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Mathematical models and methods 563
tioning of groups, use mathematics of widely different types, and have unlike
functions. Without going into details, let us look at some examples of models
applied in this domain.
First of all we find models derived from laboratory experiments on the
mechanisms of influence within groups. The most famous experiment in this
field is Ash’s consisting in exposing a ‘naive’ subject to a sequence of stimuli
in order to elicit alternately correct and incorrect answers, while the other mem-
bers of the group, who in fact are ‘accomplices’ of the experiment, systematically
give the wrong answers. This experiment has been formalized by Cohen in an
ingenious mode1,32 in which the answers given by the subject of the experiment
are assumed to depend on the state in which he is. There are 4 such states:
I. Absorbing non-conformism (an absorbing state in the sense of the theory
of Markov chains: the subject who achieves this state at the nth test wil give
non-conformist responses in all subsequent tests) ;
2. Temporary non-conformism (there is some degree of probability that the
subject achieving this state wil move to state I in the following test, and
some degree of probability that he wil move to state 3;
3. Temporary conformism (the exact reverse of (2) above);
4. Absorbing conformism.
To put it in different terms, the model leads up to the definition of a Markov
chain between 4 latent states. The transition probabilities of this model can be
estimated by iterative methods. A good fit has usually been obtained between
the curves of the observed and of the theoretical responses. As can be seen, we
have here a model whose theoretical apparatus ties in with a highly specific
experimental situation.
Other attempts at formalization - using graph theory - are associated with
experiments which are akin to Ash’s but are of a more general type: the question
is not how an individual reacts to an opinion advanced unanimously by the rest
of the group, but how he modifies one of his opinions according to the links he
maintains with the rest of the group, the opinions of these others and his own
opinions on themes having a logical connexion with the opinion under consid-
eration. The theory underlying these formalization attempts is that an individ-
ual seeks to equilibrate his social ties and his opinions at the least cost.
Many instances could accordingly be cited of models dealing with the forma-
tion of individual opinions in social situations. But at the time of writing formal-
ization is not sufficiently advanced to allow us to speak in terms of a general
theory: all we find is a collection of relatively unconnected specific models, none
of which has yet engendered a genuine research line.
Apart from the models treating of the formation of opinions within thepgroup,
models are to be found which analyse the functioning of groups, the best-known
of which is perhaps Simon’s.33 Here again, the picture is one of dispersed and
unrelated probings.
These different examples are sufficient to show that theoretical mathematical
models take different forms according to the particular discipline in the social
and human sciences. Game theory is of course the only example of a theory
whose subject-matter is formally defined and whose developments consist in a