ABM models for the COVID-19 pandemic

In an earlier post I mentioned that agent-based models provide a substantially different way of approaching the problem of pandemic modeling. ABM models are generative simulations of processes that work incrementally through the behavior of discrete agents; so modeling an epidemic using this approach is a natural application.

In an important recent research effort Gianluca Manzo and Arnout van de Rijt have undertaken to provide an empirically calibrated ABM model of the pandemic in France that pays attention to the properties of the social networks that are found in France. They note that traditional approaches to the modeling of epidemic diseases often work on the basis of average population statistics. (The draft paper is posted on ArXiv; link; they have updated the manuscript since posting). They note, however, that diseases travel through social networks, and individuals within a society differ substantially in terms of the number of contacts they have in a typical day or week. This implies intuitively that the transmission of a disease through a population should be expected to be influenced by the social networks found within that population and the variations that exist across individuals in terms of the number of social contacts that they have in a given time period. Manzo and van de Rijt believe that this feature of disease-spread through a community is crucial to consider when attempting to model the progression of the disease. But more importantly, they believe that consideration of contact variation across a population suggests public health strategies that might be successful in reducing the spread of a disease at lower social and public cost.

Manzo offers a general framework for this approach in “Complex Social Networks are Missing in the Dominant COVID-19 Epidemic Models,” published last month in Sociologica (link). Here is the abstract for this article:

In the COVID-19 crisis, compartmental models have been largely used to predict the macroscopic dynamics of infections and deaths and to assess different non-pharmaceutical interventions aimed to contain the microscopic dynamics of person-to-person contagions. Evidence shows that the predictions of these models are affected by high levels of uncertainty. However, the link between predictions and interventions is rarely questioned and a critical scrutiny of the dependency of interventions on model assumptions is missing in public debate. In this article, I have examined the building blocks of compartmental epidemic models so influential in the current crisis. A close look suggests that these models can only lead to one type of intervention, i.e., interventions that indifferently concern large subsets of the population or even the overall population. This is because they look at virus diffusion without modelling the topology of social interactions. Therefore, they cannot assess any targeted interventions that could surgically isolate specific individuals and/or cutting particular person-to-person transmission paths. If complex social networks are seriously considered, more sophisticated interventions can be explored that apply to specific categories or sets of individuals with expected collective benefits. In the last section of the article, I sketch a research agenda to promote a new generation of network-driven epidemic models. (31)

Manzo’s central concern about what he calls compartmental models (SIR models) is that “the variants of SIR models used in the current crisis context address virus diffusion without modelling the topology of social interactions realistically” (33).

 Manzo offers an interesting illustration of why a generic SIR model has trouble reproducing the dynamics of an epidemic of infectious disease by comparing this situation to the problem of traffic congestion:

It is as if we pretended realistically to model car flows at a country level, and potentially associated traffic jams, without also modelling the networks of streets, routes, and freeways. Could this type of models go beyond recommendations advising everyone not to use the car or allowing only specific fractions of the population to take the route at specific times and days? I suspect they could not. One may also anticipate that many drivers would be highly dissatisfied with such generic and undifferentiated instructions. SIR models currently in use put each of us in a similar situation. The lack of route infrastructure within my fictive traffic model corresponds to the absence of the structure of social interactions with dominant SIR models. (42)

The key innovation in the models constructed by Manzo and van de Rijt is the use of detailed data on contact patterns in France. They make highly pertinent use of a study of close-range contacts that was done in France in 2012 and published in 2015 (Béraud et al link). This study allows for estimation of the frequency of contacts possessed by French adults and children and the extensive variation that exists across individuals. Here is a graph illustrating the dispersion that exists in number of contacts for individuals in the study:

This graph demonstrates the very wide variance that exists among individuals when it comes to “number of contacts”; and this variation in turn is highly relevant to the spread of an infectious disease.

Manzo and van de Rijt make use of the data provided in this COMES-F study to empirically calibrate their agent-based model of the diffusion of the disease, and to estimate the effects of several different strategies designed to slow down the spread of the disease following relaxation of extreme social distancing measures.

The most important takeaway from this article is the strategy that it suggests for managing the reopening of social interaction after the peak of the epidemic. Key to transmission is frequency of close contact, and these models show that a small number of individuals have disproportionate effect on the spread of an infectious disease because of the high number of contacts they have. Manzo and van de Rijt ask the hypothetical question: are there strategies for management of an epidemic that could be designed by selecting a relatively small number of individuals for immunization? (Immunization might take the form of an effective but scarce vaccine, or it might take the form of testing, isolation, and intensive contact tracing.) But how would it be possible to identify the “high contact” individuals? M&R consider two strategies and then represent these strategies within their base model of the epidemic. Both strategies show dramatic improvement in the number of infected individuals over time. The baseline strategy “NO-TARGET” is one in which a certain number of individuals are chosen at random for immunization, and then the process of infection plays out. The “CONTACT-TARGET” strategy is designed to select the same number of individuals for immunization, but using a process that makes it more likely that the selected individuals will have higher-than-average contacts. The way this is done is to select a random group of individuals from the population and then ask those individuals to nominate one of their contacts for immunization. It is demonstrable that this procedure will arrive at a group of individuals for immunization who have higher-than-average numbers of contacts. The third strategy, HUB-TARGET, involves selecting the same number of individuals for treatment from occupations that have high levels of contacts.

The simulation is run multiple times for each of the three treatment strategies, using four different “budgets” that determine the number of individuals to be treated on each scenario. The results are presented here, and they are dramatic. Both contact-sensitive strategies of treatment result in substantial reduction in the total number of individuals infect over the course of 50, 100, and 150 days. And this  in turn translates into substantial reduction of the number of ICU beds required on each strategy.

Here is how Manzo and van de Rijt summarize their findings:

As countries exit the Covid-19 lockdown many have limited capacity to prevent flare-ups of the coronavirus. With medical, technological, and financial resources to prevent infection of only a fraction of its population, which individuals should countries target for testing and tracking? Together, our results suggest that targeting individuals characterized by high frequencies of short-range contacts dramatically improves the effectiveness of interventions. An additional known advantage of targeting hubs with medical testing specifically is that they serve as an early-warning device that can detect impending or unfolding outbreaks (Christakis & Fowler 2010; Kitsak et al. 2010).

This conclusion is reached by moving away from the standard compartmental models that rely on random mixing assumptions toward a network-based modeling framework that can accommodate person-to-person differences in infection risks stemming from differential connectedness. The framework allows us to model rather than average out the high variability of close-contact frequencies across individuals observed in contact survey data. Simulation results show that consideration of realistic close-contact distributions with high skew strongly impacts the expected impact of targeted versus general interventions, in favor of the former.

If these simulation results are indeed descriptive of the corresponding dynamics of spread of this disease through a population of socially connected people, then the research seems to provide an important hint about how public health authorities can effectively manage disease spread in a post-COVID without recourse to the complete shut-down of economic and social life that was necessary in the first half of 2020 in many parts of the world.

