Mathematical Analysis of War
Richardson also applied his mathematical skills in the service of his pacifist principles, in particular in understanding the basis of international conflict. For this reason, he is now considered the initiator, or co-initiator (with Quincy Wright and Pitirim Sorokin as well as others such as Kenneth Boulding, Anatol Rapaport and Adam Curle), of the scientific analysis of conflict-- an interdisciplinary topic of quantitative and mathematical social science dedicated to systematic investigation of the causes of war and conditions of peace. As he had done with weather, he analyzed war using mainly differential equations and probability theory. Considering the armament of two nations, Richardson posited an idealized system of equations whereby the rate of a nation's armament build-up is directly proportional to the amount of arms its rival has and also to the grievances felt toward the rival, and negatively proportional to the amount of arms it already has itself. Solution of this system of equations allows insightful conclusions to be made regarding the nature, and the stability or instability, of various hypothetical conditions which might obtain between nations.
He also originated the theory that the propensity for war between two nations was a function of the length of their common border. And in Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950), he sought to analyze the causes of war. statistically Factors he assessed included economics, language, and religion. In the preface of the latter, he wrote: "There is in the world a great deal of brilliant, witty political discussion which leads to no settled convictions. My aim has been different: namely to examine a few notions by quantitative techniques in the hope of reaching a reliable answer."
In Statistics of Deadly Quarrels Richardson presented data on virtually every war from 1815 to 1945. As a result he hypothesized a base 10 logarithmic scale for conflicts. In other words, there are many more small fights, in which only a few people die, than large ones that kill many. While no conflict's size can be predicted beforehand—- indeed, it is impossible to give an upper limit to the series—- overall they do form a Poisson distribution. On a smaller scale he showed the same pattern for gang murders in Chicago and Shanghai. Others have noted that similar statistical patterns occur frequently, whether planned (lotteries, with many more small payoffs than large wins), or by natural organization (there are more small towns with grocery stores than big cities with superstores).
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