On the Scalability of Social Order - Modeling the Problem of Double and Multi Contingency Following Luhmann

We investigate an algorithmic model based first of all on Luhmann?s description of how so-cial order may originate [N. Luhmann, Soziale Systeme, Frankfurt/Main, Suhrkamp, 1984, pp. 148-179]. In a basic ?dyadic? setting, two agents build up expectations during their interac-tion process. First, we include only two factors into the decision process of an agent, namely, its expectation about the future and its expectation about the other agent's expectation (called ?expectation-expectation? by Luhmann). Simulation experiments of the model reveal that ?social? order appears in the dyadic situation for a wide range of parameter settings, in accor-dance to Luhmann. If we move from the dyadic situation of two agents to a population of many interacting agents, we observe that the order usually disappears. In our simulation ex-periments, scalable order appears only for very specific cases, namely, if agents generate ex-pectation-expectations based on the activity of other agents and if there is a mechanism of ?information proliferation?, in our case created by observation of others. In a final demonstra-tion we show that our model allows the transition from a more actor oriented perspective of social interaction to a systems-level perspective. This is achieved by deriving an ?activity system? from the microscopic interactions of the agents. Activity systems allow to describe situations (states) on a macroscopic level independent from the underlying population of agents. They also allow to draw conclusions on the scalability of social order.