Reduction and Elimination in Philosophy and the Sciences

of the world. It only matters that certain structural features
are modelled, such as interaction between the parts of a
multi-agent system or the possibility of strategy change.
Once these features are incorporated, the employed
microscopic models of financial markets may be
surprisingly unrealistic in various other features. For
instance, microscopic models of financial markets abstract
from material details about traders and transactions that
are considered as irrelevant for understanding the basic
features of financial markets (‘Aristotelian idealization’).
But microscopic models of financial markets also involve
certain distortions, which simplify the situation considerably
(‘Galilean idealization’). Moreover, playing around with
numerous different more or less unrealistic models has the
advantage that it is possible to single out exactly which
structural mechanisms are responsible for the statistical
effects one wants to explain (see Morgan 1999 for a
related conclusion). In contrast, an approach with a
detailed realistic model might not reveal what it is that is
actually crucial for the explanation (cf. Wimsatt 1987 and
Cartwright 1983). My point is that agent-based models
help to explain by concentrating on significant structural
features while there is hardly any pretence to realism in
many other respects. Batterman (2004) has a similar point,
when he argues that highly idealized and oversimplified
models can sometimes be better for the explanation of the
dominant phenomenon than a detailed model in terms of
micro-constituents.
3. Complexity and Robust Mechanisms in
Agent-Based Models
Roughly, I understand a complex system not as an object
with a complicated compositional structure but rather as an
object with highly non-trivial dynamical features, on the
basis of a structurally simple arrangement of a large number
of non-linearly interacting constituents. One example is
dynamical multi-agent systems in socio-economic contexts,
which deal with ‘microscopic’ agents in a very simple
arrangement and with a very simple individual behaviour.
Whereas for a classical mechanism it is usually easy to
predict its behaviour once the compositional structure and
the behaviour of its parts is known, this is radically different
in the case of complex systems. Here the knowledge of the
compositional structure, e.g. spins on a square lattice,
together with the knowledge of the behaviour of its parts in
isolation as well as in simple composites, allows for hardly
any straightforward predictions of the dynamical behaviour
of the complex system.
Although higher-level interactions and thereby
higher-level mechanisms are ultimately ontologically
determined by the underlying physics, higher-level
mechanisms are explanatorily autonomous. For instance, if
financial market crashes were described in terms of the
material processes that obtain between investors and their
telephones, traders and their computers, electronic
processes within the computer system of the NASDAQ
etc., then the mechanisms involved in a crash could never
be appropriately understood. As it turns out it is sensible to
abstract so much from these material manifestations that it
is possible to realize that the same mechanisms obtains in
other contexts, notably in statistical physics (see Kuhlmann
2006). These consideration show that it can be extremely
important for explanations, in particular for explanations in
terms of mechanisms, not to eliminate level-specific
vocabulary, notions and methods.
For mechanistic explanations in agent-based
complex systems, the occurrence of the type of dynamical
Reducing Complexity in the Social Sciences — Meinard Kuhlmann
higher-level pattern one wants to explain, e.g. a statistical
phenomenon, must be robust. The qualification type of
pattern is essential since in complex systems the single
tokens of a dynamical pattern are usually not robust due to
the high sensitivity to variations of the initial conditions. In
contrast to a classical mechanism like a thermostat, from
which we expect a predictable output in each single case
of its working, mechanisms in complex systems mostly do
not generate token outcomes that we can predict, but
rather bring about a certain type of outcome. But when it
comes to the explanation of statistical features, the
sensitivity to variations of the initial conditions in each
single case dissolves in the collective statistics, which is
not sensitive to such perturbations, provided the
explanation is successful. To put it the other way around: a
mechanistic explanation of a statistical phenomenon in a
complex system is only successful if the resulting collective
statistics of many simulation runs is not sensitive to
perturbations of the system’s parameters in a reasonable
range of values. If this condition were not fulfilled one
would rather classify the phenomenon as an artefact of the
model, which does not help to identify an explanatory
mechanism.
4. Structural Mechanisms
The above considerations show that a more abstract structural
conception of mechanisms is prerequisite for understanding
explanations in complex systems theories. The
notion of mechanisms I want to suggest applies to many
cases in the social sciences but also in physics, and biology,
as far as they are complex systems in the sense I
specified abobe. Currently, mechanisms are often discussed
on the basis of case studies about biological systems
(see e.g. Machamer, Darden, and Craver 2000).
Naturally, this brings about limitations in the applicability. I
propose the following more general notion of a mechanism
in a complex system:
A property of the time-dependent relation between
locally interacting lower-level components and a
higher-level quantity of a complex system is a candidate
for a mechanism if it fulfils the following requirements:
(i) The dynamics of the higher-level
quantity exhibits a discernible type of pattern, which
we want to be explained. (ii) The occurrence of this
type of higher-level pattern is robust, i.e. it remains
qualitatively the same under small variations of
lower-level quantities.
My emphasis on the local nature of interaction is meant in
the following way. If the occurrence of the higher-level
pattern was due to an external influence with a global effect,
e.g. a coordinating external force on all constituents,
then I think one should not say that the higher-level pattern
was generated by a mechanism. In other words, the
higher-level pattern must emerge purely out of the interaction
of the system’s constituents.
I want to illustrate my characterisation of mechanisms
in complex systems for the above-mentioned multiagent
model by Lux and Marchesi. The higher-level quantity
is the price of some asset, e.g. a stock, currency or
bond, and the corresponding example for interacting
lower-level components are traders in the respective financial
market. An example for a discernible pattern in the
dynamics of this higher-level quantity is the so-called ‘volatility
clustering’, i.e. the tendency of quiet and turbulent (or
‘volatile’) periods to cluster together. The agent-based
explanation of this phenomenon rests on idealized assumptions
about the relation between interacting lower-
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