bills, the simulated agents were able to survive for months on end.

At present, the primary aim of the simulation is to serve as a way of capturing and experimenting with the rules that people tell us they use in budgeting. The model provides a formal notation for expressing respondents' budgeting rules and it allows us to check the rules for consistency and completeness, pointing out areas and issues that neither we nor the respondents had realised needed to be considered. One of our aims, however, is to move beyond this descriptive mode to explore the consequences of different budgeting behaviours.

Deciding what to spend one's money on is surely not a purely individual matter of strict economics. Very few people are so poor that they do not have some choice about what they buy and the great majority probably have much more potential choice than they can possibly cope with rationally. It may be for this reason that rational choice theories of consumption work so badly. Instead, one might assume that people make consumption decisions on the basis of social learning and social imitation (and here I am talking about deciding what proportion of one's income to spend on, for example, housing, not whether to buy an apple or an orange). That is, people adopt bunches of consumption decisions or what one might call `lifestyles' from a selection available to them from their friends and neighbours and once, they have adopted a life style, this is adjusted in the light of circumstances through a process of trial and error or evolution.

Towards the end of the project, we hope to be able to experiment with this notion by building a simulation in which the simulated people or `agents' evolve their own budgeting rules under the constraint that they have to live on their income, just as people do. When I use the word `evolve', I mean this quite literally. Living things evolve through a process of repeated reproduction in which the genes, a way of coding information about the characteristics of an individual, are transmitted from parent to offspring. Genes are combined from both parents in sexual reproduction and occasionally mutate. The chances of an individual reproducing and passing on their genes depends on the `fitness' of that individual in its environment. These basic ideas of evolution have been simulated in computer programs using sequences of bits as a model for a gene, and implementing sexual reproduction and mutation as combining and randomly changing those bit sequences. Such `genetic algorithms' now have a respectable history and have been applied in many domains: not just for biological research, but also in engineering and financial applications where the algorithm is used to evolve designs which fit their environments well (Goldberg 1989, Koza 1992). We hope to use a genetic algorithm to evolve a set of budgeting rules and then compare these rules with the ones described by our respondents.

Collective misbelief
Our work has both practical and theoretical implications: practical in that we are discovering more about how people budget and how they learn to manage on low incomes, and theoretical in that we may ultimately be able to improve on economists' theories of consumption. Let me turn next to discuss some work, also in the artificial intelligence tradition, which is closer to being basic research. It started as a study of the emergence of social complexity among pre-historic hunter-gatherers in south-west France about 20,000 years ago. Archaeologists believe that around this time there was a change from societies with a very simple organisation of rather small groups of close relatives to much larger bands with a clearly identifiable leader or `big man', the development of status differences and the evolution of ritual and decoration, including cave art. Two slightly different theories have been proposed to account for the emergence of social complexity, both of them suggesting that population concentration resulting from glaciation during the ice age was an important factor. Distinguishing between the theories on the basis of the very limited archaeological evidence is impossible and so Jim Doran at Essex University proposed to compare the theories by examining their implications through a simulation(Doran 1994, 1995).

To do so, he created a simulated landscape, a large virtual space over which his agents could move. Agents can harvest food resources which are distributed randomly in this space. The resources are inexhaustible. You could imagine them to be herds of reindeer or salmon rivers. On this landscape agents are randomly distributed. Each agent has three important parts (remember that this is not a description of physical objects, but of a virtual landscape and virtual agents, simulated by means of computer programs). Each agent has a working memory, in which facts are stored (or strictly speaking beliefs, since its knowledge may not be true). For example, the working memory could hold the location of the last food resource encountered. In addition the working memory stores `perceptions' recorded by simple simulated sensory organs. Secondly, the agent has a set of rules of the form `if this is the situation, then carry out this action'. For example, one rule might be, `if next to a food resource, eat it'. In order to determine whether the first, condition part of the rule is true, the agent looks in its own working memory. The second, action part of the rule may either instruct the agent to carry out some kind of action (e.g. move or eat) or may change the state of the working memory (e.g. `remember that there is a food supply here'). Finally, there is a part of the agent which repeatedly scans the rules to find a rule whose condition part is true and then carries out the action specified in that rule. All the agents share the same set of rules (but not the same memory) and interact within the same environment. They can send each other messages. As time goes on, they use up energy which has to be replenished by eating food and they come to learn about each other's existence and positions. If they fail to find and eat enough food, they starve to death. The agents are set up with rules to: consume food that is immediately adjacent; move towards food to which they believe they are the nearest agent; or move randomly a small distance.