*.    *.    *

Here is a very interesting set of simulations by Grant Sanderson of the spread of infectious disease on YouTube (link). The video is presented with truly fantastic graphics allowing sophisticated visualization of the dynamics of the disease under different population assumptions. Sanderson doesn’t explain the nature of the simulation, but it appears to be an agent-based model with parameters representing probability of infection through proximity. It is very interesting to look at this simulation through the eyes of the Manzo-van de Rijt critique: this model ignores exactly the factor that Manzo and van de Rijt take to be crucial — differences across agents in number of contacts and the networks and hubs through which agents interact. This is reflected in the fact that every agent is moving randomly across space and every agent has the same average probability of passing on infection to those he/she encounters.

ABM fundamentalism


I’ve just had the singular opportunity of participating in the habilitation examination of Gianluca Manzo at the Sorbonne, based on his excellent manuscript on the relevance of agent-based models for justifying causal claims in the social sciences. Manzo is currently a research fellow in sociology at CNRS in Paris (Centre National de la Recherche Scientifique), and is a prolific contributor to analytical sociology and computational social science. The habilitation essay is an excellent piece of work and I trust it will be published as an influential monograph. Manzo has the distinction of being expert both on the philosophical and theoretical debates that are underway about social causation and an active researcher in the field of ABM simulations. Pierre Demeulenaere served as a generous and sympathetic mentor. The committee consisted of Anouk Barberousse, Ivan Ermakoff, Andreas Flache, Olivier Godechot, and myself, and reviewer comments and observations were of the highest quality and rigor. It was a highly stimulating session.

One element of our conversation was especially enlightening to me. I have written a number of times in Understanding Society and elsewhere about the utility of ABM models, and one line of thought I have developed is a critique of what I have labeled “ABM fundamentalism” — the view that ABM models are the best possible technique for constructing social explanations for every possible subject in the social sciences (link). This view is expressed in Joshua Epstein’s slogan, “If you didn’t grow it, you didn’t explain it.” I maintain that ABM is a useful technique, but only one of many methods appropriate to the problem of constructing explanations of interesting sociological outcomes (link). So I advocate for theoretical and methodological pluralism when it comes to the ABM program.

I asked Gianluca whether he would agree that ABM fundamentalism is incorrect, and was surprised to find that he defends the universal applicability of ABM as a tool to implement any sociological theory. According to him, it is a perfectly general and universal modeling platform that can in principle be applied to any sociological problem. He also made it clear that he does not maintain that the use of ABM methods is optimal for every sociological problem of explanation. His defense of the universal applicability of ABM simulation techniques therefore does not imply that Manzo privileges these techniques as best for every sociological problem. But as a formal matter, he holds that ABM technology possesses the resources necessary to represent any fully specified social theory within a simulation.

The subsequent conversation succeeded in clarifying the underlying source of disagreement for me. What I realized in the discussion that ensued is that I was conflating two things in my label of ABM fundamentalism: the simulation technology and the substantive doctrine of generative social science. Epstein is a generativist, in the sense that he believes that social outcomes need in principle to be generated from a representation of facts about the individuals who make it up (Generative Social Science: Studies in Agent-Based Computational Modeling). Epstein is also an advocate of ABM techniques because they represent a particularly direct way of implementing a generativist explanation. But what Gianluca showed me is that ABM is not formally committed to the generativist dogma, and that an ABM simulation can perhaps incorporate factors at any social level. The insight that I gained, then, is that I should separate the substantive view of generativism from the formal mathematical tools of ABM simulations techniques.

I am still unclear how this would work — that is, how an ABM simulation might be created that did an adequate job of representing features at a wide range of levels — actors, organizations, states, structures, and ideologies. For example, how could an ABM simulation be designed that could capture a complex sociological analysis such as Tilly’s treatment of the Vendée, with peasants, protests, and merchants, the church, winegrowers’ associations, and the strategies of the state? Tilly’s historical narrative seems inherently multi-stranded and irreducible to a simulation. Similar points could be made about Michael Mann’s comparative historical account of fascisms or Theda Skocpol’s analysis of social revolutions.

So there is still an open question for me in this topic. But I think I am persuaded that the fundamentalism to which I object is the substantive premise of generativism, not the formal computational methods of ABM simulations themselves. And if Gianluca is correct in saying that ABM is a universal simulation platform (as a Turing machine is a universal computational device) then the objection is misplaced.

So this habilitation examination in Paris had exactly the effect for me that we would hope for in an academic interaction — it led me to look at an important issue in a somewhat different way. Thank you, Gianluca!

Computational social science

Is it possible to elucidate complex social outcomes using computational tools? Can we overcome some of the issues for social explanation posed by the fact of heterogeneous actors and changing social environments by making use of increasingly powerful computational tools for modeling the social world? Ken Kollman, John Miller, and Scott Page make the affirmative case to this question in their 2003 volume, Computational Models in Political Economy. The book focuses on computational approaches to political economy and social choice. Their introduction provides an excellent overview of the methodological and philosophical issues that arise in computational social science.

The subject of this book, political economy, naturally lends itself to a computational methodology. Much of political economy concerns institutions that aggregate the behavior of multiple actors, such as voters, politicians, organizations, consumers, and firms. Even when the interactions within and rules of a political or economic institution tion are relatively simple, the aggregate patterns that emerge can be difficult to predict and understand, particularly when there is no equilibrium. It is even more difficult to understand overlapping and interdependent institutions…. Computational methods hold the promise of enabling scholars to integrate aspects of both political and economic institutions without compromising fundamental features of either. (kl 27)

The most interesting of the approaches that they describe is the method of agent-based models (linklink, link). They summarize the approach in these terms:

The models typically have four characteristics, or methodological primitives: agents are diverse, agents interact with each other in a decentralized manner, agents are boundedly rational and adaptive, and the resulting patterns of outcomes comes often do not settle into equilibria…. The purpose of using computer programs in this second role is to study the aggregate patterns that emerge from the “bottom up.” (kl 51)

Here is how the editors summarize the strengths of computational approaches to social science.

First, computational models are flexible in their ability to encode a wide range of behaviors and institutions. Any set of assumptions about agent behavior or institutional constraints that can be encoded can be analyzed. 

Second, as stated, computational models are rigorous in that conclusions follow from computer code that forces researchers to be explicit about assumptions. 

Third, while most mathematical models include assumptions so that an equilibrium exists, a system of interacting political actors need not settle into an equilibrium point. It can also cycle, or it can traverse an unpredictable path of outcomes. 

The great strength of computational models is their ability to uncover dynamic patterns. (kl 116)

And they offer a set of criteria of adequacy for ABM models. The model should explain the results; the researcher should check robustness; the model should build upon the past; the researcher should justify the use of the computer; and the researcher should question assumptions (kl 131).

To summarize, models should be evaluated based on their ability to give insight and understanding into old and new phenomena in the simplest way possible. Good, simple models, such as the Prisoner’s Dilemma or Nash bargaining, with their ability to frame and shed light on important questions, outlast any particular tool or technique. (kl 139)

A good illustration of a computational approach to problems of political economy is the editors’ own contribution to the volume, “Political institutions and sorting in a Tiebout model”. A Tiebout configuration is a construct within public choice theory where citizens are permitted to choose among jurisdictions providing different bundles of goods.

