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An approach to modelling and inference based on Axelrod's Ising model of alliance formation

Alliances have critical value. This observation is especially pertinent given the dynamics of the most recent conflicts of our time. Traditional military modeling and simulation has focused on understanding the dynamics of the physical aspects of conflict. This is in contrast to role-playing games in which the formation of alliances is essential to victory (take Diplomacy as the perennial example and the modern game SuperPower as a recent example). It therefore seems reasonable to consider the formation of alliances as a subject that warrants modelling and simulation-based research. This paper outlines and extends a political science approach to modelling the formation of alliances, termed landscape theory. Landscape theory was formulated by the political scientist Robert Axelrod and is based on the Ising model of statistical mechanics. Between each nation or group an interaction propensity is calculated measuring the level of inter-nation influence and support. This propensity can range from positive values, in which nations are affable to negative where hostility exists. It is this collection of propensities that determines the global alliance structure. In Axelrod's model, the nation or group is characterised by a measure of its size or influence along with its propensities. Alliances are specified by defining a distance between the group or nation. The collection of distances between the nations is termed the configuration. If the distance between two nations is zero then they are considered to be in the same alliance. If greater than zero, then the nations are in different alliances. Given a collection of nations and propensities, any given configuration of alliances induces an energy function, which is the Ising equation of statistical mechanics. This function is a measure of the collective tension between nations. The principal of alliance prediction is based on the assumption that nations or groups seek to minimise this collective tension. Nations can alter their alliance structure by altering their configuration of distances. They seek to minimise the distance with nations that share a positive propensity and distance themselves to nations that have a negative propensity. Collectively, this process minimises the energy (Ising) function. Thus to predict a stable alliance configuration, given a set of nations and the corresponding propensities, the energy function is minimised and the resulting configuration is viewed. Our contribution is to extend landscape theory by a number of methods for calculating propensity based on importance weighted attributes from national statistics or historical data. Such attributes could include import/export levels, religious commonality, or data concerning past conflicts. These methods are applied to a dataset derived from hypothetical international data to make predictions of alliance structures. Methods for adjusting the importance of different attributes that make up the propensity values, in light of new alliance data are then briefly discussed. Here, a predicted structure does not match the outcome and therefore the adjustment of attribute importance is vital. Finally, we discuss future topics of research in the modelling of alliance formation.