With this system, one can perform various experiments to find factors which increase or decrease the overall likelihood that the population of agents will survive (that is, not die of starvation). Doran has carried out experiments in which the agents form themselves into groups which collectively carry out plans to obtain resources. He has also experimented with the consequences of mis-beliefs. In the latter experiments, agents can attack other agents and take over their food. But agents will not attack agents whom they believe are their friends, nor agents whom have a friend in common with them. In addition, agents are programmed such a way that they can make mistakes that lead them to believe in the existence of `pseudo-agents', agents which do not in fact exist. Because agents exchange beliefs with their friends, such mis-beliefs may spread leading to the formation of what Doran calls a `cult', a group of agents all of whom believe they have a pseudo-agent as their friend. The consequence is that cult members will not attack each other and this leads to an overall higher rate of survival. The advantage of a cult being focused around a pseudo-agent rather than a real agent is that pseudo-agents, being virtual, never die or move out of range, while real agents have both these limitations.

There are many interesting issues stemming from these experiments, but the one I want to comment on now is the way that they demonstrate how modelling can deal with functionalist hypotheses. The hypothesis that the existence of mis-belief in a society may be functional can lead, as I mentioned in my introduction, to a number of philosophical and methodological problems if it is considered simply in functionalist terms. However, recast into the framework of computational modelling, it is much more precise and in particular, testable. We can specify what we mean by `a society', we can define `functional for' in terms of the average survival time (or any other indicator we choose) and we can then, crucially, carry out experiments to see whether the hypothesis is true under controlled conditions. Of course, these experiments are performed not on a society itself, but on a model of a society, but in methodological terms there is nothing unusual or unsafe about this provided that we are aware of the limits of the conclusions that can be drawn.

An approach to social processes

Non-linear dynamics
Now that I have provided you with some examples of simulation based research, I would like to draw out some general principles about social phenomena that seem to be suggested by the work I have mentioned and other current work in the field. One of the themes of current social simulation research is that agents can be programmed with very simple rules (consider, for example, the simulation of social impact) but the behaviour of the system as a whole can turn out to be extremely complex. Scientists are coming to the same kind of conclusion about physical systems. You have probably heard about chaos theory. Chaos theory is essentially about how to understand complex and unpredictable systems such as the weather in terms of very simple principles. As Sir Robert May put it recently ``Previously if we saw complicated, irregular or fluctuating behaviour --- weather patterns, marginal rates of Treasury Bonds, colour patterns of animals or shapes of leaves --- we assumed the underlying causes were complicated. Now we realise that extraordinarily complex behaviour can be generated by the simplest of rules.'' One of the most important findings of chaos theory is that the behaviour of chaotic systems can be extremely sensitive to the starting conditions. This is the origin of the story about the chances of rain today depending on a butterfly beating its wings in China.

But it would not be right to push the link between chaos theory and sociology too far. It is not the case that sociologists, even those interested in simulation, are trying to apply chaos theory to sociological problems. It is most unlikely that such an attempt would succeed. Rather, there is a spirit in the air which suggests that we should look for simple explanations of apparent complexity; and in particular that this complexity may be the result of `non-linearities'.

As I mentioned at the beginning of this talk, conventional statistical methods are more or less all based on the assumption of a linear relationship between variables. That is, the effect on the dependent variable is proportional to a sum of a set of independent variables. But this is a very restrictive assumption. A new inter-disciplinary field called Complexity Theory (Waldrop 1992) is trying to develop rather general results about non-linear systems, those where the effect on a dependent variable is not a linear function of the independent variables. An example: consider pouring a steady stream of sand out of a pipe so that it mounts up into a pyramid. As you pour on more sand, there will be little landslides down the side of the pile. While the pyramidal shape of the pile and, in particular, the angle of the side is predictable, depending on the properties of the average sand grain, the timing, location and scale of the landslides are unpredictable because the slippage is non-linear: once a grain of sand starts sliding, it pulls others along with it and there is positive feedback leading to a mass of sand slipping. Much the same argument can be made about stock market crashes, another case of non-linear behaviour.

From the point of view of the scientist or mathematician, non-linear systems are a nightmare because most cannot be understood analytically. There is no set of equations that can be solved to relate the characteristics of the system. The only generally effective way of exploring non-linear behaviour is to simulate it by building a model and then running the simulation. Even when one can get some understanding of how non-linear systems work, they remain unpredictable. However much one understands stock markets or the properties of sand, it will still be impossible (in principle) to predict the timing of a crash or a landslide.

