A statistical model for the duration of wars and strikes

Abstract

This paper proposes an explanation for the observed regularity in the percentage of conflicts settled as a function of time. Each individual conflict is regarded as a probabilistic process in which the impediments to resolution fluctuate continually. Presumably the conflict ends when the barrier to settlement reaches its lowest value. In a sample of similar conflicts, the percentage ending by any particular time should therefore be represented by a distribution of lowest values. The theory of extremes as developed by Frechet, Fisher, Tippett, Gumbel, von Mises, and others is therefore applicable to this situation. This theory indicates that for large sample size, the distribution function will have one of three asymptotic forms depending on the nature of the underlying fluctuations. The particular form found to fit the conflict data analyzed here has been widely used in fatigue and failure studies in engineering, where it is called the Weibull distribution. Because of the generality of the explanation, it is suggested that this sort of model can be applied to other social and psychological processes where the statistics of large populations are involved.