The Better Angels of Our Nature: Why Vio - By Steven Pinker Page 0,135

in psychology called Weber’s Law: for an increase in intensity to be noticeable, it must be a constant proportion of the existing intensity. (If a room is illuminated by ten lightbulbs, you’ll notice a brightening when an eleventh is switched on, but if it is illuminated by a hundred lightbulbs, you won’t notice the hundred and first; someone would have to switch on another ten bulbs before you noticed the brightening.) Richardson observed that people perceive lost lives in the same way: “Contrast for example the many days of newspaper-sympathy over the loss of the British submarine Thetis in time of peace with the terse announcement of similar losses during the war. This contrast may be regarded as an example of the Weber-Fechner doctrine that an increment is judged relative to the previous amount.”68 The psychologist Paul Slovic has recently reviewed several experiments that support this observation. 69 The quotation falsely attributed to Stalin, “One death is a tragedy; a million deaths is a statistic,” gets the numbers wrong but captures a real fact about human psychology.

If escalations are proportional to past commitments (and a constant proportion of soldiers sent to the battlefield are killed in battle), then losses will increase exponentially as a war drags on, like compound interest. And if wars are attrition games, their durations will also be distributed exponentially. Recall the mathematical law that a variable will fall into a power-law distribution if it is an exponential function of a second variable that is distributed exponentially.70 My own guess is that the combination of escalation and attrition is the best explanation for the power-law distribution of war magnitudes.

Though we may not know exactly why wars fall into a power-law distribution, the nature of that distribution—scale-free, thick-tailed—suggests that it involves a set of underlying processes in which size doesn’t matter. Armed coalitions can always get a bit larger, wars can always last a bit longer, and losses can always get a bit heavier, with the same likelihood regardless of how large, long, or heavy they were to start with.

The next obvious question about the statistics of deadly quarrels is: What destroys more lives, the large number of small wars or the few big ones? A power-law distribution itself doesn’t give the answer. One can imagine a dataset in which the aggregate damage from the wars of each size adds up to the same number of deaths: one war with ten million deaths, ten wars with a million deaths, a hundred wars with a hundred thousand deaths, all the way down to ten million murders with one death apiece. But in fact, distributions with exponents greater than one (which is what we get for wars) will have the numbers skewed toward the tail. A power-law distribution with an exponent in this range is sometimes said to follow the 80:20 rule, also known as the Pareto Principle, in which, say, the richest 20 percent of the population controls 80 percent of the wealth. The ratio may not be 80:20 exactly, but many power-law distributions have this kind of lopsidedness. For example, the 20 percent most popular Web sites get around two-thirds of the hits.71

Richardson added up the total number of deaths from all the deadly quarrels in each magnitude range. The computer scientist Brian Hayes has plotted them in the histogram in figure 5–11. The gray bars, which tally the deaths from the elusive small quarrels (between 3 and 3,162 deaths), don’t represent actual data, because they fall in the criminology-history crack and were not available in the sources Richardson consulted. Instead, they show hypothetical numbers that Richardson interpolated with a smooth curve between the murders and the smaller wars.72 With or without them, the shape of the graph is striking: it has peaks at each end and a sag in the middle. That tells us that the most damaging kinds of lethal violence (at least from 1820 to 1952) were murders and world wars; all the other kinds of quarrels killed far fewer people. That has remained true in the sixty years since. In the United States, 37,000 military personnel died in the Korean War, and 58,000 died in Vietnam; no other war came close. Yet an average of 17,000 people are murdered in the country every year, adding up to almost a million deaths since 1950.73 Likewise, in the world as a whole, homicides outnumber war-related deaths, even if one includes the indirect deaths from hunger and disease.74

FIGURE 5–11. Total deaths from quarrels of different magnitudes

Source: Graph