In a Tiebout model, local jurisdictions compete for citizens by offering bundles of public goods. Citizens then sort themselves among jurisdictions according to their preferences. Charles M. Tiebout’s (1956) original hypothesis challenged Paul Samuelson’s (1954) conjecture that public goods could not be allocated efficiently. The Tiebout hypothesis has since been extended to include additional propositions. (kl 2012)

Using an agent-based model they compare different sets of political institutions at the jurisdiction level through which policy choices are made; and they find that there are unexpected outcomes at the population level that derive from differences in the institutions embodied at the jurisdiction level.

Our model departs from previous approaches in several important respects. First, with a few exceptions, our primary interest in comparing paring the performance of political institutions has been largely neglected in the Tiebout literature. A typical Tiebout model takes the political institution, usually majority rule, as constant. Here we vary institutions and measure performance, an approach more consistent with the literature on mechanism design. Second, aside from an example used to demonstrate the annealing phenomenon, we do not explicitly compare equilibria. (kl 2210)

And they find significant differences in collective behavior in different institutional settings.

ABM methodology is well suited to the kind of research problem the authors have posed here. The computational method permits intuitive illustration of the ways that individual preferences in specific settings aggregate to distinctive collective behaviors at the group level. But the approach is not so suitable to the analysis of social behavior that involves a higher degree of hierarchical coordination of individual behavior — for example, in an army, a religious institution, or a business firm. Furthermore, the advantage of abstractness in ABM formulations is also a disadvantage, in that it leads researchers to ignore some of the complexity and nuance of local circumstances of action that lead to significant differences in outcome.


There is a seductive appeal to the idea of a “generative social science”. Joshua Epstein is one of the main proponents of the idea, most especially in his book, Generative Social Science: Studies in Agent-Based Computational Modeling. The central tool of generative social science is the construction of an agent-based model (link). The ABM is said to demonstrate the way in which an observable social outcome of pattern is generated by the properties and activities of the component parts that make it up — the actors. The appeal comes from the notion that it is possible to show how complicated or complex outcomes are generated by the properties of the components that make them up. Fix the properties of the components, and you can derive the properties of the composites. Here is Epstein’s capsule summary of the approach:

The agent-based computational model — or artificial society — is a new scientific instrument. It can powerfully advance a distinctive approach to social science, one for which the term “generative” seems appropriate. I will discuss this term more fully below, but in a strong form, the central idea is this: To the generativist, explaining the emergence of macroscopic societal regularities, such as norms or price equilibria, requires that one answer the following question: 

The Generativist’s Question 

*How could the decentralized local interactions of heterogeneous autonomous agents generate the given regularity?  

The agent-based computational model is well-suited to the study of this question, since the following features are characteristic: [heterogeneity, autonomy, explicit space, local interactions, bounded rationality]


And a few pages later:

Agent-based models provide computational demonstrations that a given microspecification is in fact sufficient to generate a macrostructure of interest. . . . To the generativist — concerned with formation dynamics — it does not suffice to establish that, if deposited in some macroconfiguration, the system will stay there. Rather, the generativist wants an account of the configuration’s attainment by a decentralized system of heterogeneous autonomous agents. Thus, the motto of generative social science, if you will, is: If you didn’t grow it, you didn’t explain its emergence. (8)

Here is how Epstein describes the logic of one of the most extensive examples of generative social science, the attempt to understand the disappearance of Anasazi population in the American Southwest nearly 800 years ago.

The logic of the exercise has been, first, to digitize the true history — we can now watch it unfold on a digitized map of Longhouse Valley. This data set (what really happened) is the target — the explanandum. The aim is to develop, in collaboration with anthropologists, microspecifications — ethnographically plausible rules of agent behavior — that will generate the true history. The computational challenge, in other words, is to place artificial Anasazi where the true ones were in 80-0 AD and see if — under the postulated rules — the simulated evolution matches the true one. Is the microspecification empirically adequate, to use van Fraassen’s phrase? (13)

Here is a short video summarizing the ABM developed under these assumptions:

The artificial Anasazi experiment is an interesting one, and one to which the constraints of an agent-based model are particularly well suited. The model follows residence location decision-making based on ground-map environmental information.

But this does not imply that the generativist interpretation is equally applicable as a general approach to explaining important social phenomena.

Note first how restrictive the assumption is of “decentralized local interactions” as a foundation to the model. A large proportion of social activity is neither decentralized nor purely local: the search for muons in an accelerator lab, the advance of an armored division into contested territory, the audit of a large corporation, preparations for a strike by the UAW, the coordination of voices in a large choir, and so on, indefinitely. In all these examples and many more, a crucial part of the collective behavior of the actors is the coordination that occurs through some centralized process — a command structure, a division of labor, a supervisory system. And by its design, ABMs appear to be incapable of representing these kinds of non-local coordination.

Second, all these simulation models proceed from highly stylized and abstract modeling assumptions. And the outcomes they describe capture at best some suggestive patterns that might be said to be partially descriptive of the outcomes we are interested in. Abstraction is inevitable in any scientific work, of course; but once recognizing that fact, we must abandon the idea that the model demonstrates the “generation” of the empirical phenomenon. Neither premises nor conclusions are fully descriptive of concrete reality; both are approximations and abstractions. And it would be fundamentally implausible to maintain that the modeling assumptions capture all the factors that are causally relevant to the situation. Instead, they represent a particular stylized hypothesis about a few of the causes of the situation in question.  Further, we have good reason to believe that introducing more details at the ground level will sometimes lead to significant alteration of the system-level properties that are generated.

So the idea that an agent-based model of civil unrest could demonstrate that (or how) civil unrest is generated by the states of discontent and fear experienced by various actors is fundamentally ill-conceived. If the unrest is generated by anything, it is generated by the full set of causal and dynamic properties of the set of actors — not the abstract stylized list of properties. And other posts have made the point that civil unrest or rebellion is rarely purely local in its origin; rather, there are important coordinating non-local structures (organizations) that influence mobilization and spread of rebellious collective action. Further, the fact that the ABM “generates” some macro characteristics that may seem empirically similar to the observed phenomenon is suggestive, but far from a demonstration that the model characteristics suffice to determine some aspect of the macro phenomenon. Finally, the assumption of decentralized and local decision-making is unfounded for civil unrest, given the important role that collective actors and organizations play in the success or failure of social mobilizations around grievances (link).
The point here is not that the generativist approach is invalid as a way of exploring one particular set of social dynamics (the logic of decentralized local decision-makers with assigned behavioral rules). On the contrary, this approach does indeed provide valuable insights into some social processes. The error is one of over-generalization — imagining that this approach will suffice to serve as a basis for analysis of all social phenomena. In a way the critique here is exactly parallel to that which I posed to analytical sociology in an earlier post. In both cases the problem is one of asserting priority for one specific approach to social explanation over a number of other equally important but non-equivalent approaches.

Patrick Grim et al provide an interesting approach to the epistemics of models and simulations in “How simulations fail” (link). Grim and his colleagues emphasize the heuristic and exploratory role that simulations generally play in probing the dynamics of various kinds of social phenomena.


Modifying an epidemiological model for party recruitment


Here I’ll follow up on the idea of using an epidemiological model to capture the effects of political mobilization through organization. One of the sample models provided by the NetLogo library is EpiDEM Basic (link). This model simulates an infectious disease moving through a population through person-to-person contact.

