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The Role of Agent-Based Modelling in Demographic Explanation Edmund Chattoe Department of Sociology University of Oxford 3, George Street Mews, Oxford, Oxon, OX1 2AA, UK
[email protected] http://www.sociology.ox.ac.uk/chattoe.html 26th July 2001 (Version 1) Abstract This chapter outlines five difficulties with modelling demographic behaviour using Agent-Based Modelling (ABM), with particular reference to innovation diffusion in the use of contraceptive practices. The first difficulty is the thin character of information and activities relevant to contraception within the wider framework of social action. The second difficulty is ensuring the correct relationship between ABM and existing theories, either based on aggregate statistical patterns or strong homogeneity assumptions about individuals. The third difficulty is ensuring an adequate representation of the contextual nature of social action, both in time and space. The fourth difficulty is to represent the complexity of decision processes adequately, so they can take account of the transmission of different kinds of information: norms, costs and benefits, practices and so on. The final difficulty is the possibility of collecting relevant data for building and testing ABMs. The chapter also draws attention to the connections between these difficulties and suggests solutions where these exist. In some cases, like the modelling of thin processes and cognitive complexity, considering social behaviour from an ABM perspective reveals important challenges for social science research that are obscured by other approaches to modelling. 1. Introduction This paper considers five potential difficulties with ABM applied to demographic systems. Raising these potential difficulties is not intended to downplay the value of the approach. Instead, they are more in the nature of challenges and the issues they raise have important general implications for our understanding of social behaviour. These difficulties have been largely obscured by traditional approaches to modelling and can be seen much more clearly within the AB perspective. Even if it can take us no further, which is unlikely, the AB approach therefore has value in recasting existing research in a thought provoking way. I will use the diffusion of innovative contraceptive practices as a running example throughout the paper. This is a clearly demographic problem, with links to the core population process of transition from high to low fertility in industrialising societies. In
2 addition, this is an example of a problem of manageable1 scale, which has been extensively discussed in the literature from a number of perspectives. Making use of a concrete example shows how the various difficulties with applying the ABM approach to demographic behaviour are connected. The five difficulties are introduced in an order that allows new concepts to be developed at a manageable pace. The order of discussion does not reflect their relative “difficulty” or “importance”. 2. The Problem of Thin Social Processes It is very common in the social sciences to model only a particular aspect of social behaviour. For example, we might use a statistical approach to investigate the effect of divorce on children’s subsequent attitudes to having children themselves. For such an approach, it is assumed that a lot of social action (like hobbies or school subject choice) can be completely disregarded. In ABM, we must be careful about the extent to which assumptions of this kind are still possible. Taking the example of contraceptive practices, only a very small proportion of social interaction is causally relevant to innovation decisions.2 However, a much larger proportion of social interactions are indirectly relevant in the sense that they still need to be modelled if we are to understand the actual temporal and spatial patterns of diffusion and behaviour change. For example, we need to know how (and with whom) friendships are maintained even though most of the conversations that take place as a result of these friendships will have nothing to do with contraception. The reason for this difference is that traditional statistical approaches present a “static” description of cause and effect (children of divorced families are perhaps less enthusiastic about having children at a particular point in time) rather than “dynamic” description of a social mechanism. (For example, how do these children maintain their negative opinions in the face of wider societal attitudes?) Since the whole point of ABM is to study dynamic processes of interaction between agents, we need to consider how to build models when the particular domain of social action we are studying is thin relative to social behaviour as a whole. Obviously, we cannot and should not model everything but, at the same time, representing friendship as a pair of fixed rates of interaction (for friends and non friends) is likely to abstract from features which are highly significant for diffusion. Two obvious examples (which will be discussed further as contextual social actions) are the dynamic nature of friendship - women with children moving into a new circle of friendship with other mothers - and correlated or many-tomany interactions. (The effect of a lively discussion among five women is likely to be very different from the effect of a number of one-to-one discussions.) Unlike statistical approaches, ABM therefore requires us to distinguish between causal factors in social action and what might be called “structuring” factors. These are the patterns of social action that define such overall societal properties as “viscosity” (how 1
Despite the role of government policy, marketing, promotional agencies and so on, it still makes sense to treat this as an individual (or perhaps couple) decision, albeit one taking place in a rich social context. 2 Even those conversations that do take place may have significant redundancy, although this may be used by actors in “weighting” different information. Furthermore, some information will be mistrusted, filtered out as irrelevant and so on. This makes the proportion of information “effective” in influencing behaviour even smaller.
