Methodological Investigations in Agent-Based Modelling: With Applications for the Social Sciences

Front matter

Methodos Series 13

Eric Silverman

Methodological Investigations in Agent-Based Modelling

Foreword

Following the aims of the Methodos Series perfectly, this 13th volume on agent-based models provides a general view of the problems raised by this approach and shows how these problems may be solved.

These methods are derived from computer simulation studies used by mathematicians and physicists. They are now applied in many social disciplines such as artificial life (Alife), political sciences, evolutionary psychology, demography, and many others. Those who introduced them often took care not to consider each social science separately but to view them as a whole, incorporating a wide spectrum of social processes — demographic, economic, sociological, political, and so on.

Rather than modelling specific data, this approach models theoretical ideas and is based on computer simulation. Its aim is to understand how the behaviour of biological, social, or more complex systems arises from the characteristics of the individuals or agents composing the said system. As Billari and Prskawetz (2003, p. 42) said,

Different to the approach of experimental economics and other fields of behavioural science that aim to understand why specific rules are applied by humans, agent-based computational models pre-suppose rules of behaviour and verify whether these micro based rules can explain macroscopic regularities.

This is, therefore, a bottom-up approach, with population-level behaviour emerging from rules of behaviour of autonomous individuals. These rules need to be clearly discussed; unfortunately, this approach is now used without sufficient discussions in many social sciences. It eliminates the need for empirical data on personal or social characteristics to explain a phenomenon, as it is based on simple decision-making rules followed by individuals, which can explain some real-world phenomena. But how can we find these rules? As Burch (2003, p. 251) puts it,

A model explains some real-world phenomenon if a) the model is appropriate to the real-

world system [...] and b) if the model logically implies the phenomenon, in other words, if the phenomenon follows logically from the model as specified to fit a particular part of the real world.

Vii viii Foreword

Also, a theoretical model of this kind cannot be validated in the same way as an empirical model with the “covering law” approach, which hinders social research and leads to a pessimistic view of the explanatory power of the social sciences. In Franck’s words (Franck 2002, p. 289),

But, one has ceased to credit deduction with the power of explaining phenomena. Explaining phenomena means discovering principles which are implied by the phenomena. It does not mean discovering phenomena which are implied by the principles.

As the agent-based approach focuses on the mechanisms driving the actions of individuals or agents, it will simulate the evolution of such a population from simple rules of behaviour. It may thus use game theory, complex systems theory, emergence, evolutionary programming and — to introduce randomness — Monte Carlo methods. It may also use survey data, not to explain the phenomenon studied, but only to verify if the parameters used in the simulation lead to a behaviour similar to the one observed in the survey.

As we have already said, such an approach raises many problems which this volume will try to answer. We will present here these main problems, letting the reader see how Silverman has treated it.

The first problem is that these models “are intended to represent the import and impact of individual actions on the macro-level patterns observed in a complex system” (Courgeau et al. 2017, p. 38). This implies that a phenomenon emerging at the aggregate level can be entirely explained by individual behaviour. Holland (2012, p. 48), however, states that agent-based models include “little provision for agent conglomerates that provide building blocks and behaviour at a higher level of organisation.” For instance, a multilevel study on the effects of an individual characteristic (being a farmer) and the corresponding aggregate characteristic (the proportion of farmers living in an area) on the probability of internal migration in Norway shows that the effects are contradictory (Courgeau 2007): it seems hard to explain a macro-characteristic acting positively by a micro-characteristic acting negatively. In fact, micro-level rules are often hard to link to aggregate-level rules, and I believe that aggregate-level rules cannot be modelled with a purely micro approach, for they transcend the behaviours of the component agents.

The second problem is that this approach is basically bottom-up. However, it seems important to take into consideration simultaneously a top-down process from higher-level properties to lower-level entities. More specifically, we should speak of a micro-macro link (Conte et al. 2012, p. 336) that “is the loop process by which behaviour at the individual level generates higher-level structures (bottom-up process), which feedback to the lower level (top-down), sometimes reinforcing the producing behaviour either directly or indirectly”. The bottom-up approach of a standard agent-based model cannot take such a reciprocal micro-macro link into account, given that it only simulates one level of analysis.

The third problem concerns the validation of an agent-based model. Such an approach imitates human behaviour using some well-chosen mechanisms. It may be judged successful when it accurately reproduces the structure of this behaviour.

