Emergentism and generationism

media: lecture by Stanford Professor Robert Sapolsky on chaos and reduction

 

Several recent posts have focused on the topic of simulations in the social sciences. An interesting question here is whether these simulation models shed light on the questions of emergence and reduction that frequently arise in the philosophy of the social sciences. In most cases the models I've mentioned are "aggregation" models, in which the simulation attempts to capture the chief dynamics and interaction effects of the units and then work out the behavior and evolution of the ensemble. This is visibly clear when it comes to agent-based models. However, some of the scholars whose work I admire are "complexity" theorists, and a common view within complexity studies is the idea that the system has properties that are difficult or impossible to derive from the features of the units.

So does this body of work give weight to the idea of emergence, or does it incline us more in the direction of supervenience and ontological unit-ism?

John Miller and Scott Page provide an accessible framework within which to consider these kinds of problems in Complex Adaptive Systems: An Introduction to Computational Models of Social Life. They look at certain kinds of social phenomena as constituting what they call "complex adaptive systems," and they try to demonstrate how some of the computational tools developed in the sciences of complex systems can be deployed to analyze and explain complex social outcomes. Here is how they characterize the key concepts:

Adaptive social systems are composed of interacting, thoughtful (but perhaps not brilliant) agents. (kl 151)

Page and Miller believe that social phenomena often display "emergence" in a way that we can make sense of. Here is the umbrella notion they begin with:

The usual notion put forth underlying emergence is that individual, localized behavior aggregates into global behavior that is, in some sense, disconnected from its origins. Such a disconnection implies that, within limits, the details of the local behavior do not matter to the aggregate outcome. (kl 826)

And they believe that the notion of emergence has "deep intuitive appeal". They find emergence to be applicable at several levels of description, including "disorganized complexity" (the central limit theorem, the law of large numbers) and "organized complexity" (the behavior of sand piles when grains have a small amount of control).

Under organized complexity, the relationships among the agents are such that through various feedbacks and structural contingencies, agent variations no longer cancel one another out but, rather, become reinforcing. In such a world, we leave the realm of the Law of Large Numbers and instead embark down paths unknown. While we have ample evidence, both empirical and experimental, that under organized complexity, systems can exhibit aggregate properties that are not directly tied to agent details, a sound theoretical foothold from which to leverage this observation is only now being constructed. (kl 976)

Organized complexity, in their view, is a substantive and important kind of emergence in social systems, and this concept plays a key role in their view of complex adaptive systems.

Another -- and contrarian -- contribution to this field is provided by Joshua Epstein. His three-volume work on agent-based models is a fundamental text book for the field. Here are the titles:

Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science
Growing Artificial Societies: Social Science From the Bottom Up
Generative Social Science: Studies in Agent-Based Computational Modeling

Chapter 1 of Generative Social Science provides an overview of Epstein's approach is provided in "Agent-based Computational Models and Generative Social Science", and this is a superb place to begin (link). Here is how Epstein defines generativity:

Agent-based models provide computational demonstrations that a given microspecification is in fact sufficient to generate a macrostructure of interest.... 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. (42)

Epstein describes an extensive attempt to model a historical population using agent-based modeling techniques, the Artificial Anasazi project (link). This work is presented in Dean, Gumerman, Epstein, Axtell, Swedlund, McCarroll, and Parker, "Understanding Anasazi Culture Change through Agent-Based Modeling" in Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes. The model takes a time series of fundamental environmental, climate, and agricultural data as given, and he and his team attempt to reconstruct (generate) the pattern of habitation that would result. Here is the finding they arrive at:

Generativity seems to be directly incompatible with the idea of emergence, and in fact Epstein takes pains to cast doubt on that idea.

I have always been uncomfortable with the vagueness--and occasional mysticism--surrounding this word and, accordingly, tried to define it quite narrowly.... There, we defined "emergent phenomena" to be simply "stable macroscopic patterns arising from local interaction of agents." (53)

So Epstein and Page both make use of the methods of agent based modeling, but they disagree about the idea of emergence. Page believes that complex adaptive systems give rise to properties that are emergent and irreducible; whereas Epstein doesn't think the idea makes a lot of sense. Rather, Epstein's view depends on the idea that we can reproduce (generate) the macro phenomena based on a model involving the agents and their interactions. Macro phenomena are generated by the interactions of the units; whereas for Page and Miller, macro phenomena in some systems have properties that cannot be easily derived from the activities of the units.

