Computational Simulation as Theoretical Experiment


CPM Report No.: 03-106
By: Bruce Edmonds and David Hales
Date: 12th Jan 2003.
 

Published as: Edmonds, B. and Hales, D. (2005) Computational Simulation as Theoretical Experiment, Journal of Mathematical Sociology 29(3):209-232.

Introduction

Formal models have long been used to inform sociological thought.  In the past many of these models have often used the language of mathematics. In essence, sets of variables are related to each other via a system of equations, the values of the variables are interpreted in terms of the intensity or amount of a social phenomenon. In sociology such equations have not been taken in a positivist sense to directly reflect real social intensities or quantities, and the fundamental difficulties of attempting this have been repeatedly pointed out.  Sometimes such systems of equations have closed-form solutions but when this is not feasible their results are simulated. 

However such models have, on the whole, been used as an analogy that can be used to illuminate or illustrate ideas expressed in the richer medium of natural language.  The model only plays a supporting role to the main argument.  In many cases if a paper that uses such a model were re-written without it, the conclusions would not greatly differ.  This is also why the use of analytic solutions (as opposed to numerical simulations) is not greatly important to their use.

Recently a new kind of formal model is being increasingly used: that of the computational model.  This is a model where 'crisp' qualities are modified in a precise way by the action of specified algorithms.  Of course, this is not very new - back in 1969 Thomas Schelling used a simple cellular automata model to demonstrate that even low levels of preference for neighbours of similar race or culture could result in emergent segregation.  This model resembled a board game with black and white counters being moved around a chequerboard according to fixed rules and throws of a die. 

This second type of model has been greatly facilitated (some would say empowered) by the development of the computer.  The computer allows such computational models to be easily built and animated in a fluid and interactive manner.  Thus it allows for such models to be explored and played with in a way that previously would have only been possible for skilled mathematicians. 

The computer has also made it possible to construct and use much more complicated simulations.  This has made possible a type of simulation where individuals are separately represented by parts of the model.  Each of these parts has its own states and can have its own algorithm - the states of these parts can be used to stand for the states of social actors and the messages passed between the parts of the program to represent the interaction between actors.  If the computation of these parts can be interpreted in cognitive terms these parts are often called 'agents'.  Thus we have a style of computational model called agent-based social simulation. 

Agent-based social simulation can thus been seen as a move to a more transparent and accessible style of modelling.  The relation between the model and what it stands for does not require mathematical 'averaging' techniques (as in statistics) but can be very direct: one agent in the model stands for one actor; one message passed from one agent to another in the model stands for one communication or action; on change in the state of the agent stands for one change in the state of the actor; and so on.  This, more direct style of representation in the model makes it far more readily comprehensible.

The transparency and interactive nature of such models endow them with a persuasiveness that 'cold' analytic models do not have.  This has both advantages and disadvantages. On one hand they are more amenable to criticism in both detailed and general terms, but on the other hand they can be seductively misleading.  In particular, it is often unclear with simulation models, how wide their scope is.  That is, it is impossible to tell from a small set of simulation results whether these results are particular or are more widely applicable, even when the algorithm of the simulation is completely specified.

We argue that a simulation should be seen as a formal model of intermediate generality, but one which needs to be treated not as an analytic model but more like a partly understood phenomena.  The simulation does encode a theory which, along with an interpretation can be used to represent some aspects of social phenomena.  However the nature of this theory is one that is only accessible via the experimentation of running the simulation.  Thus to use a simulation as a model of observed phenomena one also needs a theory of how the simulation works.

One consequence of the fact that simulations (as used in sociology) are necessarily experimental objects is that, like other experiments, they need to be replicated before they can start to be trusted.  In this paper we replicate two simulations, and use these replications to start to map out how far their scope extends whilst retaining consistency with their original interpretation.  The two simulations are Schelling's model of racial segregation (Schelling 1969) and Takahashi's model of generalised exchange (Takahashi 2000). Finally we present a new model of generalised exchange that is a modification of Takahashi’s incorporating recently discovered novel “tag” mechanisms (Hales 2000, Riolo 2001). We also map the scope of this model and compare it with Takahashi’s original model. In this latter section we demonstrate how results from different models can be combined into hybrids that throw new light onto on-going debates.

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