We can adapt this model to a political context by understanding “infection” as “recruitment to the party”. I’ve modified the model to allow for re-infection after an agent has been cured [disaffiliated from the party]. This corresponds to exit and re-entrance into a party or political organization. This leads the model to reach various levels of equilibrium within the population depending on the settings chosen for infectiousness, cure rates, and cure time frames. The video above represents a sample run of my extension of EpiDEM Basic. The graph represents the percentage of the population that have been recruited to the party at each iteration. The infection rate [mobilization success] surges to nearly 100% in the early ticks of the model, but then settles down to a rough equilibrium for the duration of the run. Orange figures are party members, while blue are not members (either because they have never affiliated or they have dis-affiliated).

An important shortcoming in this approach is that it is forced to represent every agent as a “cadre” for the organization as soon as he/she is recruited; whereas on the ground it is generally a much smaller set of professional cadres who serve as the vectors of proselytization for the party. This accounts for the early surge in membership to almost 100%, which then moderates to the 30% level. The initial surge derives from the exponential spread of infection prior to the period in which cures begin to occur. I’ve referenced this flaw in the realism of the model by calling this a “grassroots” party. On the current settings of recruitment and defection the population stabilizes at about 30% membership in the party. Ideally the model could be further modified to incorporate “infection” by only a specified set of cadres rather than all members.

It seems possible to merge this party-mobilization model with the Epstein model of rebellion (also provided in the NetLogo library), allowing us taking party membership into account as a factor in activation. In other words, we could attempt to model two processes simultaneously: the “infection” of new party members through a contagion model, and the differential activation of agents according to whether they are exposed to a party member or not. This is complicated, though, and there is a simpler way of proceeding: try to represent the workings of the model with an exogenously given number of party cadres. This can be implemented very simply into the Epstein Rebellion model.

As a first step, I introduce party membership as a fixed percentage of population and assume that the threshold for activation is substantially lower for members than non-members. The causal assumption is this: the presence of a party member in a neighborhood increases the threshold for action. The logic of this modification is this: for a given agent, if there is a party member in the neighborhood, then the threshold for action is low; whereas if there is no party member in the neighborhood, the threshold for action is high.

Now run the model with two sets of assumptions: no party members and 1% party members.

Scenario 1: occurrence of mobilization with no party members

Scenario 2: occurrence of mobilization with 1% party members

The two panels represent these two scenarios. As the two panels illustrate, the behavior of the population of agents is substantially different in the two cases. In both scenarios there are sudden peaks of activism (measured on the “Rebellion Index” panel). But those peaks are both higher and more frequent in the presents of a small number of activists. So we might say the model succeeds in illustrating the difference that organization makes in the occurrence of mobilization. A few party activists substantially increase the likelihood of rebellion.

Or does it? Probably not.

The modifications introduced here are very simple, and they succeed in addressing a primary concern I raised in an earlier post about the original version of Epstein’s model: the fact that it does not take the presence of organization into account as a causal factor in civil unrest. But the realism of the model is still low. For example, the Rebellion model is specifically intended to capture the relationship between cops and agents. But it is not interactive in the other way in which rebellious behavior spreads: the process in which rising density of activation in a neighborhood increases the probability of activation for each individual. In other words, neither the original implementation nor this simple extension allows introduction of the spatial dimensions of mobilization and civil unrest (aside from the original random location of party activists).

But most fundamentally, the extension I’ve presented here is still a highly abstract representation of the workings of organizations in the context of civil unrest and mobilization. I’ve boiled the workings of a political organization down to a single effect: if a neighborhood is exposed to a party cadre, the individuals in that neighborhood are substantially more likely to become active. And the model behaves accordingly; there is more activism when there are more cadres. But we can’t really interpret this as the derivation of a social effect from an independent set of assumptions; rather, the implementation of the idea of organization simply assumes the model the fact that cadres amplify activation by others in the neighborhood. In other words, the model is built to embody the effect I was expecting to see.

This exercise makes a couple of points. First, agent-based models have the virtue of being very explicit about the logic of action that is represented. So it is possible for anyone to review the code and to modify the assumptions, or to introduce factors that perhaps should be considered. (NetLogo is particularly welcoming to the non-expert in this regard, since it is easy to go back and forth between the code and the graphical representation of the model.)

But second, no one should imagine that agent-based models reproduce reality. Any ABM is implemented by (1) codifying one or more assumptions about the factors that influence a given collective phenomenon, and (2) codifying the rules of action for the kinds of agents that are to be represented. Both kinds of assumption require extreme abstraction from the reality of a social setting, and therefore models can almost invariably be challenged for a lack of realism. It is hard for me to see how an agent-based model might be thought to be explanatory of a complex social reality such as the Cairo uprising.

Microfoundations and causal powers

Image: Three Mile Island control room



There isn’t a lot of cross-over between the microfoundations literature (Peter Hedstrom, Dissecting the Social: On the Principles of Analytical Sociology) and the causal-powers literature (Greco and Groff, Powers and Capacities in Philosophy: The New Aristotelianism). People who advocate the importance of microfoundations in the social sciences are usually looking for something like the individual-level mechanisms through which a higher-level pattern or entity comes about and persists. So the most natural relation is between microfoundations and mechanisms. And it is rare to find a powers theorist discussing the issue of microfoundations at all.

But it seems that this lack of intersection is the result of a clash of philosophical styles rather than an inherent logical or ontological fissure. The microfoundations group (e.g. Hedstrom, Elster, or myself in earlier versions) tends to be somewhat inclined towards an enlightened reductionism — showing how higher level properties are produced by the workings of a lower level of phenomena. The causal powers group (e.g. Groff, Mumford and Anjum) are stoutly anti-reductionist; they seem to want to maintain that the powers of a thing are an irreducible and essential feature of the thing, not derivative from anything more fundamental.

But this opposition between the two research communities doesn’t really seem compelling; it seems to derive from an abstract ontological preference rather than analytical arguments. So let’s consider the question directly: how do the theories of microfoundations and causal powers relate to each other? Is it legitimate for microfoundations stories to invoke causal powers? And do causal-powers claims themselves require (or admit of) microfoundations?

The latter question seems to be the easier one. Whenever we attribute a causal power to a kind of stuff (conductivity to metal, violent volatility to a crowd, propensity to accidents to an organization), it is logical and appropriate to ask what it is about the substrate of the stuff that creates the power in question. What is it about the microstructure of metals that leads them to conduct electricity? What is it about crowds that leads them to be vulnerable to surges of violence? And what is it about certain kinds of organizations that leads them to be conducive to accidents like Three Mile Island or Bhopal? And when we answer these questions by detailing the microstructure of the stuff (metal, crowd, organization) and demonstrate how it is that this structure creates the durable power in question, then we have provided a microfoundation for the power. So powers admit of microfoundations. This response highlights the fact that the quest for microfoundations is really just an illustration of a pervasive explanatory strategy: investigate and measure the micro structure of the thing in question in order to discover why and how it behaves as it does.

Here is how I tried to sort out these relations in an earlier post on current thinking concerning the metaphysics of causality:

On this standpoint, powers are attributions we make to things when we don’t know quite enough about their composition to work out the physics (or sociology) of the underlying mechanisms. They do attach to the entity or structure in question, surely enough; but they do so in virtue of the physical or sociological composition of the entity, not because of some inherent metaphysical property.

