Opinion Formation — an Elementary Example of Semi-Quantitative Sociology

Abstract

In this chapter the type of model structure to be developed will be illustrated using an explicit example. The model of opinion formation presented here and first introduced to quantitative sociology by one of the authors [1.36, 37], is an appropriate example for the following reasons:

• a) All the relevant types of equation (master equation, Fokker-Planck equation, Langevin equation and mean value equation) and their interrelations can be set up in an elementary, essentially self-contained manner. The illustration therefore serves simultaneously as an introduction to these equations and some of their important properties.

• b) The equations can be solved for relevant situations either exactly or (quite well) approximately.

• c) The solutions illustrate the important processes of phase transition and bifurcation accompanied by critical fluctuations in a most simple way.

• d) The characteristics of the model are stable with respect to detailed and realistic extensions in the modelling of relevant features. It therefore lends itself to a semi-quantitative interpretation of certain political processes.