Regensburg 2007 – scientific programme

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 12: Social, Information-, and Production Networks III

AKSOE 12.3: Talk

Thursday, March 29, 2007, 11:15–11:45, H8

Quantifying autonomy and differentiation in social networks - an information theoretic approach — •Eckehard Olbrich, Nils Bertschinger, Nihat Ay, and Jürgen Jost — Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

The modern theory of social systems achieves substantial insights through abstract concepts like differentiation and integration, operational closure or autonomy as exemplified in particular by the work of Niklas Luhmann. Yet these concepts, including the fundamental one of complexity, are only verbally defined and therefore do not yet readily connect with newer developments from network analysis and other mathematically formulated complex systems approaches.

We present a tentative proposal for a quantitative measure of autonomy. This is something that, surprisingly, seems to be missing from the literature, even though autonomy is considered to be a basic concept in many disciplines, including social systems. We work in an information theoretic setting for which the distinction between system and environment is the starting point. As a measure for autonomy, we propose the conditional mutual information between consecutive states of the system conditioned on the history of the environment. Levels of differentiation can be distinguished by using iterated differences of (conditional) entropies that reveal finer and finer distinctions between the behaviors of elements of an interaction network.

In simulations using an abstract model of a social network we show how these measures can be used to study the interrelation between the differentiation of a system and the autonomy of its subsystems.