3 long things take to happen), “sociability” (how many people are typically involved) and so on.3 The fact that someone only rarely meets their friends may have little impact on the contraceptive practice they choose but it will certainly have an influence on how long it takes before that choice is made. One possible solution to this problem is simply to treat causally “irrelevant” behaviours as a background or inert “substrate”. If we set the probability of talking about contraception in each period at a very low level, then this takes account of the infrequency of meetings, redundancy and so on.4 There are two reasons why this approach is likely to be unsatisfactory. Firstly, it is precisely the importance of such phenomena as coincidences of need and chance meetings across clique boundaries (“lumpiness” in the patterns of interaction in space and time) that are likely to have a crucial impact on adoption dynamics (Abrahamson and Rosenkopf 1997). Smoothing these processes out into constant probabilities will generate very different dynamics for the system. Secondly, although certain behaviours are not causally relevant to contraceptive innovations, this does not mean that they can be treated as separable “exogenous” factors. For example, decision processes are heavily path dependent because the transfer of information (normative judgements, practices, evaluations of costs and benefits) take place continuously. Decisions may proceed very fast or very slowly depending on the order in which information happens to be acquired. Knowledge acquired in one context (or for one purpose) may turn out to be relevant in another. In practice, other such parallel dynamic processes will also be occurring which bear on the issue of contraception. For example, a person will undoubtedly be collecting “scraps” of information about contraception all the time, but these scraps may not be put in any sort of order until contraception becomes relevant to the individual, perhaps after they have reached their target family size. At that stage, the individual may become more attentive to contraceptive information, place themselves in a position to hear more, perhaps by starting to associate with older married women and have a greater incentive to initiate conversations which fill specific knowledge gaps. Such a shift in behaviour may in turn have a “knock on” effect, perhaps leading to gossip and speculation in the wider community. The parallel (and independent) evolution of both cognitive process and structuring factors (development of friendships, sexual relationships, family structure) mean that it is very unlikely that we can effectively separate out causal factors from all others as neatly as we do in statistical approaches. The first step in solving this problem is simply to recognise it. The next step is to start developing “generic” models of social structure from which networks and other structuring factors can naturally and concisely emerge. To pre-empt the discussion on contextual action (in section 4) slightly, most simple ABM of “checkerboard” societies neglect social structure. Agents interact only because they are homing in on the same 3
Another way of putting this is to say that social science often treats time (and space) as non-social dimensions, equating them simplistically with the clock and the ruler. In fact, subjective time and space are socially determined by interactions: time planning, activities and meetings and it is these subjective dimensions that are relevant to things like the speed of innovation diffusion. 4 Of course, it will be very difficult to decide at what level to set it! This problem of calibrating theoretical constructs with real data is discussed further in Chattoe (forthcoming).
