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Statistics of Deadly Quarrels

Brian Hayes

Random Violence

Richardson's war list (as refined by Wilkinson) includes 315 conflicts of magnitude 2.5 or greater (or in other words with at least about 300 deaths). It's no surprise that the two World Wars of the 20th century are at the top of this list; they are the only magnitude-7 conflicts in human history. What is surprising is the extent to which the World Wars dominate the overall death toll. Together they account for some 36 million deaths, which is about 60 percent of all the quarrel deaths in the 130-year period. The next largest category is at the other end of the spectrum: The magnitude-0 events (quarrels in which one to three people died) were responsible for 9.7 million deaths. Thus the remainder of the 315 recorded wars, along with all the thousands of quarrels of intermediate size, produced less than a fourth of all the deaths.

The list of magnitude-6 wars also yields surprises, although of a different kind. Richardson identified seven of these conflicts, the smallest causing half a million deaths and the largest about 2 million. Clearly these are major upheavals in world history; you might think that every educated person could name most of them. Try it before you read on. The seven megadeath conflicts listed by Richardson are, in chronological order, and using the names he adopted: the Taiping Rebellion (1851–1864), the North American Civil War (1861–1865), the Great War in La Plata (1865–1870), the sequel to the Bolshevik Revolution (1918–1920), the first Chinese-Communist War (1927–1936), the Spanish Civil War (1936–1939) and the communal riots in the Indian Peninsula (1946–1948).

Looking at the list of 315 wars as a time series, Richardson asked what patterns or regularities could be discerned. Is war becoming more frequent, or less? Is the typical magnitude increasing? Are there any periodicities in the record, or other tendencies for the events to form clusters?

A null hypothesis useful in addressing these questions suggests that wars are independent, random events, and on any given day there is always the same probability that war will break out. This hypothesis implies that the average number of new wars per year ought to obey a Poisson distribution, which describes how events tend to arrange themselves when each occurrence of an event is unlikely but there are many opportunities for an event to occur. The Poisson distribution is the law suitable for tabulating radioactive decays, cancer clusters, tornado touchdowns, Web-server hits and, in a famous early example, deaths of cavalrymen by horse kicks. As applied to the statistics of deadly quarrels, the Poisson law says that if p is the probability of a war starting in the course of a year, then the probability of seeing n wars begin in any one year is e-ppn/n!. Plugging some numbers into the formula shows that when p is small, years with no onsets of war are the most likely, followed by years in which a single war begins; as n grows, the likelihood of seeing a year with n wars declines steeply.

Figure 3 compares the Poisson distribution with Richardson's data for a group of magnitude- 4 wars. The match is very close. Richardson performed a similar analysis of the dates on which wars ended—the "outbreaks of peace"—with the same result. He checked the wars on Quincy Wright's list in the same way and again found good agreement. Thus the data offer no reason to believe that wars are anything other than randomly distributed accidents.

Richardson also examined his data set for evidence of long-term trends in the incidence of war. Although certain patterns catch the eye when the data are plotted chronologically, Richardson concluded that the trends are not clear enough to rule out random fluctuations. "The collection as a whole does not indicate any trend towards more, nor towards fewer, fatal quarrels." He did find some slight hint of "contagion": The presence of an ongoing war may to some extent increase the probability of a new war starting.

Figure 4. Distribution of wars in time . . .Click to Enlarge Image

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