Logo IMG


Statistics of Deadly Quarrels

Brian Hayes

"Thinginess Fails"

The catalogue of conflicts in Statistics of Deadly Quarrels covers the period from about 1820 until 1950. Richardson's aim was to count all deaths during this interval caused by a deliberate act of another person. Thus he includes individual murders and other lesser episodes of violence in addition to warfare, but he excludes accidents and negligence and natural disasters. He also decided not to count deaths from famine and disease associated with war, on the grounds that multiple causes are too hard to disentangle. (Did World War I "cause" the influenza epidemic of 1918–1919?)

Figure 2. Magnitude of a war . . .Click to Enlarge Image

The decision to lump together murder and war was meant to be provocative. To those who hold that "murder is an abominable selfish crime, but war is a heroic and patriotic adventure," Richardson replies: "One can find cases of homicide which one large group of people condemned as murder, while another large group condoned or praised them as legitimate war. Such things went on in Ireland in 1921 and are going on now in Palestine." (It's depressing that his examples, 50 years later, remain so apt.) But if Richardson dismissed moral distinctions between various kinds of killing, he acknowledged methodological difficulties. Wars are the province of historians, whereas murders belong to criminologists; statistics from the two groups are hard to reconcile. And the range of deadly quarrels lying between murder and war is even more problematic. Riots, raids and insurrections have been too small and too frequent to attract the notice of historians, but they are too political for criminologists.

For larger wars, Richardson compiled his list by reading histories, starting with the Encyclopaedia Britannica and going on to more diverse and specialized sources. Murder data came from national crime reports. To fill in the gap between wars and murders he tried interpolating and extrapolating and other means of estimating, but he acknowledged that his results in this area were weak and incomplete. He mixed together civil and international wars in a single list, arguing that the distinction is often unclear.

Figure 3. Frequency of outbreaks of war . . .Click to Enlarge Image

An interesting lesson of Richardson's exercise is just how difficult it can be to extract consistent and reliable quantitative information from the historical record. It seems easier to count inaccessible galaxies or invisible neutrinos than to count wars that swept through whole nations just a century ago. Of course some aspects of military history are always contentious; you can't expect all historians to agree on who started a war, or who won it. But it turns out that even more basic facts—Who were the combatants? When did the fighting begin and end? How many died?—can be remarkably hard to pin down. Lots of wars merge and split, or have no clear beginning or end. As Richardson remarks, "Thinginess fails."

In organizing his data, Richardson borrowed a crucial idea from astronomy: He classified wars and other quarrels according to their magnitude, the base-10 logarithm of the total number of deaths. Thus a terror campaign that kills 100 has a magnitude of 2, and a war with a million casualties is a magnitude-6 conflict. A murder with a single victim is magnitude 0 (since 100=1). The logarithmic scale was chosen in large part to cope with shortcomings of available data; although casualty totals are seldom known precisely, it is usually possible to estimate the logarithm within ±0.5. (A war of magnitude 6±0.5 could have anywhere from 316,228 to 3,162,278 deaths.) But the use of logarithmic magnitudes has a psychological benefit as well: One can survey the entire spectrum of human violence on a single scale.

comments powered by Disqus


Of Possible Interest

Computing Science: Computer Vision and Computer Hallucinations

Feature Article: Candy Crush's Puzzling Mathematics

Feature Article: The Statistical Crisis in Science


Foreign-Language PDFs


Subscribe to American Scientist