Simplicity and Complexity in Agent-Based Modeling

ions, Ensembles, and Virtualizations Simplicity and Complexity in Agent-Based Modeling Ian S. Lustick and Dan Miodownik The Unique Analytic Leverage of Agent-Based Modeling Models are analytically focused metaphors. For example, “the moon is a ghostly galleon” is a metaphor. Thinking of the moon as if it were a ghostly galleon evokes particular moods and images associated with the moon and not others. Analyzing a polity as an array of competing factions arising from social and economic interests models the polity in a particular and limited way. Portraying a political struggle in exact terms as a game of chicken involves application of a formal model to highlight certain simple, highly abstract, strategic elements in a complex multilevel reality. The distinctive advantage of a formal model is that it can be expressed unambiguously. That is, the model can be written as a computer program (as can any proper algebraic formula) and run successfully without the exercise of human interpretation or discretion. Accordingly, to translate problems of scientific interest into a language a computer can understand is to model them formally. Agent-Based Modeling (ABM) is a computerassisted methodology that allows researchers to design, analyze, and investigate formal models realized as artificial worlds inhabited by agents that interact with each other following prespecified simple rules. Agent-based models vary considerably, but they all consist of arrays of autonomous, myopic units. Whether these units are modeled as states, individuals, corporations, ethnic groups, villages, or kinship groups is up to the experimenter and his or her theoretical domain of interest. Units in an ABM environment seek to adapt to their environment as they see it based on whatever goals they are programmed to pursue. Although individual actions are wholly determined at the micro level, when large numbers of such agents operate by interacting with one another, the macro state of the array as a whole is not predictable (though patterns in multiple “runs” of the array can be). As is the case in the “real” world, the specific trajectory the array will take is an empirical matter. It results from the initial condition of the array, the rules implemented to govern individual behavior of units, the complexly interdependent effects of adaptive behavior by the units, and whatever exogenous perturbations are streamed toward the array by the Comparative Politics January 2009 224 experimenter. Standard procedure is to generate large numbers of trajectories of these virtual worlds by perturbing them randomly or introducing randomized adjustments in initial conditions. By carefully calibrating these experiments, crucial experiments can be designed to bring reliable data into contact with isolated, theoretically informed claims. To the extent that the rules governing agent behavior are derived from clear, corroborated or widely accepted theories, this methodology offers a powerful technique for refining, evaluating, and testing specific theoretical claims. The visual, controlled experimental, and transparent nature of the technique, as well as the ease with which it exports results in tabulated, statistically analyzable form, also supports its use as an idea pump for the development of theory. Traditional formal modeling methods rely on algebraic formulas to translate simple relationships into mathematical expressions. But the limits of algebra prevent such techniques from incorporating many of the things known to be true of most of the worlds social scientists find interesting, including their multidimensionality, the presence of large numbers of interacting and autonomous units, and the predominance of highly irregular but nonrandomized patterns in the distribution of traits or interaction styles. The constraint of algebraic solvability therefore limits the ability of traditional formal modeling methods to capture the richness of interesting and even well-established substantive theories. Reliance only on traditional formal modeling techniques (such as game theory and rational choice) thus often entails ignoring what the modelers actually believe to be true about analytically crucial parts of the world. However, ABM, and the computer-assisted bottom-up simulations it produces, can be designed to capture beliefs about the real world embedded in or expressed by good substantive theories, thereby providing researchers with new opportunities to examine possible and probable outcomes associated with specific theory-based claims. The revolutionary potential of this technique is associated with the fact that very large numbers of alternatively possible “futures” (or “histories”) can be produced by varying initial conditions or a specific parameter setting of interest or by subjecting the theoretically specified model to random perturbations. Because of the automatic operation of the computer, every trajectory produced by a given model is consistent with the assumptions and propositions instantiated in the operating rules of the computer programs. Arising from the specific assumptions of the model, these unique counterfactual outcomes can yield reliable data about the implications of changing assumptions, boundary conditions of claims, sufficient conditions for particular outcomes, and robustness of results. The degree