At the moment, anyway, I find myself attracted to Herbert Simon's effort to split the difference by referring to "weak emergence" (link):

... 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. (Sciences of the Artificial 3rd edition 172)

This view emphasizes the computational and epistemic limits that sometimes preclude generating the phenomena in question -- for example, the problems raised by non-linear causal relations and causal interdependence. Many observers have noted that the behavior of tightly linked causal systems may be impossible to predict, even when we are confident that the system outcomes are the result of "nothing but" the interactions of the units and sub-systems.

Verisimilitude in models and simulations

Modeling always requires abstraction and simplification. We need to arrive at a system for representing the components of a system, the laws of action that describe their evolution and interaction, and a way of aggregating the results of the representation of the components and their interactions. Simplifications are required in order to permit us to arrive at computationally feasible representations of the reality in question; but deciding which simplifications are legitimate is a deeply pragmatic and contextual question. Ignoring air resistance is a reasonable simplification when we are modeling the trajectories of dense, massive projectiles through the atmosphere; it is wholly unreasonable if we are interested in modeling the fall of a leaf or a feather under the influence of gravity (link).

Modeling the social world is particularly challenging for a number of reasons. Not all social actors are the same; actors interact with each other in ways that are difficult to represent formally; and actors change their propensities for behavior as a result of their interactions. They learn, adapt, and reconfigure; they acquire new preferences and new ways of weighing their circumstances; and they sometimes change the frames within which they deliberate and choose.

Modeling the social world certainly requires the use of simplifying assumptions. There is no such thing as what we might call a Borges-class model -- one that represents every feature of the terrain. This means that the scientist needs to balance realism, tractability, and empirical adequacy in arriving at a set of assumptions about the actor and the environment, both natural and social. These judgments are influenced by several factors, including the explanatory and theoretical goals of the analysis. Is the analysis intended to serve as an empirical representation of an actual domain of social action -- the effects on habitat of the grazing strategies of a vast number of independent herders, say? Or is it intended to isolate the central tendency of a few key factors -- short term cost-benefit analysis in a context of a limited horizon of environmental opportunities, say?

If the goal of the simulation is to provide an empirically adequate reconstruction of the complex social situation, permitting adjustment of parameters in order to answer "what-if" questions, then it is reasonable to expect that the baseline model needs to be fairly detailed. We need to build in enough realism about the intentions and modes of reasoning of the actors, and we need a fair amount of detail concerning the natural, social, and policy environments in which they choose.

The discipline of economic geography provides good examples of both extremes of abstraction and realism of assumptions. At one extreme we have the work of von Thunen in his treatment of the Isolated State, producing a model of habitation, agriculture, and urbanization that reflects the economic rationality of the actors.

At the other extreme we have calibrated agent-based models of land use that build in more differentiated assumptions about the intentions of the actors and the legal and natural environment in which they make their plans and decisions. A very good and up-to-date volume dedicated to the application of calibrated agent-based models in economic geography is Alison Heppenstall, Andrew Crooks, Linda See, and Michael Batty, Agent-Based Models of Geographical Systems. The contribution by Crooks and Heppenstall provides an especially good introduction to the approach ("Introduction to Agent-Based Modelling"). Crook and Heppenstall describe the distinguishing features of the approach in these terms:

To understand geographical problems such as sprawl, congestion and segregation, researchers have begun to focus on bottom-up approaches to simulating human systems, specifically researching the reasoning on which individual decisions are made. One such approach is agent-based modelling (ABM) which allows one to simulate the individual actions of diverse agents, and to measure the resulting system behaviour and outcomes over time. The distinction between these new approaches and the more aggregate, static conceptions and representations that they seek to complement, if not replace, is that they facilitate the exploration of system processes at the level of their constituent elements. (86)

The volume also pays a good deal of attention to the problem of validation and testing of simulations. Here is how Manson, Sun, and Bonsal approach the problem of validation of ABMs in their contribution, "Agent-Based Modeling and Complexity":

Agent-based complexity models require careful and thorough evaluation, which is comprised of calibration, verification, and validation (Manson 2003 ) . Calibration is the adjustment of model parameters and specifications to fit certain theories or actual data. Verification determines whether the model runs in accordance with design and intention, as ABMs rely on computer code susceptible to programming errors. Model verification is usually carried out by running the model with simulated data and with sensitivity testing to determine if output data are in line with expectations. Validation involves comparing model outputs with real-world situations or the results of other models, often via statistical and geovisualization analysis. Model evaluation has more recently included the challenge of handling enormous data sets, both for the incorporation of empirical data and the production of simulation data. Modelers must also deal with questions concerning the relationship between pattern and process at all stages of calibration, verification, and validation. Ngo and See ( 2012 ) discuss these stages in ABM development in more detail. (125)

An interesting current illustration of the value of agent-based modeling in analysis and explanation of historical data is presented by Kenneth Sylvester, Daniel Brown, Susan Leonard, Emily Merchant, and Meghan Hutchins in "Exploring agent-level calculations of risk and return in relation to observed land-use changes in the US Great Plains, 1870-1940" (link). Their goal is to see whether it is possible to reproduce important features of land use in several Kansas counties by making specific assumptions about decision-making by the farmers, and specific information about the changing weather and policy circumstances within which choices were made. 