We might try to reconcile these two perspectives with a few simple ideas:

  • Entities and structures at a range of levels of being have causal powers: active capacities to influence other entities and structures.
  • Whenever we identify a causal power of a thing, it is always open to us to ask how this power is embodied; what it is about the inner constitution of the entity that gives it this power.
  • When we succeed in arriving at a good scientific answer to this question, we will have shown that the power in question is not irreducible; it is rather the consequence of a set of mechanisms set in play by the constitution of the entity.

So the discovery of a given causal power of a thing is not a metaphysical fundamental; it is rather an empirical scientific discovery that invites analysis into its underlying composition.

The harder question is whether there is any compelling reason for microfoundations theorists to think they need to refer to causal powers in their accounts. And this is where the powers theorists have a strong position: it is hard to make sense of the idea of a mechanism without referring to a real (perhaps reducible) causal power. This argument was made in an earlier post (link). Here is the key observation in that post:

My thesis of the mutual compatibility of powers and mechanisms goes along these lines. If we press down on a putative mechanisms explanation, we are led eventually to postulating a set of causal powers that provide the motive force of the postulated mechanisms. But equally, if we press down on the claim that a certain kind of entity has a specified causal power or disposition, we are led to hypotheses about what mechanisms are set in play be its constituents so as to bring about this disposition.

Begin with a causal mechanism story:
C => {x happens bringing about y, bringing about z, bringing about u, which is E} => E

How is it that the sub-links of this chain of mechanism pieces happen to work to bring about their consequent? We seem to have two choices: We can look to discover a further underlying mechanism; or we can postulate that the sub-link entity or structure has the power to bring about its consequent. So if we push downward within the terms of a mechanism explanation, one way to close the story is by postulating a causal power at some level.

So we might say that the relation among these three ideas goes something like this: A demand for microfoundations is a demand for the causal mechanisms at work within the substrate of the stuff in question. Mechanisms require provisional reference to causal powers; so microfoundations in turn require reference to causal powers. And finally, causal powers at a given level both demand and admit of provision of microfoundations to explain how they in turn work. So microfoundations theorists can’t really dispense with the topic of causal powers, and powers theorists shouldn’t dispense with microfoundations either. The diagram at the top illustrates this logic. It is turtles, all the way down.

Modeling organizational recruitment

One defect of the ABMs considered in the prior post about the emergence of civil conflict is that they do not incorporate the workings of organizations into the dynamics of mobilization. And yet scholars like Tilly (Dynamics of Contention) and Bianco (Peasants without the Party: Grassroots Movements in Twentieth Century China) make it clear that organizations are critical to the development and scope of mobilization of a populace. So a model of civil conflict needs to be able to incorporate the effects of organizations in the mobilization and activation of large groups of individual agents. Here I will explore what we might want from an ABM that incorporates organizations.

Ideally I would like to see a model that incorporates:

  • NxN individual actors (50×50 in the diagram above, or 2,500 agents)
  • M organizations with different characteristics competing for membership among the actors
  • A calculation of “uprising behavior” based on the net activation of a threshold percentage of actors in a circumscribed region
How might organizations be introduced into an agent-based model of social contention? I can imagine two quite different approaches. (A) We might look at organizations as higher-level agents within the process. As each organization works its way through the population it gains or loses members; and this affects individual behavior and the geographical distribution of activated agents. This would be an attempt to directly model the mechanism of mobilization through organizational mobilization. (B) Another possible and simpler approach is to represent organizations as environmental factors, analogous to disease vectors, which percolate through the population of first-order agents and alter their behavior. Let’s consider both. 
(A) Organizations as meso-level agents. The first approach requires that we provide rules of behavior for both kinds of agents, and recognize that the two processes (organizational recruitment and individual action) may influence each other iteratively. Organizations compete for members and strive to create collective action in support of their agendas. Membership in an organization influences the individual actor by increasing activation. And increasing membership influences the functioning of the organization.

Individual actors gain organizational properties when they are recruited to one of the organizations. Suppose that individual actors have these properties (largely drawn from the Epstein model):

  • grievance level
  • risk aversiveness
  • income level
  • salience of ethnicity for identity 
  • location
  • Organization-driven properties of activation
  • derived: level of activation (probability of involvement in response to an appeal from the organization)
If we want to model organizations as agents, then we need to specify their properties and action rules as well. We might begin by specifying that organizations have properties that affect their actions and their ability to recruit:
  • content of political agenda / call to action
  • perceived effectiveness
  • real effectiveness
  • number of cadres devoted to mobilization effort
For a simulation of inter-group conflict, we would like to include two ethnic groups, and one or more organizations competing within each group.

Mobilization occurs at the individual level: actors receive invitations to membership sequentially, and they respond according to the net effect of their current characteristics. Once an actor has affiliated, he/she remains susceptible to appeals from other organizations, but the susceptibility is reduced.

Membership in an organization affects an individual’s level of engagement in a set of grievance issues and his/her propensity for action. Individuals may express their organizational status at a range of levels of activism:

  • highly engaged 
  • moderately engaged
  • disengaged 

The model calculates each agent’s behavior as a function of grievance, risk, appeal, location, and organizational influence.

This approach suggests development of two stages of simulation: first a simulation of the competition of two organizations within a group; and second, a simulation of the individual-level results of calls to action by multiple organizations involving a specified distribution of organizational affiliations.

(B) Organizations as infection vectors. A simpler approach is to represent the various organizations as contagious diseases that have differential infection rates depending on agent properties, and differential effects on behavior depending on which “infection” is present in a given agent. Presumably the likelihood of infection is influenced by whether the individual has already been recruited by another organization; this needs to be represented in the rules governing infection. It also implies that there is a fair amount of path dependence in the simulation: the organization that starts first has an advantage over competitors.

It seems it would be possible to incorporate a disease mechanism into the Epstein model to give a role for organizations in the occurrence of civil unrest.

Now imagine running the model forward with two types of processes occurring simultaneously. The organizations recruit members iteratively and the activation status of each individual is calculated on each tick of the model. At each tick every individual has a membership status with respect to the organizations (“infections”), and each has an activation level (low, medium, high). When a concentration of, say, 40% of agents are activated to a high level in a region of a given size, this constitutes an episode of uprising / ethnic violence / civil unrest.

Two fundamental questions arise about this hypothetical simulation. First, is the simulation assumption that “organizational mobilization is like an infectious disease” a reasonable one? Or does organizational mobilization have different structural and population dynamics than the spread of a disease? For example, diseases percolate through direct contact; perhaps organizational mobilization has more global properties of diffusion. And second, does the resulting simulation give rise to patterns that have realistic application to real processes of social contention? Do we learn something new about social contention and mobilization by incorporating the additional factor of “organization” in this way that the Epstein model by itself does not reveal?

(It should be noted that organizations are a peculiar kind of agent. They have properties that are characteristic of “complex adaptive systems”: they are supra-individual, they are influenced by the actors they touch, and they influence the behavior of the actors they touch. So the behavioral properties of an organization perhaps should not be specified exogenously.)

