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But then, knowing that many of the hypotheses that researchers are obliged
to assume may not hold in the real world, and could therefore lead to deceptive
conclusions and theories, does this type of modelling representation preserve its
advantages? Quoting G.F. Shove, it could be the case that sometimes “it is better to
be vaguely right than precisely wrong”.
The third symbolic system, computer modelling, opens up the possibility of
building models that somewhat lie in between the descriptive richness of natural
language and the analytical power of traditional formal approaches. This third type
of representation is characterised by representing a model as a computer program
(Gilbert and Troitzsch 1999). Using computer simulation we have the potential to
build and study models that to some extent combine the intuitive appeal of verbal
theories with the rigour of analytically tractable formal modelling.
In Axelrod’s (1997a) opinion, computational simulation is the third way of
doing science, which complements induction, the search for patterns in data, and
deduction, the proof of theorems from a set of fixed axioms. In his opinion,
simulation, like deduction, starts from an explicit set of hypotheses, but, rather than
generating theorems, it generates data that can be inductively analysed.
While the division of modelling techniques presented above seems to be
reasonably well accepted in the social simulation community—and we certainly
find it useful—we do not fully endorse it. In our view, computer simulation does
not constitute a distinctively new symbolic system or a uniquely different reasoning
process by itself, but rather a (very useful) tool for exploring and analysing formal
systems. We see computers as inference engines that are able to conduct algorithmic
processes at a speed that the human brain cannot achieve. The inference derived
from running a computer model is constructed by example and, in the general
case, reads: the results obtained from running the computer simulation follow (with
logical consistency) from applying the algorithmic rules that define the model on
1
the input parameters used.
In this way, simulations allow us to explore the properties of certain formal
models that are intractable using traditional formal analyses (e.g. mathematical
analyses), and they can also provide fundamentally new insights even when such
analyses are possible. Like Gotts et al. (2003), we also believe that mathematical
analysis and simulation studies should not be regarded as alternative and even
opposed approaches to the formal study of social systems, but as complementary.
They are both extremely useful tools to analyse formal models, and they are
complementary in the sense that they can provide fundamentally different insights
on one same model.

1
By input parameters in this statement, we mean “everything that may affect the output of the
model”, e.g. the random seed, the pseudorandom number generator employed, and, potentially,
information about the microprocessor and operating system on which the simulation was run, if
these could make a difference.