Main trends of research in the social and human ... - unesdoc - Unesco

568 Raymond Boudon
economiclevel, etc., and the problem is to use this information to best advantage
for predicting future electoral results.
Hagerstrand’s work3* on the spread of new ideas in an agricultural milieu
provides another example of predictive models. The original model used by
Hagerstrand (a simulated model) can be considered as a more complicated ver-
sion of the logistic model and is of little interest for explication or theorizing
purposes. On the other hand, it turned out to be an excellent tool for prediction.
The complications which Hagerstrand introduced were as follows : firstly,
‘contamination’ is not assumed to be uniformly effective; operationally, this
hypothesis is worked in by assuming that the number of necessaryzcontacts is
symmetrically distributed. Secondly, the probability of an individual i meeting
an individual j is not a constant as with the logistic model, but varies with the
distance between i and j.
No more will be said here about the predictive applications of the regular
statistical methods39 than that it is to be noted specially, with regard to the
problem of prediction, that excellent predictive models can be formulated with
very simple hypotheses: the predictive quality of work like that of Hagerstrand
or of Orcutt is founded on two facts. In both cases, the actual data used are
very numerous, which amounts to introducing into the model a large number
of parameters estimated empirically; secondly, the use of computers makes it
possible to introduce these data - which it would be impossible to study by
analytic (deductive) methods - into a simulated stochastic model.
‘Structural‘ models
The term ‘structural’ can be applied to models which, like those of kinship
structure analysis, aim at analysing the coherence of the elements of a system.
Other examples of this kind of model are the models applied in the analysis of
myths (which at the present time are still on the hither side of real mathematici-
zation) and most of those used in linguistics. Also akin to these are the models
used by genetic epistemology.
The structural type of model is relatively new, and it may well be that it has
an important future in disciplines like sociology or psychology where such
questions as the coherence of collective representations, institutional systems,
and systems of values, just as much as that of individual representations, are
obviously central.
Inductive models as adjuncts of experimentation
As we noted in a preceding section, the introduction of mathematical methods
into the social and human sciences has profoundly modified the nature of
experimentation in certain fields. It will pay us to confirm this as regards
what is probably the most important example: learning theory.
It can justifiably be said that the ‘birth certificates’ of what we can now call
‘the mathematical theory of learning’ are a paper by W. K. Estes,4O and another
by Estes and Burke.4’ Before these researches the mathematical element con-
sisted mainly in attempts to discover the best function to express the relation
between performance and learning,4= an example of the type of application of