 

Here is how Sylvester and co-authors describe the problem of formulating a representation of the actors in their simulation:

Understanding the processes by which farming households made their land-use decisions is challenging because of the complexity of interactions between people and the places in which they lived and worked, and the often insufficient resolution of observed information. Complexity characterizes land-use processes because observed historical behaviors often represent accumulated decisions of heterogeneous actors who were affected by a wide range of environmental and human factors, and by specific social and spatial interactions. (1)

Here is a graph of the results of the Sylvester et al agent-based model, simulating the allocation of crop land across five different crops given empirical weather and rainfall data.

So how well does this calibrated agent-based model do as a simulation of the observed land use patterns? Not particularly well, in the authors' concluding remarks; their key finding is sobering:

Our base model, assuming profit maximization as the motive for land-use decision making, reproduced the historical record rather poorly in terms of both land use shares and farm size distributions in each township. We attribute the differences to deviations in decision making from profit-maximizing behavior. Each of the subsequent experiments illustrates how relatively simple changes in micro-level processes lead to different aggregate outcomes. With only minor adjustments to simple mechanisms, the pace, timing, and trajectories of land use can be dramatically altered.

However, they argue that this lack of fit does not discredit the ABM approach, but rather disconfirms the behavioral assumption that farmers are simple maximizers of earning. They argue, as sociologists would likely agree, that "trajectories of land-use depended not just on economic returns, but other slow processes of change, demographic, cultural, and ecological feedbacks, which shaped the decisions of farmers before and long after the middle of the twentieth century." And therefore it is necessary to provide more nuanced representations of actor intentionality if the model is to do a good job of reproducing the historical results and the medium-term behavior of the system.

 

(In an earlier post I discussed a set of formal features that have been used to assess the adequacy of formal models in economics and other mathematized social sciences (link). These criteria are discussed more fully in On the Reliability of Economic Models: Essays in the Philosophy of Economics.)

(Above I mentioned the whimsical idea of "Borges-class models" -- the unrealizable ideal of a model that reproduces every aspect of the phenomena that it seeks to simulate. Here is the relevant quotation from Jorge Borges.

On Exactitude in Science
Jorge Luis Borges, Collected Fictions, translated by Andrew Hurley.

…In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

—Borges quoting Suarez Miranda,Viajes devarones prudentes, Libro IV,Cap. XLV, Lerida, 1658)

Computational models for social phenomena

There is a very lively body of work emerging in the intersection between computational mathematics and various fields of the social sciences. This emerging synergy between advanced computational mathematics and the social sciences is possible, in part, because of the way that social phenomena emerge from the actions and thoughts of individual actors in relationship to each other. This is what allows us to join mathematics to methodology and explanation. Essentially we can think of the upward strut of Coleman’s boat — the part of the story that has to do with the “aggregation dynamics” of a set of actors — and can try to create models that can serve to simulate the effects of these actions and interactions.

source: Hedstrom and Ylikoski (2010) "Causal Mechanisms in the Social Sciences" (link)

 

Here is an interesting example in the form of a research paper by Rahul Narain and colleagues on the topic of modeling crowd behavior ("Aggregate Dynamics for Dense Crowd Simulation", link). Here is their abstract:

Large dense crowds show aggregate behavior with reduced individual freedom of movement. We present a novel, scalable approach for simulating such crowds, using a dual representation both as discrete agents and as a single continuous system. In the continuous setting, we introduce a novel variational constraint called unilateral incompressibility, to model the large-scale behavior of the crowd, and accelerate inter-agent collision avoidance in dense scenarios. This approach makes it possible to simulate very large, dense crowds composed of up to a hundred thousand agents at near- interactive rates on desktop computers.

Federico Bianchi takes up this intersection between computational mathematics and social behavior in a useful short paper called "From Micro to Macro and Back Again: Agent-based Models for Sociology" (link). His paper focuses on one class of computational models, the domain of agent-based models. Here is how he describes this group of approaches to social explanation:

An Agent-Based Model (ABM) is a computational method which enables to study a social phenomenon by representing a set of agents acting upon micro-level behavioural rules and interacting within environmental macro-level (spatial, structural, or institutional) constraints. Agent-Based Social Simulation (ABSS) gives social scientists the possibility to test formal models of social phenomena, generating a virtual representation of the model in silico through computer programming, simulating its systemic evolution over time and comparing it with the observed empirical phenomenon. (1) 

 And here is how he characterizes the role of what I called "aggregation dynamics" above:

Solving the complexity by dissecting the macro-level facts to its micro-level components and reconstructing the mechanism through which interacting actors produce a macro-level social outcome. In other words, reconstructing the micro-macro link from interacting actors to supervenient macrosociological facts. (2)

Or in other words, the task of analysis is to provide a testable model that can account for the way the behaviors and interactions at the individual level can aggregate to the observed patterns at the macro level.