Foreword ix

Determining success, however, requires a method very different from the standard tests used to verify the validity of the effects of different characteristics in the other approaches. Such tests can be performed in the natural sciences but are more difficult in the social sciences. As Küppers and Lenhard observe (Günter et al. 2005, paragraph 1.3),

The reliability of the knowledge produced by computer simulation is taken for granted if

the physical model is correct. In the second case of social simulations in general there is

no theoretical model on which one could rely. The knowledge produced in this case seems to be valid if some characteristic of the social dynamics known from experience with the social world are reproduced by the simulation.

To determine if such an exploration has been successful, we need to consider different aspects. First, how do we test that there are no other models offering a better explanation of the observed phenomenon? Researchers often try out different kinds of models so they can choose the one most consistent with empirical data. But this hardly solves the problem, as there is an infinity of models that can predict the same empirical result as well or even better. Second, how do we test that the chosen model has a good fit with the observed data? Unfortunately, there is no clearly defined procedure for testing the fit of a simulation model, such as significance tests for the approaches described earlier. We can conclude that there are no clear verification and validation procedures for agent-based models in the social sciences.

While the agent-based approach appears to resemble event-history analysis, for it focuses on individual behaviour, it nevertheless aims to explain collective behaviour. At that point, the key question is: how do we generate macroscopic regularity using simple individual rules? Conte et al. (2012, p. 340) perfectly describe the difficulties encountered:

First, how to find out the simple local rules? How to avoid ad hoc and arbitrary explanations? As already observed, one criterion has often been used, i.e., choose the conditions that are sufficient to generate a given effect. However, this leads to a great deal of alternative options, all of which are to some extent arbitrary.

Without factoring in the influence of networks on individual behaviour, we can hardly obtain a macro behaviour merely by aggregating individual behaviours. To obtain more satisfactory models, we must introduce decision-making theories. Unfortunately, the choice of theory is influenced by the researcher’s discipline and can produce highly divergent results for the same phenomenon studied.

In order to go further, Chap. 9, co-authored by Jakub Bijak, Daniel Courgeau, Robert Franck and Eric Silverman, proposes for demography the enlargement of agent-based models to a model-based research. This will not be a new paradigm in the traditional sense, as with the cross-sectional, the cohort, the event-history and the multilevel approaches, but a new way to overcome the limitations of demographic knowledge. It is a research programme which adds a new avenue of empirical relevance to demographic research. The examples given in the following chapters, despite the simplicity of the models used, give us a glimpse of the importance of model-based demography.

x Foreword

I hope I have given to the reader of this volume a clear idea of its importance for social sciences.

Billari, F., & Prskawetz, A. (2003). Agent-based computational demography: Using simulation to improve our understanding of demographic behaviour. Heidelberg: Physica Verlag.

Burch, T. K. (2003). Data, models, theory and reality: The structure of demographic knowledge. In F. Billari & A. Prskawetz (Eds.), Agent-based computational demography: Using simulation to improve our understanding of demographic behaviour (pp. 19-40). Heidelberg: Physica Verlag.

Conte, R., Gilbert, N., Bonelli, G., Cioffi-Revilla, C., Deffuant, G., Kertesz, V., Loreto, V., Moat, S., Nadal, J.-p., Sanchez, A., Nowak, A., Flache, A., San Miguel, M., & Helbing, D. (2012). Manifesto of computational social science. European Physical Journal Special Topics, 214, 325-346.

Courgeau, D. (2007). Multilevel synthesis: From the group to the individual. Dordrecht: Springer.

Courgeau, D., Bijak, J., Franck, R., & Silverman, E. (2017). Model-based demography: Towards a research agenda. In A. Grow & J. Van Bavel (Ed.), Agent-based modelling and population studies (Springer series on demographic methods and population analysis, pp. 29-51). Berlin/Heidelberg: Springer.

Franck, R. (Ed.). (2002). The explanatory power of models: Bridging the gap between empirical and theoretical research in the social sciences (Methodos series 1). Boston/Dordrecht/London: Kluwer Academic.

Holland, J. H. (2012). Signals and boundaries. Cambridge: MIT Press.

Kiippers, G., & Lenhard, J. (2005). Validation of simulation: Patterns in the social and natural sciences. Journal of Artificial Societies and Social Simulation, 8(4), 3.

