Modeling the Size of Wars.doc

Modeling the Size of Wars From Billiard Balls to Sandpiles* Lars-Erik Cederman Department of Government, Harvard University 1737 Cambridge St. Cambridge, Mass. 02138 cederman@ Phone: (617) 495-8923 January 20, 2002 VERSION 3.0. COMMENTS WELCOME! Abstract: Richardson’s finding that the severity of interstate wars is power-law distributed belongs to the most striking empirical regularities in world politics. As with earthquakes, there are many small events, fewer large ones, and a very small number of huge disasters. Yet, this is a regularity in search for a theory. Drawing on the principles of self-organized criticality, I propose an agent-based model of war and state-formation that exhibits power-law behavior in terms of war severity. As a step toward developing systematic non-equilibrium theory of world politics, the model illuminates the underlying mechanisms responsible for generating the regularities. In the current framework, wars spread due to states’ contextual reassessments of their balance-of-power relationship. The source of such changes is modeled as stochastic decision-making and two types of technological change, namely increases in states’ resource extraction and offensive shocks. *) Earlier drafts of this paper were prepared for presentation at the University of Michigan, the University of Chicago, and Ohio State University. I am grateful to the participants of those meetings and to Robert Axelrod and Claudio Cioffi-Revilla for excellent comments. Laszlo Gulyas helped me reimplement the model in Java and Repast. Needless to say, I bear the full responsibility for any inaccuracies and omissions. Since Richardson’s (1948; 1960) pioneering statistical work, we know that casualty levels of wars are power-law distributed. As with earthquakes, there are many events with few casualties, fewer large ones, and a very small number of huge disasters. More precisely, power laws tell us that the size of an event is inversely proportional to its frequency. In oth