(NetLogo is a sophisticated modeling package that permits researchers to develop small and medium-sized agent-based models, and it provides a number of relevant examples of simulations that are of interest to social scientists (link). Particularly interesting for the current purposes are a simulation of the Epstein model of rebellion discussed earlier (link) and an implementation of an AIDS contagion model that could be considered as a platform for modeling the spread of an organization or a set of ideas as well (link).  Here is the link for NetLogo: Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.)

ABM approaches to social conflict

Source: Pfautz and Salwen (link)

An earlier post addressed the question of the dynamics through which a stable community consisting of multiple groups may begin to polarize and fission into antagonisms and conflict. I speculated there that the tools of agent-based modeling might be of use here. What I had in mind was something like this. Suppose we have an urban population spread across space in a distribution that reflects a degree of differentiation of residence by income, religion, and race. Suppose religion is more segregated than either income or race across the region. And suppose we have some background theoretical beliefs about social networks, civic associations, communication processes and other factors influencing a disposition to mobilize. Perhaps ABM methods could allow us to probe different scenarios to see what effects these different settings produce for polarization and conflict.

There is a fair amount of effort at modeling this kind of social phenomena within the field of social simulation. Carlos Lemos et al provide an overview of applications of ABM techniques in social conflict and civil violence in “Agent-based modeling of social conflict, civil violence and revolution: state-of-the-art-review and further prospects” (link). Here is an overview statement of their findings about one specific approach, the threshold-based approach:

Social conflict, civil violence and revolution ABM are inspired on classical models that use simple threshold-based rules to represent collective behavior and contagion effects, such as Schelling’s model of segregation [7] and Granovetter’s model of collective behavior [15]. Granovetter’s model is a theoretical description of social contagion or peer effects: each agent a has a threshold Ta and decides to turn “active” – e.g. join a protest or riot – when the number of other agents joining exceeds its threshold. Granovetter showed that certain initial distributions of the threshold can precipitate a chain reaction that leads to the activation of the entire population, whereas with other distributions only a few agents turn active. (section 3.1)

Here is a diagram of their way of conceptualizing the actors and the processes of social conflict into which they are sometimes mobilized.

Armano Srbljinovic and colleagues attempt to model the emergence of ethnic conflict in “An Agent-Based Model of Ethnic Mobilisation” (link). Their original impulse is to better explain the emergence of polarized and antagonistic ethnic conflict in the former Yugoslavia; their method of approach is to develop an agent-based model that might capture some of the parameters that induce or inhibit ethnic mobilization. They refer to the embracing project as “Social Correlates of the Homeland War”. They believe an ABM can potentially illuminate the messy and complex processes of ethnic mobilization observed on the ground:

Our more moderate goals are based on a seemingly reasonable assumption that the results observed in a simplified, artificial society could give us some clues of what is going on, or perhaps show us where to centre our attention in further and more detailed examination of a more complex real-world society. (paragraph 1.4)

They describe the eighties and nineties in this region in these terms:

So, by the end of the eighties and the beginning of the nineties, the ethnic roles in the society of the former Yugoslavia, that were kept toward the middle of Banton’s social roles-scale for more than forty years, now under the influence of political entrepreneurs, increased in importance. (paragraph 2.5)

And they would like to explain some aspects of the dynamics of this transition. They single out a handful of important social characteristics of individuals in the region: (a) ethnic membership, (b) ethnic mobilization, (c) civic mobilization, (d)grievance degree, (e) social network, (f) environmental conditions, and (g) appeals to action. Each actor in the model is assigned a value for factors a-e; environmental conditions are specified; and various patterns of appeals are inserted into the system over a number of trials

The algorithm of the model calculates the degree of mobilization intensity for all the agents as a function of the frequency of appeals, the antecedent grievance level of the agent, and a few features of the agents’ social networks. If we add a substantive hypothesis about the threshold of M after which group action arises, we then have a model of the occurrence of ethnic strife.

The model uses a “SWARM” methodology. It postulates 200 agents, half red and half blue; and it calculates for each agent a level of mobilization intensity for a sequence of times, according to the following formula:

  • mi(t+1) = mi(t) + (miapp + misocnet + micoolt    (paragraph 3.8)

This formula calculates the i^th individual’s new level of mobilization intensity m depending on the prior intensity, the delta created by the appeal, the delta created by the social network, and the “cooling” for the current period. (It is assumed that mobilization intensity decays over time unless re-stimulated by appeals and social network effects.)

This is a very interesting experiment in modeling of a complex interactive social process. But it also raises several important issues. One thing that is apparent from careful scrutiny of this model is that it is difficult to separate “veridical” results from artifacts. For example, consider this diagram:

Is the periodicity shown by Red and Blue mobilization intensities a real effect, or is it an artifact of the design of the model?

Second, it is important to notice the range of factors the simulation does not consider, which theorists like Tilly would think to be crucial: quality of leadership, quality and intensity of organization, content of appeals, differential pathways of appeals, and variety of political psychologies across agents. This simulation captures several important aspects of this particular kind of collective action. But it omits a great deal of substantial factors that theorists of collective action would take to be critical elements of the dynamics of the situation.

Here is a second example of an attempt to simulate aspects of ethnic mobilization provided by Stacey Pfautz and Michael Salwen, “A Hybrid Model of Ethnic Conflict, Repression, Insurgency and Social Strife” (link). Pfautz and Salwen describe their work in these terms:

Ethnic Conflict, Repression, Insurgency and Social Strife (ERIS) is a comprehensive, multi-level model of ethnic conflict that simulates how population dynamics impact state decision making and, in turn, respond to state actions and policies. Population pressures (e.g., relocation, civil unrest) affect and are affected by state actions. The long term goal of ERIS is to support operations development and analyses, enabling military planners to evaluate evolving situations, anticipate the emergence of ethnic conflict and its negative consequences, develop courses of action to defuse ethnic conflict, and mitigate the second and third order effects of U.S. actions on ethnic conflict. (211)

They refer to theirs as a hybrid model, incorporating a macro-level “systems dynamics” model and a micro-level ABM model. Their model thus attempts to represent both micro and macro causal forces on ethnic mobilization, illustrated in the diagram at the top. This model increases the level of “realism” in the assumptions represented in the simulation. Agents are heterogeneous, and their decision-making is contextualized to location on a GIS grid.

Agents represent 1000 individuals and are uniform with respect to religious affiliation. Agents are sampled with respect to age and sex ratio; however, skew sampling is used to create agents with different demographic profiles with respect to these attributes. Agents also have attributes to capture propensities to conflict and tolerance, which affect agent behavior and interact in the aggregate with the macro-level model to localize reports of conflict. (212)

Key variables in their simulation are religious identity, demographic change, population density, the history of recent inter-group conflict, and geographical location. The action space for individuals is: move location, mobilize for violence. And their model is calibrated to real data drawn from four states in Northwest India. Their basic finding is this: “Conflict is predicted in this model where islands or peninsulas of one ethnicity are surrounded by a sea of another (Figure 2.1).”