Another more extensive example of work in this area is Gianluca Manzo, Analytical Sociology: Actions and Networks. Manzo's volume proceeds from the perspective of analytical sociology and agent-based models. Manzo provides a very useful introduction to the approach, and Peter Hedstrom and Petri Ylikoski extend the introduction to the field with a chapter examining the role of rational-choice theory within this approach. The remainder of the volume takes the form of essays by more than a dozen sociologists who have used the approach to probe and explain specific kinds of social phenomena.

Manzo provides an account of explanation that highlights the importance of "generating" the phenomena to be explained. Here are several principles of methodology on this topic:

• P4: in order to formulate the "generative model," provide a realistic description of the relevant micro-level entities (P4a) and activities (P4b) assumed to be at work, as well as of the structural interdependencies (P4c) in which these entities are embedded and their  activities unfold;
• P5: in order rigorously to assess the internal consistency of the "generative model" and to determine its high-level consequences, translate the "generative model" into an agent-based computational model;
• P6: in order to assess the generative sufficiency of the mechanisms postulated, compare the agent-based computational model's high-level consequences with the empirical description of the facts to be explained (9)

So agent-based modeling simulations are a crucial part of Manzo's understanding of the logic of analytical sociology. As agent-based modelers sometimes put the point, "you haven't explained a phenomenon until you've shown how it works on the basis of a detailed ABM." But the ABM is not the sole focus of sociological research, on Manzo's approach. Rather, Manzo points out that there are distinct sets of questions that need to be investigated: how do the actors make their choices? What are the structural constraints within which the actors exist? What kinds of interactions and relations exist among the actors? Answers to all these kinds of question are needed if we are to be able to design realistic and illuminating agent-based models of concrete phenomena.

Here is Manzo's summary table of the research cycle (8). And he suggests that each segment of this representation warrants a specific kind of analysis and simulation.

This elaborate diagram indicates that there are different locations within a complex social phenomenon where different kinds of analysis and models are needed. (In this respect the approach Manzo presents parallels the idea of structuring research methodology around the zones of activity singled out by the idea of methodological localism; link.) This is methodologically useful, because it emphasizes to the researcher that there are quite a few different kinds of questions that need to be addressed in order to successfully explain a give domain of phenomena.

The content-specific essays in the volume focus on one or another of the elements of this description of methodology. For example, Per-Olof Wikstrom offers a "situational action theory" account of criminal behavior; this definition of research focuses on the "Logics of Action" principle 4b.

People commit acts of crime because they perceive and choose (habitually or after some deliberation) a particular kind of act of crime as an action alternative in response to a specific motivation (a temptation or a provocation). People are the source of their actions but the causes of their actions are situational. (75)

SAT proposes that people with a weak law-relevant personal morality and weak ability to exercise self-control are more likely to engage in acts of crime because they are more likely to see and choose crime as an option. (87)

Wikstrom attempts to apply these ideas by using a causal model to reproduce crime hotspots based on situational factors (90).

The contribution of Gonzalez-Bailon et al, "Online networks and the diffusion of protest," focuses on the "Structural Interdependency" principle 4c.

One of the programmatic aims of analytical sociology is to uncover the individual-level mechanisms that generate aggregated patterns of behaviour.... The connection between these two levels of analysis, often referred to as the micro-macro link, is characterised by the complexity and nonlinearity that arises from interdependence; that is, from the influence that actors exert on each other when taking a course of action. (263)

Their contribution attempts to provide a basis for capturing the processes of diffusion that are common to a wide variety of types of social behavior, based on formal analysis of interpersonal networks.

Networks play a key role in diffusion processes because they facilitate threshold activation at the local level. Individual actors are not always able to monitor accurate the behavior of everyone else (as global thresholds assume) or they might be more responsive to a small group of people, represented in their personal networks. (271)

They demonstrate that the structure of the local network matters for the diffusion of an action and the activation of individual actors.

In short, Analytical Sociology: Actions and Networks illustrates a number of points of intersection between computational mathematics, simulation systems, and concrete sociological research. This is a very useful effort as social scientists attempt to bring more complex modeling tools to bear on concrete social phenomena.