4 food pellet and happen to come into each other’s field of vision. They do not meet each day on their way to the fields, form friendships by helping build huts together or agree to visit the village elders to settle a dispute. It is likely that these models of genuinely social environments will involve such building blocks as joint activities, patterned time spent at particular locations and so on (Chattoe 2000a). Less surprisingly, these socially structured environments will also take account of the differing attributes of different agents, such as whether they like and trust each other, are kin and so on. The hope is that an appropriate social structure for ABM will support the study of different kinds of thin behaviour without the necessity for “modelling everything”. In particular, a sensible framework should permit sensible abstraction. For example, recreation is likely to be a time for important conversations and we are typically freer to choose our company while at leisure. This means that the precise nature of the recreation is less important than the differences between it and activities where we cannot choose our company. (Many societies have strict rules about circumstances under which genders, castes, kin and sometimes even age groups can associate. These social cleavages are examples of structuring factors with a significant bearing on the diffusion of contraceptive innovations.) The issues of path dependence in cognitive process and contextual social action will be discussed in more detail in their respective sections. The important conclusion of this section is that a simple notion of causal relevance (and irrelevance), applicable to statistical models, cannot be transplanted carelessly to ABM. As a result, thin social behaviours must be modelled with an adequate representation of relevant structuring factors from the wider society. 3. The Problem of Relating Existing Theories to ABM The discussion of thin social behaviours leads on naturally to another potential difficulty. This is that, in a sense, many of our existing social theories are not Agent-Based enough to form a basis for satisfactory ABM. At one extreme, aggregate statistical regularities tell us almost nothing reliable about the behaviour of individual actors. At the other, mathematical theories presuming fundamentally homogenous agents are profoundly unrealistic and therefore uninteresting even as first approximations. These issues can be clarified by distinguishing three senses of “model” very commonly conflated in social science (Chattoe 2000b). The first is the cognitive model that each individual has of their world, which influences their actions. The second is the kind of model that a social scientist has of the way that individuals or social systems work, for example that people are self-interested utility maximisers operating in perfect markets or that social institutions can be explained by class struggle between proletariat and capitalists. The third is an ABM that explicitly represents the interactions of individual cognitive models and actions in an environment. (Thus an ABM can either be used to study the implications of a simplified model thought up by a social scientist or, in principle at least, to mirror the behaviour of a real population of individuals.) From the ABM perspective, we can now see just how strong the assumptions of the typical social science model really are. Rational choice theories, for example, assume not only that everybody in the world
5 makes decisions in the same way (in all circumstances) but that the theorist knows what that way is a priori, that is without having to consult any real individuals. Even in models that allow learning, it is frequently assumed that all agents have a common (and unchanging) model of the world (shared with the social scientist) and what they learn is the correct parameter values of the model. This assumption, not supported by any empirical evidence, is also extremely strong and thus writes out many important questions about the diffusion of innovations. Casual introspection suggests that the endemic disagreement and confusion in the social world is unlikely to be based on common models! ABM thus gives us a different perspective on existing theories by separating out technical/pragmatic reasons for making strong simplifying assumptions from empirical ones. In principle, if we wish, we can now give every agent in an ABM a completely different model of the world. The shift in perspective also suggests, as was the case with structuring and causal variables in section 2, that our existing intuitions and methods should not be transferred wholesale from statistical or homogenous individualistic approaches to ABM. It is true that ABM can be used to re-implement theories that have already been proposed but this may be a waste of its capabilities in two senses. Firstly, reimplementing existing theories does not give us the opportunity to look at social behaviour from a new perspective and thus ask new questions or develop new kinds of theories. (An example is provided by the discussion of decision-making in section 5.) Secondly, the results of such re-implementation are likely to be unsurprising “normal science” – minor relaxation of the standard assumptions while disregarding much far more dramatic assumptions which are not discussed. In a sense, the strength of ABM is that the social world is itself Agent-Based, something that existing models commonly simplify out by assumption for technical reasons of tractability. As such, the task of ABM may be to unlearn existing theories where they are either excessively restrictive, empirically unrealistic or both. 4. Representing Social Context As has already been mentioned, many existing ABM seem to take place in “checkerboard” environments lacking much social structure - although they usually have a physical structure of inputs such as food (Epstein and Axtell 1996). Where social structure is represented, it almost invariably involves one-to-one “glancing” interactions like trade or unproblematic fixed relations like kinship. One important reason for the ubiquity of thin social behaviour already discussed is the importance of spatial and temporal constraints on social action.5 We might call this phenomenon social context. Conversations about contraception must be held “in the right company” and “at the appropriate time”.6 The coincidental presence of children (or mistrusted adults) at the village well or around the grinding stone may delay a conversation that would otherwise have taken place. This notion of context can be associated with a plausible definition of 5
