Simulations

In the context of theoretical inquiry, simulations are tools by which theorists examine the consequences of assumptions. In that respect, it is equivalent to logical analysis, which seeks to derive additional propositions from a set of assumptions. Logical analysis, if possible, is always preferable: Consequences asserted as a result of the outcomes of simulations are open to the criticisms that (1) a slightly different instantiation of the assumptions would have produced different results, (2) the outcomes produced are critically dependent on the initial conditions assumed in the model, and (3) the generalizations proposed hold only for the particular space of parameter values examined. Simulations as theoretical tools are quite distinct from simulation put to other purposes such as training or entertainment (e.g., flight simulators).

As a theoretical tool, simulations are typically used for two reasons. First, a proposed model contains probabilistic elements or nonlinear relations among a large set of variables and the overwhelming complexity of possible outcomes makes it impractical or impossible to derive closed-form solutions of key properties. This use of simulations in these circumstances has a long history in social science; for instance, Rapoport in the 1950s used a deck of cards to simulate a link-tracing process on a biased net, a network composed of ties constructed from random and biased forces (1953). The second use of simulations is somewhat more recent, although it has a precursor in Schelling's famous model of segregation (1969). In this arena, agent-based modeling, the nature of the modeling exercise requires that simulations be used to analyze the model's consequences—the aim is to derive complexity at the aggregate level from the interaction of agents following relatively simple rules at the microlevel. Such complexity is “emergent” relative to the lower-level rules of interaction and agent-state change and thus, in principle, not predictable from these rules. Therefore, simulations must be used to detect such emergent regularities. In such a model, there are typically many agents, and often, probabilistic considerations figure in the determination of who interacts with whom and in the determination [Page 706]of the changes of agent-state change. Logical analysis of such a system is not feasible. The only way to explore consequences is through simulations. Both uses of simulations have been greatly aided by the development of very fast computation easily available on desktop workstations.

A simulations study can be divided into three phases: model setup, model implementation and execution, and inductive analysis of model output. In the model setup phase, decisions must be made about how variables are interconnected or how agents may interact and what rules govern their changes of state. In the implementation and execution phase, the system of agents or variables must be encoded in a computer program and various executions of this program conducted. The output of these executions must then be analyzed for patterns or regularities that can be reasonably attributed to the underlying assumptions about the connections among variables or the behavior constraints on agents encoded in the program. Care must be exercised to avoid the attribution of substantive meaning to regularities that are artifacts of the program implementation. In the best of all possible worlds, the simulation study is convincing because (1) the assumptions about behavior or variable connection are clear and intuitively reasonable or based clearly on existing theory, (2) the program implementation is transparent, (3) a full range of initial conditions and values of basic parameters is explored, and (4) clear regularities emerge and variation in these regularities can be interpretively explained in terms of the model's original assumptions.

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