Explanation and prediction
This does have some lessons for sociological explanation. For instance, the philosophy of social science has often made too ready a connection between explanation and prediction. It tends to assume that the test of a theory is that it will predict successfully. This is not an assumption that is appropriate for non-linear theories. There is an interesting consequence for debates over free will and determinism. Sociologists hardly seem to worry about this issue any more. This is as it should be, because the classic debate assumed incorrectly that if we were ever in a position to understand human action completely, we would then be able to predict it, leaving no room for free will. Complexity theory shows that even if we were to have a complete understanding of the factors affecting individual action, that would still not be sufficient to predict behaviour. The message is even stronger if we make the plausible assumption that it is not only social action that is complex, but also individual cognition.

Emergence
As I have remarked, complexity can emerge from the social consequences of playing out very simple rules at the level of the individual. The notion of emergence is one of the most important ideas to come from this approach. Like many good ideas, it formalises what we already have experience of. Sometimes thousands of spectators at a concert or football match join together in synchronised clapping. The coordinated clapping appears without a conductor to beat time. It is an example of a self-organised system which emerges from individual action. Another familiar example is the traffic jam. A traffic jam is not just a collection of cars, but a self-organised object which emerges from and exists at a level of analysis higher than that of the cars themselves. Indeed, if you look at a traffic jam from above, you may find that although the cars are slowly moving forward, the jam moves backwards! Emergence occurs when interactions among objects at one level give rise to different types of objects at another level. More precisely, a phenomenon is emergent if it requires new categories to describe it that are not required to describe the behaviour of the underlying components (the cars or the people). For example, temperature is an emergent property of the motion of atoms. An individual atom has no temperature, but a collection of them does. And wasps' nests emerge from the individual actions of many worker wasps.

That the idea of emergence is not obvious is attested by the considerable confusion that early sociologists, starting with Durkheim, had about the relationship between individual characteristics and social phenomena. Durkheim in his less cautious moments alleged that social phenomena are external to individuals while methodological individualists argued that there is no such thing as society. Both sides of this debate were confused because they did not understand the idea of emergence.

We can see social institutions, then, as emergent from individual action, just as clusters emerged from the interacting influences of Latané's cells. There is however a difficulty with this view. It appears to leave human organisations and institutions as little different in principle from wasp's nests or even piles of sand. They can all be said to emerge from the actions of the individuals. The difference is that while we assume that, for instance, wasps have no ability to reason, they just go about their business and in doing so construct a nest, people do have the ability to recognise, reason about and react to human institutions, that is, to emergent features. Behaviour which takes into account such emergent features might be called `second order emergence'. The fact that humans engage in such behaviour might be one of the defining characteristics of human societies, distinguishing them from animal societies (Gilbert 1995). It is what makes sociology different from ethology. Not only can we as scientific observers distinguish patterns of collective action, but the agents themselves can also do so and therefore their actions can be affected by the existence of these patterns.

This can be illustrated by returning to the example of the simulation of budgeting decisions I described earlier. I mentioned that we expect that one of the influences on the pattern of budgeting decisions that people make is their adoption of a `lifestyle', that is, a collection of pre-digested consumption decisions. There are two ways in which this could happen. On the one hand, people might adopt a lifestyle without any recognition that they are so doing. In fact this is probably the way it works for most people most of the time. It is only when the sociologist or economist studies their consumption patterns that it becomes clear those patterns fit into a widely shared template. On the other hand, there are some people who quite consciously adopt lifestyles and others who discover that they have adopted a lifestyle. These people are quite likely to categorise themselves as `the sort of people who follow this lifestyle', to band together as a group (e.g. `punks', `students', `old-age pensioners') and to contribute explicitly to the evolution of the lifestyle.

A simulation of such a process would therefore have to model:

the emergence of patterns of consumption in the society as a result of the social imitation of individual agents' consumption decisions;
the perception by agents that these patterns exist;
the categorisation (`social construction') by agents of these patterns into some small number of `lifestyles';
the influence of agents' adoption of these lifestyles on their consumption decision making, leading to the evolution of adapted or new consumption patterns.
The simulation would thus have to model both the emergence of societal level properties from individual actions and the effect of societal level properties on individual actions. The latter in turn may affect the societal level properties and so on. One of the present-day challenges for simulation in the social sciences is to develop convincing examples of such models. It would be fair to say that at the moment we do not know how to do so.

Conclusion

I began by presenting you with four propositions which I said you might consider to be rather peculiar. They were: Simple patterns of repeated individual action can lead to extremely complex social institutions. It is impossible, in principle, to predict the outcomes of some social changes Even when there are powerful processes tending to convert a population to a consensus view, minorities may persist.

Members' misperception and misbelief can be functional for groups and societies. In the course of this talk, I hope to have convinced you that these propositions are worth pondering and may even be true. And if you agree with me about that, I should also have little difficulty in convincing you that the computer simulation of social processes is an exciting and productive way of carrying out fundamental research on human societies

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