“Small World” Paradigm in Social Sciences: Perspectives and Problems

Ugo Pagallo


Since the idea of small worlds first appeared in the pioneering work of Stanley Milgram and later with the sociological research of Mark Granovetter, it has grown to become one of the central figures of interdisciplinary research involved with understanding the evolution of social systems in the digital age. It is sufficient to refer to the mathematical model of the small world offered by Duncan J. Watts and Steven Strogatz, published on «Nature» in 1998, not to mention the development of the theory in Linked. The New Sciences of Networks by Albert-László Barabási (2002) which proved how and why the small world-phenomenon needs to be read at the light of “free scale” laws. Recently, the small world paradigm has found interesting applications within fields such as law. In 2005, the noteworthy study of Seth Chandler outlined a network of links between the United States Supreme Court cases where the result was a complicated web resembling a map of cities linked by dozens of airlines where you could see which nodes were likeliest to fall on the shortest paths between two other nodes. Significant results have also been obtained in the related work by James Fowler and Sangick Jeon on the historical development of American jurisprudence from a small world-perspective.

The aim of my paper would be to widen and refine such a small world-model by taking into account and allowing for the algorithmic theory of information developed by the American mathematician Gregory Chaitin with whom I have been collaborating over the last years. Such an enriched model would, in fact, be adequate to analyze changing features in social interaction which are outstandingly increasing in the digital age. The area of application of the model would hence be in legal and social sciences, but might also have some encouraging effect on interdisciplinary work. Whereas I have already presented some important empirical and theoretical results of the new perspective in fields such as EU legal system and/or P2P networks, it is also relevant to stress some interesting results concerning glocalization.

First and foremost, the small world-paradigm on the background of Chaitin’s mathematical conclusions has some interesting consequences on the social level, as far as reducing complexity of the environment is considered. In deed, the phenomenon we get is all the more complex as the quantity of information grows and its theoretical compression decreases. This circumstance opens new perspectives for the analysis of the evolution of such complex systems as political and legal ones. These latter systems have been evolving in innovative ways because of the well-known paradigm-crisis of State Sovereignty and International Law in connection with the E-revolution in Technology. By using a small world-paradigm instead of more traditional political and legal models we can comprehend and interpret the ongoing glocalization in Roland Robertson’s phrase, for it seems possible to determine how centers or main-cores of the old world do work in the complex web of contemporary political and legal decisions.

Such nodes, in effect, appear to be quite similar to hubs as far as their functioning is considered. Accordingly to its mathematical model, a hub’s effectiveness depends on its grade of complexity, so the more information a hub is capable of handling on the basis of its own composite linked structure, the greater its impact on the whole. The model I am proposing could therefore give a significant contribution to the understanding of glocalization, since reducing exponentially grades of separation between nodes via hubs – treated as channels of globalization – places local and often antithetical nodes-worlds in a nearer connection. More over, these legal and political hubs cannot be adequately understood as part of the same communicative level: related to the algorithmic theory of information, the small world-model consequently offers a normative criteria on which ground it becomes possible to charter and arrange the hubs. Actually, social systems seem to be all the more capable of reducing environmental complexity and hence optimizing their functioning via hubs, as they involve a greater and more complex structure within each node of the system.

What seems to be of major importance about the small world-model, from a ICT-perspective, is not only the objective shortage of applied scholarly work in traditional legal and political science, nor the possibility to develop a well-grounded model for future case studies and reports, but mostly that it gives the opportunity to experimental assessment of the new world order both in legal and social terms. Whereas it is possible to decide as a matter of fact what have been (and are) the semantic hubs within a particular context, i.e., within a legal and political culture, such a viewpoint also necessitates a discussion about which are, practically speaking, the significant hubs in Today’s world and what centers of traditional decision-making may be filtered out as less-connected cases in the network as a whole.