Others are increasing specialisation, differentiation and novelty which will not be discussed here. Other relevant social actions like trials are also heavily constrained by notions of appropriateness and privacy. 6
6 social structures (or at least an addition to the current attenuated notion). Individuals either want (or are expected to be) at certain places and with certain people at a certain time. This general description covers everything from family meal times to hunting parties and “nights out with the girls”. These expectations determine the speed with which thin social behaviours can evolve. They provide a large part of the kind of structuring already discussed. This kind of social structure means that different information will be transmitted through different networks at differing speed. It also underpins the evolution of social networks. People who meet often (and in common contexts) are more likely to become friends. Conversely, friends are more likely to take steps to meet and to introduce their friends to each other, giving rise to cliques. Context is therefore a phenomenon likely to introduce considerable non-linearity and clustering into processes of information transmission. These will in turn have significant effects on the diffusion process. Representing spatial and temporal structure is thus necessary to “underpin” processes of information transmission and decision since the conclusions from this “thick” (and multiply constrained) environment are likely to be very different from those in which each person has a fixed chance of meeting every other in every period. The dynamic nature of friendship provides one example of this kind of contextual effect. Women with children, particularly young children, will find themselves “automatically” synchronised (at least to some extent) with others in the same situation, not necessarily through choice or cultural expectations (although these will play a part), but through coincidence of necessary activities.7 They are similarly likely to find themselves distanced, through patterns of activity, from young single men who might stand to benefit from changed attitudes to contraception. Another contextual effect is the difference that many-to-many versus one-to-one communication is likely to have on the transmission of information. In an individual context, for example, new information may be transmitted with caution (or only to close friends) for fear of censure. In a meeting, the existence of common knowledge may mean both that a lot of information can be transmitted in a relatively short time and that a sense of “acceptable consensus” emerges, making individuals more confident both in the information they carry away and perhaps in their willingness to pass it on. (It is recognised that coming to feel like part of a group and recognising a shared situation is one way of building individual confidence.) In a sense, thin social behaviours and context can now be seen as opposite sides of the same coin. In simulated “checkerboard” societies with a very small set of activities, it is always a good time to eat or trade. Humans in these environments are actually still rather like ants in that their actions, while not reactive, are mainly orientated to physical objects and subsistence rather than towards social structures and meanings. In a society with genuine simulated sociality, collective action, differentiated roles, meaningful places (like “home”), expectations of social practice and so on mean that certain activities and interactions can only be carried out at appropriate times and places. This is what makes some behaviours thin and, at the same time, what structures them.
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There are also sets of activities they are less likely to engage with young children. This too will have a synchronising effect.
7 5. Representing Cognitive Complexity I have already discussed the tendency of existing theories to make very strong assumptions about the homogeneity of agent models which may make for relatively uninteresting ABM. Even if full rational choice is not assumed, learning parameters of a common model can typically be relied upon to produce systems which will converge to equilibrium even if there is little sign of such stability in society itself. The cognitive complexity problem arises for two reasons. Firstly, once we recognise the extreme nature of assuming that populations have common models, this opens up a very broad set of issues about what dynamic decision making actually does involve in terms of information processing and transmission. Secondly, thin behaviour and context both have implications for the complexity of decision processes. Context means that certain actions and kinds of information transmission may or may not be carried out conditionally in different places or at different times. Thinness means that agents (like social scientists) have to be able to handle large amounts of information that doesn’t necessarily bear on what they are currently doing or thinking about.8 Both of the factors necessarily involve ABMs in more sophisticated representations of cognitive structure than are currently typical. Starting with a concrete example, we can consider a number of systematically different kinds of information that agents can transmit about a particular contraceptive practice: • • • • •
That it exists at all That it is considered morally acceptable or unacceptable to an individual, to particular groups (like men) or to the community at large. How it is carried out. What one or more costs and benefits of the practice are. How a contraceptive practice should be evaluated.