Kent McClelland offers a computational model that responds to Randall Collins’ concepts of “C-Escalation” and “D-Escalation” in inter-group conflict. McClelland’s piece is “CYCLES OF CONFLICT A Computational Modeling Alternative to Collins’s Theory of Conflict Escalation” (link). Here is how he describes his approach:

In this paper, I use a variation of systems theory to construct a multi-agent computational model of dynamic social interaction that shows how the conflict-escalation processes described by Collins can be generated in computer simulations. Like his, my model relies on feedback loops, but the mathematical formulas in my model use negative feedback loops, rather than positive feedback loops, to generate the collective processes of positive feedback described in Collins’s model of conflict escalation. My analysis relies on perceptual control theory (PCT), a dynamic-systems model of human behavior, which proposes that neural circuits in the brain are organized into hierarchies of negative-feedback control systems, and that individuals use these control systems to manipulate their own environments in order to control the flow of perceptual input in accordance with their internally generated preferences and expectations. (6)

Lars-Erik Cederman uses an ABM approach to model geopolitical boundaries (link). Here is how he describes his goals:

A decade ago, the Soviet Union ceased to exist, Yugoslavia started to disintegrate, and Germany reunified. Marking the end of the Cold War, these epochal events illustrate vividly that change in world politics features not just policy shifts but also can affect states’ boundaries and, sometimes, their very existence. Clearly, any theory aspiring to explain such transformations or, more generally, the longue durée of history, must endogenize the actors themselves.The current paper describes how agent based modeling can be used to capture transformations of this boundary transforming kind. This is a different argument from that advanced by most agent-based modelers, who resort to computational methods because they lend themselves to exploring heterogeneous and boundedly rational, but otherwise fixed, actors in complex social environments (1, 2). Without discounting the importance of this research, I will use illustrations from my own modeling framework to illustrate how it is possible to go beyond this mostly behavioral agenda. The main emphasis will be on the contribution of specific computational techniques to conceptualization of difficult to grasp notions such as agency, culture, and identity. Although a complete specification of the models goes beyond the current scope, the paper closes with a discussion of some of their key findings.

Cederman’s model incorporates three primary dynamics: “Emergent Polarity” (the idea that boundaries result from a process of conquest); “Democratic Cooperation” (the idea that “Democracy” functions as a tag facilitating cooperation among subsets of actors); and “Nationalist Systems Change” (the idea that boundaries result from actors seeking locations placing them in proximity to other actors possessing the same ethnic identity).

Here is a diagram representing stylized results of the simulation.

Epstein, Steinbruner, and Parker offer a model of civil violence (link). Here are the parameters that are assigned to all actors (population and cops): grievance, hardship, perceived legitimacy, risk aversiveness, field of vision, net risk, location, and decision to act. This is a very simple analysis of collective action, plainly derivative from a rational-choice approach. Each actor decides to act or not depending on his/her calculation of risk and hardship/grievance. These assumptions are vastly weaker than those offered by students of contentious politics like McAdam, Tarrow, and Tilly; but they generate interesting collective results when embodied in a generative ABM.

This research is specifically interesting in the context of the question posed here about fissioning. Consider this series of frames from an animation reflecting the results of random fluctuation of densities in an ethnically mixed community:

Peaceful coexistence
Animation of process leading to ethnic separation / ethnic cleansing

With “peace-keepers” the results are different:

These are interesting results. Plainly the presence or absence of peace-enforcers is relevant to the extent of ethnic violence that occurs. But notice once again how sparse the behavioral assumptions are. The simulations essentially serve to calculate the interactive effects of this particular set of assumptions about agents’ behavior — with no ability to represent organizations, communication, variations in motivation, etc.

All these models warrant study. They attempt to codify the behavior of individuals within geographic and social space and to work out the dynamics of interaction that result. But it is very important to recognize the limitations of these models as predictors of outcomes in specific periods and locations of unrest. These simulation models probably don’t shed much light on particular episodes of contention in Egypt or Tunisia during the Arab Spring. The “qualitative” theories of contention that have been developed probably shed more light on the dynamics of contention than the simulations do at this point in their development.

A survey of agent-based models


Federico Bianchi and Flaminio Squazzoni have published a very useful survey of the development and uses of agent-based models in the social sciences over the past twenty-five years in WIREs Comput Stat 2015 (link). The article is a very useful reference and discussion for anyone interested in the applicability of ABM within sociology.

Here is their general definition of an ABM:

Agent-based models (ABMs) are computer simulations of social interaction between heterogeneous agents (e.g., individuals, firms, or states), embedded in social structures (e.g., social networks, spatial neighborhoods, or institutional scaffolds). These are built to observe and analyze the emergence of aggregate outcomes. By manipulating behavioral or interaction model parameters, whether guided by empirical evidence or theory, micro-generative mechanisms can be explored that can account for macro-scale system behavior, that is, an existing time series of aggregate data or certain stylized facts. (284)

This definition highlights several important features of the ABM approach:

  • unlike traditional rational choice theory and microeconomics, it considers heterogeneous agents
  • it explicitly attempts to represent concrete particulars of the social environment within which agents act
  • it is a micro to macro strategy, deriving macro outcomes from micro activities
  • it permits a substantial degree of “experimentation” in the form of modification of base assumptions
  • it is possible to provide empirical evidence to validate or invalidate the ABM simulation of a given aggregate outcome 

Bianchi and Squazzoni note that the primary areas of application of agent-based models in social-science research include a relatively limited range of topics. The first of these topics included uncoordinated cooperation, reciprocity, and altruism. Robert Axelrod’s work on repeated prisoners’ dilemmas represents a key example of modeling efforts in this area (link).

A peculiar form of altruism is punishment: imposition of a cost on non-cooperators by other actors. Without punishment the exploitation strategy generally extinguishes the cooperation strategy in a range of situations. A “reciprocator” is an actor who is open to cooperation but who punishes previous non-cooperators on the next interaction. Bianchi and Squazzoni spend time describing an ABM developed by Bowles and Gintis (link) to evaluate the three strategies of Selfish, Reciprocator, and Cooperator, and a derived Shirking rate in a hypothetical and heterogeneous population of hunter-gatherers. Here is Bowles and Gintis’ hypothesis:

The hypothesis we explore is that cooperation is maintained because many humans have a predisposition to punish those who violate group-beneficial norms, even when this reduces their fitness relative to other group members. Compelling evidence for the existence and importance of such altruistic punishment comes from controlled laboratory experiments, particularly the study of public goods, common pool resource, ultimatum, and other games.

And here is their central finding, according to Bianchi and Squazzoni:

They found that the robustness of cooperation depended on the coexistence of these behaviors at a group level and that strong reciprocators were functional in keeping the level of cheating under control in each group (see the shirking rate as a measure of resources lost by the group due to cheating in Figure 1). This was due to the fact that the higher the number of cooperators in a group without reciprocators, the higher the chance that the group disbanded due to high payoffs for shirking. (288)

Here is the graph of the incidence of the three strategies over the first 3000 periods of the simulation published in the Bowles and Gintis article:


This graph represents the relative frequency of the three types of hunter-gatherers in the population, along with a calculated shirking rate for each period. The Selfish profile remains the most frequent (between 40% and 50%, but Reciprocators and Cooperators reach relatively stable levels of frequency as well (between 30% and 40%, and between 20% and 30%). As Bowles and Gintis argue, it is the robust presence of Reciprocators that keeps the Selfish group in check; the willingness of Reciprocators to punish Selfish actors keeps the latter group from rising to full domination.

