Reduction and Elimination in Philosophy and the Sciences

Reducing Complexity in the Social Sciences
Meinard Kuhlmann, Bremen, Germany
1. Explanation, Reduction, and Mechanisms
in the Social Sciences
Reductions are attractive since they enhance the unity of
our knowledge and allow for a sparser ontology or conceptual
scheme. Reduction is intimately connected with explanation
since reductive relations between different theories,
i.e. ‘intertheory relations’, figure prominently in at least two
of the main accounts of explanation. According to the covering
law model, explanations of phenomena or special
laws are viewed as derivations from (more) general laws,
or conversely, in their reduction to more general laws. In
the unificationist account, the core of explanations is considered
to be their unifying power. Concerning the explanation
of special laws, for instance, explanation consists in
the overall reduction of independent laws, says the unificationist.
Eventually, certain causal theories of explanations
can also be rated as reductive in the sense that a diversity
of phenomena is subsumed under universal generating
mechanisms.
In the social sciences (i.e. including economics)
methodological individualism, first introduced by Max
Weber, makes a clear and still today very influential claim
about how explanations ought to proceed, namely in terms
of micro reductions to (individual) human actions (see
Udehn 2001 for a comprehensive account). For this
reason it is often said that methodological individualism
expresses a particular version of reductionism, applicable
in the social sciences. Methodological individualism is a
bottom-up approach since the starting point is always the
bottom level of individual constituents. The main thrust of
methodological individualism that matters for my concerns
is the emphasis that social phenomena cannot be
sufficiently understood by analysing statistical correlations
between macro quantities, e. g. macroeconomic variables,
but that it is necessary to refer to the micro level of actors.
However, as I will show below, very often not all micro
details are relevant, and moreover, the attention must not
be restricted to individuals in isolation.
Friedrich August von Hayek, explicitly endorsing
Weber’s doctrine of methodological individualism,
underlined that an understanding of economic phenomena
presupposes explanations in terms of rational actions by
economic agents. Hayek’s ideas must not be
misunderstood as a form of rationalism since he even
emphasizes the limits of rationalism in the sense of social
planning and control, arguing that economic phenomena
often emerge as unintended consequences of the
economic agent’s actions, whose perspectives are always
very limited (cf. Heath 2005). For this reason, systematic
economic analyses should always start by considering the
perspective of the economic agents, i. e. by following the
doctrine of methodological individualism. In the 1980s, the
advent of rational choice theory and in particular of game
theory triggered new debates about methodological
individualism, arguing again that “there do not exist
collective desires or collective beliefs” (Elster 1986: 3).
These ideas shed some light on modern agent-based
models of financial markets, studied among others by
physicists. In both cases it is assumed that the
constituents of the system have no access to information
on the level of the whole system. Nevertheless, the net
effect of all the individual contributions can be large-scale
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structures that seem unexpected given the uncoordinated
behaviour of the constituents.
Explanations in terms of social mechanisms,
advocated among others by Elster, can be seen as a way
to overcome the divide between methodological
individualism and holism, its classical opponent, since they
enable explanations in the middle between microsociological
and macro-sociological research, which is
often desirable for explanatory purposes. They “provide
more fine-grained accounts of social processes than do
macro structural theories, but they do not require a
commitment to the strictures of methodological
individualism” (Pickel 2004: 177). In particular, modeling
with artificial societies combines methodological
individualism on the one side and the search for
mechanistic explanations on the other side. The
corresponding formal manifestation is a “shift from
equation-based modeling to agent-based modeling”
(Sawyer 2004: 263).
In the following I want to reflect upon one particular
strand of agent-based modeling. In the last decade
economists and physicists investigated various so-called
microscopic models of financial markets, for instance the
Kim-Markowitz, the Levy-Levy-Solomon, the Cont-
Bouchaud, the Solomon-Weisbuch, the Lux-Marchesi, the
Donangelo-Sneppen and the Solomon-Levy-Huang model
(see Samanidou et al. 2007 for a review). In the stochastic
multi-agent model of Lux and Marchesi (1999), for
instance, there are two types of traders, ‘fundamentalists’
and ‘noise traders’ (or ‘chartists’). Fundamentalists are
rational traders in the sense that their action is based on
the comparison of the fundamental value of the traded
asset (e.g. stocks, bonds or currencies) and the actual
market price. Fundamentalists buy if the asset is
undervalued, and they sell if it is overvalued. In the case of
noise traders the behaviour only depends on the current
price trend and the opinion of other traders. In the
following I will use this approach as an exemplary agentbased
model.
2. False Models as a Path towards Real
Mechanisms
In non-law-based accounts of explanation, such as Woodward's
(2003) causal approach, models often play a crucial
role in discovering causal relations (also see Glennan
2002). I want to claim that in agent-based explanations,
the identification and understanding of causal mechanisms
is in fact the main function of modelling. Mechanisms are
not simply very detailed descriptions of what is happening,
but their identification is crucial for causal explanations of
why things behave the way we observe them. The specification
of mechanisms is explanatory because it abstracts
from as many details as possible with respect to the explanatory
target. Thus simplicity is a crucial characteristic
of mechanisms and the best way to identify mechanisms in
complex systems is by constructing simple idealized models.
It is not essential that the mechanism is completely
realistic. Gibbard and Varian 1978 point out that even
‘caricature models’ can help to understand certain aspects