Models based on preference have difficulties dealing with genuine ignorance, but it is clear that knowing something exists is a different and prior process to weighing its advantages. (This is particularly true in the transition from traditional behaviour to having a choice at all. It is a much bigger step from taking fertility as an “act of God” to something that can be controlled technically than it is from one contraceptive practice to another.) Philosophers argue conclusively that moral judgements cannot be reduced to statements of fact and as such, they must be treated separately in innovation diffusion. Different again are physical skills (inserting a diaphragm effectively) and material requirements (secure storage when not in use). These bear on the ex post costs and benefits of a particular practice but ex ante information, based on the experiences of others, is also likely to influence decision.9 The last category is the most novel one from the perspective of ABM. Once we relax the assumption of common models, we may also be interested in the transmission of models themselves. For example, should 8
To a certain extent, this problem is solved for us by our extraordinarily powerful associative memories. The magnitude of differences between ex ante and ex post costs and benefits may also bear on the level of satisfaction which adopters report to others. 9
8 contraception be evaluated within a moral and technical10 framework - as a Catholic might - or within a cost-benefit framework - as an economist might? Within each of these frameworks, what kinds of information (and how much of it) are considered necessary for effective decision? What should be done with the information once it has been acquired? For some decisions the appropriate decision framework may have been socialised years before, but for novel social practices, part of the diffusion process may be the extent to which different methods of choice become acceptable. (This can be seen as another example of a structuring factor. It may only be once choice based on costs and benefits has become acceptable enough in a particular society that individuals are prepared to countenance contraceptive choice on this basis. The gradual encroachment of “means end” rationality into more and more aspects of social life is a recognised feature of modernisation.) This sketch of the kinds of information that might be transmitted during innovation diffusion is a provisional one and can be criticised.11 Nonetheless, the basic point remains. Once we recognise systematically different kinds of information, we must also recognise the need for ABM models that allow for greater levels of cognitive complexity to handle the kind of information that is in fact transmitted in real societies. How, in practice, do actors synthesise all this information to make a decision? This problem can be ignored if there are common models, because the only relevant action is parameter updating. In societies with more complex information transmission, there is a much wider class of decision mechanisms within which we are now obliged to identify the empirically plausible subset. For each new piece of data received by the agent, we can ask: • •
•
Is this data perceived (and then stored) as relevant to a particular problem within the current framework of decision? Does it affect the nature of other data already stored in the mind or not? (Depending on the representation, a fact may cause the deletion of its negation or cause a connected fact to be modified. A free sample not only allows costs and benefits to be identified but also provides instant proof of existence.) Does it provoke any cognitive processing relevant to a subsequent decision?
For example, one decision rule might be to deal only with cost and benefit information and evaluate only when ten facts of this kind had been received - a kind of search model. Another might be to collect facts of all kinds, but only synthesise them into a decision when the prevailing moral evaluation had become sufficiently positive - which might never happen of course. The latter decision rule also draws attention to the need to model large and well-organised memories for agents.12 10
By this I mean that Catholic doctrine on contraception permits certain practices - like the “rhythm method” - on the grounds that they do not intervene in “natural” fertility - while rejecting those that do. 11 Additional possibilities clearly exist, though further consideration would be needed to decide if they constitute separate classes. As well as physical techniques, there are also social ones - “what to tell your husband to soothe his pride”. Other possible kinds of information are caveats - “you can’t use this technique if…” and domains of applicability - “don’t use this technique when…” 12 It may be that our impressive recall and pattern recognition skills are far more important for our ability to make good decisions than any evaluation of costs and benefits.