Acknowledgements

This volume covers more than 10 years of research, stretching back to the start of my PhD in 2003. Over this lengthy period, this work has been supported by a number of institutions and funders. Chapters | through 8 are substantially based on my PhD research, completed at the School of Computing at the University of Leeds from 2003 to 2007. Chapters 9 through 11 are based on a work completed at the University of Southampton between 2010 and 2015 during the Care Life Cycle Project, funded by Engineering and Physical Sciences Research Council grant EP/H021698/1. Teesside University supported my work on the manuscript between 2015 and 2017. The completion of the manuscript was also supported by the Complexity in Health Improvement programme at the MRC/CSO Social and Public Health Sciences Unit at the University of Glasgow, with QQR funding code MC_UU_12017/14.

Of course this work has also benefitted from the collaboration, vital input and feedback from a host of colleagues and friends. At Leeds, my thanks go out to Jason Noble for being such a good friend, close colleague and trusted confidant throughout my years in research; Seth Bullock for his supervision and collaboration during my PhD; David Hogg for taking on supervision duties and supporting me during a critical period in my PhD; John Bryden for being a close collaborator and dear friend and for introducing me to Babylon 5; and Roger Boyle and Peter Jimack for being so supportive throughout my PhD studies.

At Southampton, thanks once again go to Jason and Seth, for supporting me throughout my postdoc experience and for fostering a great community within the research group. Special mention must go to Jakub Bijak, close collaborator on key chapters of this volume, trusted friend and a spectacularly talented researcher. Without his support and encouragement, this volume would never have come into being. Part III of this volume came to life thanks to exciting collaborations with Daniel Courgeau, Robert Franck and Jakub, and I feel very privileged to have been part of those conversations. I was also fortunate to be able to discuss the future of model-based demography with Thomas Burch, whose work I hold in very high esteem.

xi xii Acknowledgements

At Teesside, I was lucky to share offices with Ian Wood, who was a great source of support and a great colleague, without whom my time there would have been much poorer. Thanks also to Mark Cavazza for his support during his time there and his dedication to the union. Thanks as well to colleagues Julie Porteous, Fred Charles and The Anh Han — I am glad we will continue working together in the coming years.

For all their encouragement and kindness, I am indebted to my parents, Lewis and Linda Silverman, who have never failed to be a continuous source of inspiration throughout my academic career. Takashi Ikegami has been an inspiration to me since we first met in Boston in 2004; his enthusiasm and belief in Alife and his willingness to break boundaries in research have been a pleasure to experience. A heartfelt thanks also go to my friend and former housemate David Mitchell, who defined my years in Leeds and made my time there a true joy.

Last but certainly not least, thank you to my wife, Takako, who has showed such endless patience with my strange working hours, bizarre sleeping schedule and rambling monologues on obscure topics. Thank you for sticking with me, even when my brain was wandering off somewhere else entirely.

PartI Agent-Based Models

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XV

Part II Modelling Social Systems Eric Silverman and John Bryden

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Contents xvii

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Part III Case Study: Simulation in Demography

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Acronyms

In general I have attempted to keep this volume free of excessive abbreviations, but the acronyms below will appear at times given their widespread usage in related fields of research.

ABCD Agent-Based Computational Demography. This term describes an approach to the discipline of demography which incorporates agent-based modelling.

ABM Agent-Based Model. These are computer simulations designed to examine the behaviour and interactions of autonomous agents.

ABSS Agent-Based Social Simulation. An approach to social simulation which explicitly focuses on the use of agent-based models.

xxiii

Part I Agent-Based Models

This first part of the text examines the theory and practice of computational modelling, much of it viewed through the lens of artificial life. Artificial life, or Alife for short, is a discipline that focuses on ‘the simulation and synthesis of living systems’, most frequently through the use of simulation. Using agent-based models, evolutionary algorithms, and other recent innovations in simulation and robotics, Alife researchers hope to unravel the mysteries of how life develops and evolves in the real world by studying digital manifestations of ‘life as it could be’.

As Alife has itself evolved over the years, researchers have sought closer connections to the real world and to real biology. This has brought about difficult questions concerning the integration of real data into simulated worlds, and the relationship between digital biology and physical biology. As early Alife has slowly given way to a greater desire for empirical relevance, it has become increasingly important to understand the potential role Alife and Alife-inspired approaches can play in understanding real biological systems.