In this simulation the frequencies of Selfish and Shirking begin high (>85%) and quickly decline to a relatively stable rate. After 1000 iterations the three strategies attain relatively stable frequencies, with Selfish at about 38%, Reciprocator at 37%, Cooperator at 25%, and a shirking rate at about 11%.

It is tempting to read the study as representing a population that reaches a rough equilibrium. However, it is possible that the appearance of equilibrium conveyed by the graph above is deceptive. Other areas of complex phenomena raise the possibility that this is not a longterm equilibrium, but rather that some future combination of percentages of the three strategies may set off a chaotic redistribution of success rates. This is the key characteristic of a chaotic system: small fluctuations in parameters can lead to major deviations in outcomes.

Also interesting in Bianchi and Squazzoni’s review is their treatment of efforts to use ABMs to model the diffusion of cultural and normative attitudes (293ff.). Attitudes are treated as local “contagion” factors, and the goal of the simulation is to model how different adjacencies influence the pattern of spread of the cultural features.

Agents interacted with neighbors with a probability dependent on the number of identical cultural features they shared. A mechanism of interpersonal influence was added to align one randomly selected dissimilar cultural feature of an agent to that of the partner, after interaction. (294ff.)

Social network characteristics have been incorporated into ABMs in this area.

Bianchi and Squazzoni also consider ABMs in the topic areas of collective behavior and social inequality. They draw a number of useful conclusions about the potential role that ABMs can play in sociology, including especially the importance of considering heterogeneous agents:

At a substantive level, these examples show that exploring the fundamental heterogeneity of individual behavior is of paramount importance to understand the emergence of social patterns. Cross-fertilization between experimental and computational research is a useful process. It shows us that by conflating the concept of rationality with that of self-interest, as in standard game theory and economics, we cannot account for the subtle social nuances that characterize individual behavior in social contexts. (298)

And they believe — perhaps unexpectedly — that the experience of building ABMs in a range of sociological contexts underlines the importance of institutions, norms, and social context:

Moreover, these ABM studies can help us to understand the importance of social contexts even when looking at individual behavior in a more micro-oriented perspective. The role of social influence and the fact that we are embedded in complex social networks have implications for the type of information we access and the types of behavior we are exposed to. (301)

This is a useful contribution for sociologists, as a foundation for a third alternative between statistical studies of sociological phenomena and high-level deductive theories of those phenomena. ABMs have the potential of allowing us to derive large social patterns from well chosen and empirically validated behavioral assumptions about actors.
I mentioned the common finding in complexity studies that even fairly simple systems possess the capacity for sudden instability. Here is a simulation of a three-body gravitational system which illustrates periods of relative stability and then abrupt destabilization.

ABMs permit us to model populations of interactive adaptive agents, and often the simulation produces important and representative patterns at the aggregate level. Here is an interesting predator-prey simulation on YouTube using an ABM approach by SSmithy87:

The author makes a key point at 2:15: the pattern of variation of predator and prey presented in the simulation is a well-known characteristic of predator-prey populations. (Red is predator and blue is prey.)


But the equations representing this relationship were not built into the model; instead, this characteristic pattern is generated by the model based on the simple behavioral assumptions made about prey and predators. This is a vivid demonstration of the novelty and importance of ABM simulations.


Simulating social mechanisms



A key premise of complexity theory is that a population of units has “emergent” properties that result from the interactions of units with dynamic characteristics. Call these units “agents”.  The “agent” part of the description refers to the fact that the elements (persons) are self-directed units.  Social ensembles are referred to as “complex adaptive systems” — systems in which outcomes are the result of complex interactions among the units AND in which the units themselves modify their behavior as a result of prior history.

Scott Page’s Complex Adaptive Systems: An Introduction to Computational Models of Social Life provides an excellent introduction. Here is how Page describes an adaptive social system:

Adaptive social systems are composed of interacting, thoughtful (but perhaps not brilliant) agents. It would be difficult to date the exact moment that such systems first arose on our planet — perhaps it was when early single-celled organisms began to compete with one another for resources…. What it takes to move from an adaptive system to a complex adaptive system is an open question and one that can engender endless debate. At the most basic level, the field of complex systems challenges the notion that by perfectly understanding the behavior of each component part of a system we will then understand the system as a whole. (kl 151)

Herbert Simon added a new chapter on complexity to the third edition of The Sciences of the Artificial – 3rd Edition in 1996.

By adopting this weak interpretation of emergence, we can adhere (and I will adhere) to reductionism in principle even though it is not easy (often not even computationally feasible) to infer rigorously the properties of the whole from knowledge of the properties of the parts. In this pragmatic way, we can build nearly independent theories for each successive level of complexity, but at the same time, build bridging theories that show how each higher level can be accounted for in terms of the elements and relations of the next level down. (172).

This formulation amounts to the claim of what I referred earlier to as “relative explanatory autonomy”; link. It is a further articulation of Simon’s view of “pragmatic holism” first expressed in 1962 (link).

So how would agent-based models (ABM) be applied to mechanical systems? Mechanisms are not intentional units. They are not “thoughtful”, in Page’s terms. In the most abstract version, a mechanism is an input-output relation, perhaps with governing conditions and with probabilistic outcomes — perhaps something like this:


In this diagram A, B, and D are jointly sufficient for the working of the mechanism, and C is a “blocking condition” for the mechanism. When A,B,C,D are configured as represented the mechanism then does its work, leading with probability PROB to R and the rest of the time to S.

So how do we get complexity, emergence, or unpredictability out of a mechanical system consisting of a group of separate mechanisms? If mechanisms are determinate and exact, then it would seem that a mechanical system should not display “complexity” in Simon’s sense; we should be able to compute the state of the system in the future given the starting conditions.

There seem to be several key factors that create indeterminacy or emergence within complex systems. One is the fact of causal interdependency, where the state of one mechanism influences the state of another mechanism which is itself a precursor to the first mechanism.  This is the issue of feedback loops or “coupled” causal processes. Second is non-linearity: small differences in input conditions sometimes bring about large differences in outputs. Whenever an outcome is subject to a threshold effect, we will observe this feature; small changes short of the threshold make no change in the output, whereas small changes at the threshold bring about large changes. And third is the adaptability of the agent itself.  If the agent changes behavioral characteristics in response to earlier experience (through intention, evolution, or some other mechanism) then we can expect outcomes that surprise us, relative to similar earlier sequences. And in fact, mechanisms display features of each of these characteristics. They are generally probabilistic, they are often non-linear, they are sensitive to initial conditions, and at least sometimes they “evolve” over time.

So here is an interesting question: how do these considerations play into the topic of understanding social outcomes on the basis of an analysis of underlying social mechanisms? Assume we have a theory of organizations that involves a number of lesser institutional mechanisms that affect the behavior of the organization. Is it possible to develop an agent-based model of the organization in which the institutional mechanisms are the units? Are meso-level theories of organizations and institutions amenable to implementation within ABM simulation techniques?

Here is a Google Talk by Adrien Treuille on “Modeling and Control of Complex Dynamics”.


The talk provides an interesting analysis of “crowd behavior” based on a new way of representing a crowd.

%d bloggers like this: