How do Non-Linear Relations of Social Macro-Variables Arise from Aggregation of Individual Decisions?

Abstract

ABSTRACT There are three different reasons why non-linear functions between social macro-variables (aggregates) may arise. They can be related to three basic steps of a specific model of explanation of social phenomena, defined by Coleman: the logic of situation, the logic of selection and the logic of transition. Starting with a model of one linear difference equation, a change to three different non-linear system equations can generate stable cycles, bifurcations, and chaos. These non-linear system equations can be deduced from simple assumptions about individual or institutional social attributes. It is shown that a) non-linear individual reactions, b) different selection rules for actors having different social attributes and c) institutional constraints resulting in different transition processes are possible causes for non-linearity at the system level. Furthermore it is demonstrated that the assumption of non-linear but homogeneous reactions of all persons have a similar effect on non-linearity, like it is the case for different selection rules. However, despite of being able to show mathematically the possibility of chaos, it has to be said that chaos as a durable state of social systems is very improbable.