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In the limited space available, it would not be appropriate to propose a general theory of human decision. The purpose is instead to show how the ABM approach can open up our understanding of decision and is capable of implementing the new kinds of theories we might develop as a result. There is a strong rhetorical tendency, particularly with economic models, to justify them on an ambiguous mixture of pragmatic and empirical grounds. An important role of ABM is to remove the pragmatic justification for overly restrictive assumptions leaving the weakness of the empirical grounds revealed where appropriate. There may be justifications for assuming that everybody has the same model of the world but ABM renders this unnecessary from a technical point of view and it then becomes clear that it is not empirically very likely either. In conclusion, just as thin social behaviour and context can be seen as opposite sides of the same coin, so can rich social interaction and cognitive complexity. If we postulate very simple models of decision then the majority of information transmission can be regarded as mere noise or not even considered. If we take communication seriously, we have to ask how agents deal with all this information they receive. (What is the role of gossip in normative regulation for example?)13 6. Collecting Appropriate Data A final difficulty in ABM is its relationship with data. Not enough thought is given in many MAS designs to what data will be needed to calibrate them and how (perhaps even whether) this can be collected.14 This problem is particularly acute in implementing theories like rational choice where categories like “preference” are not measured empirically but inferred from behaviour. Since ABM require the specification of explicit cognitive models, we need some way of accessing those models if our ABM is to be empirically grounded. I have argued elsewhere (Chattoe forthcoming) that accessibility of data (and the strengths and weaknesses of different methods of collecting it) might be used as a design principle for ABM. Rather than starting with a theory and translating it into an ABM, it might be better to start with the data that is available, and what might be collected in principle, and see what kind of ABM it suggests. This approach draws attention to a number of issues. Firstly, a substantial amount of the attribute based data and stylised fact that has already been produced cannot easily be exploited in calibrating ABM. The discussion of causal and structuring factors has already illustrated how the underlying assumptions of the correlative and process based approaches to social behaviour are very different. Secondly, many kinds of data and theories necessary for the ABM approach 13
In fact, this equivalence is a strict one. There is no point in trying to produce a definitive list of “kinds” of information ex ante because the cognitive models for the ABM will determine what kinds of information are available to be transmitted in that simulated world. Needless to say, not all this information will be transmitted. In particular, agents with different cognitive models may be unable to use certain kinds of data within their decision frameworks, as with rational choice and moral evaluations. 14 There is debate over whether validation is a realistic exercise for social simulation models, but calibration can hardly be avoided.
10 have not been developed, because they were not suggested by the existing approaches. Given the common models assumption, not much thought was given to sequential organisation and processing of multiple kinds of data. As a result, not only are there few theories of this kind of decision process, but there is not much useful data on which to base such theories. Thirdly, moving ABM from “checkerboards” to real domains will significantly increase the data requirements and scale of the model building exercise. At present the sets of cognitive models, objects in the world and possible actions are small enough that a single modeller can cover all the possible outcomes. Different disciplines and different data collection methods will have to be integrated to study individual cognitive models, environmental evolution, the dynamics of social interactions and so on. In fact, this is the direction in which many larger research projects are moving anyway, but it is still rather rare for the final product to be an integrated ABM rather than a set of overlapping studies. In a way, the relationship between data and ABM can be seen as an outgrowth of two aspects of modelling that have already been discussed. We have already seen how the ABM approach casts light on the restrictive assumptions of existing theories and suggests new ones. In turn these theories suggest the need for different kinds of data and appropriate data collection techniques. Just as economics seldom justifies the common model assumption, it seldom provides convincing arguments for its rejection of qualitative data. Interviews are one way of eliciting information about how people actually make decisions (Gladwin 1989) and of answering some of the questions proposed about information transmission and processing in section 5. Despite their faults, interviews are almost the only technique that attempts to elicit cognitive models directly rather than inferring them.15 As before, ABM removes the “pragmatic” justification for neglecting qualitative method - that their findings cannot be incorporated into traditional models16 - while at the same time highlighting the empirical weakness of this strategy. If we want to find out how people decide things (rather than making assumptions from our theories), we need a method that accesses that data directly. 7. Conclusion This paper has considered a number of potential difficulties with the application of ABM to demographic behaviour. Some, like the ability to collect relevant data and the relationship between ABM and existing theories, are only in the nature of caveats or issues to be borne in mind at the design stage. The bottom line in these cases is to be cautious in “importing” preconceptions into the application of a novel technique with dramatic implications for our ways of thinking about social behaviour. Other difficulties, like methods of modelling thin social behaviour and the role of cognitive complexity in decision making show how the ABM approach can open up new questions with wider relevance to our understanding of social behaviour. Dynamic decision, complex information transmission and structuring factors are not an artefact of the ABM approach, 15
Experimentation is the other exception but in practice many social science experiments are carried out in a positivist framework using inference from behaviour rather than actual reports. 16 Perhaps this should be seen as a weakness of the models rather than an opportunity for rejecting additional data?