Of course the difficulties inherent in modelling complex biological processes and populations are familiar to population biologists just as much as digital ones — perhaps even more so, given the short history of Alife. We will examine in detail some of the theoretical frameworks developed by population biologists in order to develop their models and position them as a valid form of enquiry, and investigate how we might use these frameworks as a way to understand and categorise computational modelling efforts in disciplines such as Alife. In so doing, we will lay the foundations for Part I, in which we will investigate the additional modelling complexities we encounter when we begin to model social systems.

Chapter 1 Introduction

As computer simulation has developed as a methodology, so its range of applications has grown across different fields. Beyond the use of mathematical models for physics and engineering, simulation is now used to investigate fields as varied and disparate as political science, psychology, evolutionary biology, and many other disciplines.

With simulation becoming such a common adjunct to conventional empirical research, debate regarding the methodological merits of computer simulation continues to develop. Some fields, artificial life being the primary example used in this text, have developed using computer simulation as a central driving force. In such a case, researchers have developed theoretical frameworks to delineate the function and purpose of computer simulation within their field of study.

However, the expansion of computer simulation into fields which use empirical study as a central methodology means that new frameworks for the appropriate use of simulation must develop. How might simulation enhance one’s use of conventional empirical data? Can simulations provide additions to empirically-collected data-sets, or must simulation data be treated entirely differently? How does theoretical bias influence the results of a simulation, and how can such biases be investigated and accounted for?

The central goal of this text is to investigate these increasingly important concerns within the context of simulation for the social sciences. Agent-based models in particular have become a popular method for testing sociological hypotheses that are otherwise difficult or impossible to analyse empirically, and as such a methodological examination of social simulations becomes critical as social scientists begin to use such models to influence social policy. Without a clear understanding of the relationship between social simulation and social sciences as a whole, the use of models to explain social phenomena becomes difficult to justify.

© The Author(s) 2018 3 E. Silverman, Methodological Investigations in Agent-Based Modelling, Methodos Series 13, https://doi.org/10.1007/978-3-319-72408-9_1

Bearing in mind this central theme, this text will utilise a modelling example which will be revisited regularly in Parts I and II. This example will serve as a means for illustrating the important concepts described in the various modelling frameworks under discussion, and for tying together these frameworks by showing the effect of each upon the construction and implementation of a simulation. This central example takes the form of a model of bird migration; this example seemed most appropriate as this sort of problem can be examined through various modelling means, from mathematical to agent-based computational models. The context and purpose of this hypothetical model will vary from example to example, but the central concern of developing an understanding of the behaviour of migratory birds will remain throughout.

Toward the latter half of Part II, we will use the classic example of Schelling’s residential segregation model (Schelling 1971) to discuss some particular methodological points in detail. Part III will delve deeply into specific examples of agent-based modelling work in the field of demography in order to illustrate how the modelling concepts discussed in Parts I and II can influence the practice of modelling in social science.

1.2 Artificial Life as Digital Biology

The field of artificial life provides a useful example of the development of theoretical frameworks to underwrite the use of simulation models in research. The Artificial Life conference bills itself as a gathering to discuss ‘the simulation and synthesis of living systems’; with such potentially grandiose claims about the importance of artificial life simulations, theoretical debate within the field has been both frequent and fierce.

In the early days of Alife, Langton and other progenitors of this novel research movement viewed simulation as a means to develop actual digital instantiations of living systems. Beyond being an adjunct to biology, Alife was viewed as digital biology, most famously described as the investigation of ‘life-as-it-could-be’ (Langton 1992). Ray boasted of his Tierra simulation’s explosion of varied digital organisms (Ray 1994), and theorists proposed this sort of digital biology as a means for divining the nature of living systems.

1.2.1 Artificial Life as Empirical Data-Point

Since these heady days Artificial life has sought more conventional forms of methodological justification, seeking to link simulation with more conventional means of data-gathering in biology. This has lead to varying forms of theoretical justification within Alife, ranging from further explorations of Langton’s early ideas

1.3 Social Simulation and Sociological Relevance 5

(Bedau 1998; Silverman and Bullock 2004) to the use of Alife simulation as a form of ‘opaque thought experiment’ (Di Paolo et al. 2000).