to which that potential is realized is a function of the empirical validity of substantive models and the degree to which these theoretical ideas have been implemented clearly and accurately. No formal tool can substitute for empirical work based on the deep study of a single case, structured comparisons of a small number of cases, and/or the statistical analysis of data in the large N tradition. But formal techniques, and especially computer-assisted ABM simulation, are powerful complements to those techniques. An important attraction of ABM is that it can be used to explore the justification for many claims that ordinarily would be impossible to evaluate, in particular in regard to rare but interesting events. Indeed, computer-assisted ABM is the most effective technique available for conducting Ian S. Lustick and Dan Miodownik 225 very large numbers of complicated but disciplined thought experiments about futures (or pasts) that could occur or could have occurred according to available theories. Careful design of artificial worlds, including exact control of all theoretically significant parameters, allows systematic manipulation of putatively significant independent variables and precise observation of the results. Using standard techniques of controlled experimentation and producing batches of theoretically consistent but unique outcomes, social scientists can expand the realms within which their variable-rich theories encounter numbers of cases much larger than the number of variables contained in the theories. However, the method of computer assisted agent-based modeling also raises new challenges, especially in the realm of research design. As is the case with informal verbal models, there are limits to the amount of complexity it may be useful to include in a study. For example, a researcher studying political participation may well believe that participation is affected by culture, aspirations to move into elite positions, beliefs about the efficacy and responsiveness of government, or alternatives available if participation opportunities are foregone. But the research design adopted will require taking only a strictly limited subset of variables into account. If the researcher were required to specify and integrate the best model he or she considered relevant for political culture, elite recruitment, government responsiveness, or exit opportunities, the complexity of the task would paralyze the project. No form of modeling should hold out as its goal the complete theoretical specification of all relevant variables and constants. On the other hand, for many problems the availability of computer-assisted simulations allows researchers not to settle for radically stylized models with key parameter values stipulated purely for analytic convenience. Computer assisted ABM can be used to integrate multiple theoretical modules, thereby leveraging the considerable knowledge available. This capability represents an enormous opportunity, but also a challenge as unfamiliar to formal modelers wedded to algebraic solvability as it is familiar to most other researchers—the problem of balancing parsimony with verisimilitude. A model that includes too many interacting modules explosively increases both the internal complexity of the model and the size of the space of possible outcomes. This sacrifice of parsimony can interfere with both confidence in theoretical operationalizations and in the interpretation of experimental results. Typically, the question of how much complexity to include in the design of a game theoretic or rational choice model is solved by the radical simplicity enforced on problem definition, dimensionality, and other features by the need for algebraic tractability. The claim or hope is then offered, implicitly or explicitly, that the solution of the game applies equally to more complex settings. However, once the move is made to computational modeling, the “algebraic tractability” constraint vanishes. The research design options open to ABM modelers are even richer thanks to the availability of cheap computer power and modeling platforms that do not require computer programming skills. The wider horizons for formal modeling opened up by ABM make the problem of research design both more important and more difficult. ABM researchers are forced to decide whether, for a particular project, the formal model to be built should be simple, complex. This article aims to help researchers cope with this problem. After consideration Comparative Politics January 2009 226 of the turn toward ABM taken by many political scientists, a typology of three different kinds of ABM research designs used to address crucial problems in political science— problems otherwise resistant to formal modeling strategies—will be illustrated. This typology—abstractions, ensembles, and virtualizations—will then be applied to work done on a family of problems pertaining to the evolution of collective identities and norms and their contribution to collective action. This illustrative treatment will present the range of ways political scientists using ABM have reacted to the greatly increased degrees of freedom this method of investigation permits them. We hope that this typology will encourage wider and more systematic use of ABM techniques and help improve the correspondence between the problem under consideration and the research design