11 but phenomena which can be observed in society but were not captured (or in some cases even noticed) by existing theories. It is also interesting to see how these novel issues are related to one another. Social structure generates thin behaviours because social actions are situated in time and space. In “checkerboard” worlds with no social structure, behaviour is not thin because it is not situated. Outbreaks of fighting are well explained by conflicts over food because one follows directly on the other according to the way the environment and the agents are set up. There are no festering grudges or, more social still, family vendettas. (If such phenomena existed in the simulation, predicting fights would become considerably harder. If you have a grudge, an important reason for a fight is catching the person you resent alone and out of reach of help. This is another example of a contextual effect.) By contrast, contraceptive innovation requires us to understand considerably more about how agents orient themselves to social structure, both the way they represent it cognitively and the way it patterns actions and interactions. Social structure determines such things as who meets, how often, where and when (that is to say under what circumstances), and what they can appropriately talk about. The challenge for demography, as well as other distinctively social sciences is the move away from “checkerboard” models by developing theories of social structure which are adequate to support the understanding of particular behaviours without becoming impossibly all encompassing. References Abrahamson, Eric and Rosenkopf, Lori (1997) ‘Social Network Effects on the Extent of Innovation Diffusion: A Computer Simulation’, Organization Science, 8(3), May, pp. 289-309. Chattoe, Edmund (1999) ‘Unanimous Indifference and Diversity in Social Systems: Simulating Mechanisms for Maintenance and Change’, IMAGES Working Paper UOS99-02, November, . Chattoe, Edmund (2000a) ‘Good Times and Old Clothes: The Importance of Time Planning and Time Use in Consumption’, paper presented at the BSA Annual Conference “Making Time/Marking Time”, University of York, 17-20 April, . Chattoe, Edmund (2000b) ‘Why Is Building Multi-Agent Models of Social Systems So Difficult? A Case Study of Innovation Diffusion’, paper presented at the XXIV International Conference of Agricultural Economists (IAAE), Mini-Symposium on “Integrating Approaches for Natural Resource Management and Policy Analysis: Bioeconomic Models, Multi-Agent Systems and Cellular Automata”, Berlin, 13-19 August, . Chattoe, Edmund (forthcoming) ‘Building Empirically Plausible Multi-Agent Systems: A Case Study of Innovation Diffusion’, in Dautenhahn, Kerstin, Bond, Alan, Canamero, Dolores and Edmonds, Bruce (eds.) Socially Intelligent Agents: Creating Relationships with Computers and Robots (Dordrecht: Kluwer). Epstein, Joshua M. and Axtell, Robert (1996) Growing Artificial Societies: Social Science from the Bottom Up (Washington, DC: Brookings Institution Press and Cambridge, MA: The M. I. T. Press).
12 Gladwin, Christina H. (1989) Ethnographic Decision Tree Modelling, Sage University Paper Series on Qualitative Research Methods Volume 19 (London: Sage Publications).