Within this text, these varying theoretical frameworks for Alife will be examined in turn, both within the context of biology and within Alife itself. Once Alife seeks direct links with conventional biology, theoretical justification becomes correspondingly more difficult, and thus the debate must branch out into more in-depth discussions of biological modelling methodology. An investigation of the use of modelling in population biology, beginning with the somewhat-controversial ideas of Levins (1966, 1968) provides a means for describing and categorising the most important methodological elements of biological models. Having developed an understanding of the complex relationship between biology and Alife, we can then proceed to a discussion of the future of modelling within the social sciences.

1.3 Social Simulation and Sociological Relevance

Social simulation has appeared in the limelight within social science quite recently, starting with Schelling’s well-known residential segregation model (Schelling 1978) and continuing into Axelrod’s explorations of cooperative behaviour (Axelrod 1984). The development of simple algorithms and rules that can describe elements of social behaviour has led to an increasing drive to produce simulations of social systems, in the hopes that such systems can provide insight into the complexity of human society.

The current state-of-the-art within social simulation relies upon the use of agent-based models similar to those popularised in Alife. Cederman’s influential book describing the use of such models in political science has helped to bolster an increasing community of modellers who hope that such individual-based simulations can reveal the emergence of higher-order complexity that we see around us in human society (Cederman 1997). Social science being a field where the empirical collection of data is already a significant difficulty, the prospect of using simulation to produce insights regarding the formation and evolution of human society is an enticing one for many.

1.3.1 Methodological Concerns in Social Simulation

Of course, with such possibilities comes great debate from within the social science community. Proponents offer varying justifications of the potential power of simulation in social science; Epstein echoes the Alife viewpoint by proposing that social simulation can provide “generative social science,’ a means to generate new empirical data-points (Epstein 1999). Similarly, Axelrod stresses the ability of social simulation to enhance conventional empirical studies (Axelrod and Tesfatsion 2006).

Others however are more cautious with their endorsement of social simulation. Kluver and Stoica stress the difficulty in creating models consistent with social theory (Kliiver et al. 2003), noting that social systems do not lend themselves to the same hierarchical deconstruction as some other complex systems. Others theorise that social simulation faces the danger of incorporating vast theoretical biases into its models, eliminating one of the potential strengths of social models: a means for developing more general social theory (Silverman and Bryden 2007).

Further examinations of these questions within this text will seek to link such ideas with the methodological frameworks developed within Alife modelling and biology. While both fields display obvious differences in both methodological and theoretical objectives, the philosophical difficulties facing agent-based modelling in these contexts are much the same. In both cases the link between empirical data-gathering and simulated data-generation is difficult to develop, and as a consequence the use of simulation can be difficult to justify without a suitable theoretical justification.

1.4 Case Study: Schelling’s Residential Segregation Model

Having developed a detailed comparison between the use of models in biology and social science, this text will use Schelling’s residential segregation model as a case study for examining the implications of the theoretical frameworks discussed and outlined in that comparison. Schelling’s model is famously simple, its initial version running on nothing more than a chequerboard, but its conclusions had a far-reaching impact on social theory at the time (Schelling 1978). Schelling’s ideas regarding the ‘micromotives’ of individuals within a society, and the resulting effects upon that larger society, sparked extensive discussion of the role of individuals in collective social behaviour.

1.4.1 Implications of Schelling’s Model

With this in mind, our investigation will explore the reasons for Schelling’s great success with such a simple model, and its ramifications for future modelling endeavours. How did such an abstract formulation of the residential segregation phenomenon become so powerful? What theoretical importance did Schelling attribute to his model’s construction, and how did that influence his interpretation of the results? Finally, how does his model illuminate both the strengths and weaknesses of social simulation used for the purpose of developing social theory? All of these questions bear upon our final examination of the most appropriate theoretical framework for social simulation as a whole.

1.6 General Summary 7

1.5 Social Simulation in Application: The Case of Demography

Having developed some theoretical approaches to social simulation, we will need to move on to discuss the establishment of these methods as a trusted and functional element of the social scientist’s toolbox. We will take on this problem by investigating the field of demography, the study of human population change. Demography is a fundamentally data-focused discipline, relying on at times vast amounts of complicated survey data to understand and predict the future development of populations (Silverman et al. 2011). We will investigate the core assumptions underlying demographic research, discuss and analyse the methodological shifts that have occurred in the field over the last 350 years (Courgeau et al. 2017), and develop a framework for a model-based demography that incorporates simulation as a central conceit.