COMPUTING SCIENCE

# Statistics of Deadly Quarrels

# Love Thy Neighbor

If the temporal dimension fails to explain much about war, what about spatial relations? Are neighboring countries less likely than average to wind up fighting one another, or more likely? Either hypothesis seems defensible. Close neighbors often have interests in common and so might be expected to become allies rather than enemies. On the other hand, neighbors could also be rivals contending for a share of the same resources—or maybe the people next door are just plain annoying. The existence of civil wars argues that living together is no guarantee of amity. (And at the low end of the magnitude scale, people often murder their own kin.)

Richardson's approach to these questions had a topological flavor. Instead of measuring the distance between countries, he merely asked whether or not they share a boundary. Then, in later studies, he refined this notion by trying to measure the length of the common boundary—which led to a fascinating digression. Working with maps at various scales, Richardson paced off the lengths of boundaries and coastlines with dividers, and realized that the result depends on the setting of the dividers, or in other words on the unit of measurement. A coastline that measures 100 steps of 10 millimeters each will not necessarily measure 1,000 steps of 1 millimeter each; it is likely to be more, because the smaller units more closely follow the zigzag path of the coast. This result appeared in a somewhat out-of-the-way publication; when Benoit Mandelbrot came across it by chance, Richardson's observation became one of the ideas that inspired Mandelbrot's theory of fractals.

During the period covered by Richardson's study there were about 60 stable nations and empires (the empires being counted for this purpose as single entities). The mean number of neighbors for these states was about six (and Richardson offered an elegant geometric argument, based on Euler's relation among the vertices, edges and faces of a polyhedron, that the number *must* be approximately six, for any plausible arrangement of nations). Hence if warring nations were to choose their foes entirely at random, there would be about a 10 percent chance that any pair of belligerents would turn out to be neighbors. The actual proportion of warring neighbors is far higher. Of 94 international wars with just two participants, Richardson found only 12 cases in which the two combatants had no shared boundary, suggesting that war is mostly a neighborhood affair.

But extending this conclusion to larger and wider wars proved difficult, mainly because the "great powers" are effectively everyone's neighbor. Richardson was best able to fit the data with a rather complex model assigning different probabilities to conflicts between two great powers, between a great power and a smaller state, and between two lesser nations. But rigging up a model with three parameters for such a small data set is not very satisfying. Furthermore, Richardson concluded that "chaos" was still the predominant factor in explaining the world's larger wars: The same element of randomness seen in the time-series analysis is at work here, though "restricted by geography and modified by infectiousness."

What about other causative factors—social, economic, cultural? While compiling his war list, Richardson noted the various items that historians mentioned as possible irritants or pacifying influences, and then he looked for correlations between these factors and belligerence. The results were almost uniformly disappointing. Richardson's own suppositions about the importance of arms races were not confirmed; he found evidence of a preparatory arms race in only 13 out of 315 cases. Richardson was also a proponent of Esperanto, but his hope that a common language would reduce the chance of conflict failed to find support in the data. Economic indicators were equally unhelpful: The statistics ratify neither the idea that war is mainly a struggle between the rich and the poor nor the view that commerce between nations creates bonds that prevent war.

The one social factor that does have some detectable correlation with war is religion. In the Richardson data set, nations that differ in religion are more likely to fight than those that share the same religion. Moreover, some sects seem generally to be more bellicose (Christian nations participated in a disproportionate number of conflicts). But these effects are not large.

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