Arms Races

Lewis Richardson’s work has dominated serious discussion of arms races and its conspiratorial cousins of war profiteering and the military-industrial complex as the cause of war since the publication of his Statistics of Deadly Quarrels in 1960 seven years after his death.

First, Richardson identified key concepts as the basic independent and dependent variables. Think of the former as inputs and the latter as outputs. Second, he made specific assumptions about the relationships among the variables. For example, he sensibly assumed that the more difficult and costly it was to produce a weapon, the fewer there would be. Third, he put these assumptions into mathematical form—that is, he attempted a parsimonious explanation of the phenomenon under study. This was common practice in the physical sciences but relatively new to social scientists when Richardson was doing his research. He wrapped everything up in a formula for country or alliance x reacting to a potential enemy y:

That is, the change (dx) in armament levels of nation or alliance x over time (dt) is a function of the reaction to the threat of another country (ay), the difficulty and expense of producing armaments (mx) and the extent and severity of accumulated grievances (g). A similar equation represents the other side:

Finally, he collected historical data on the independent variables (ay, bx, mx, nx, g and h) to determine if his theory described reality.

· The two sides move quickly to a stable equilibrium. This happens when factors such as cost outweigh the accumulation of grievances.

· The sides move quickly toward disarmament when goodwill outweighs grievances: g and h are negative. Braking factors and costs outweigh reactivity.

· The runaway arms race happens when accumulated grievances and reactivity (a and b) outweigh the braking factors (m and n).

· The result could be either disarmament or runaway arms race depending on initial armaments levels.

How well does the model meet the criteria for good theory (Chapter 1)? First, Richardson predicts all three possible outcomes of an arms race and throws in a fourth to cover anything he might have missed, with little guidance as to which is the most likely.

Second, Richardson did all his analysis based on the conditions leading up to World War 1, so his evidence is limited to a specific time and place in human history. Third, there were not just two countries involved in World War I, so they must either be reduced to the two main alliances (ignoring neutrals), or the same formulas repeated for each. The first oversimplifies and the second sacrifices parsimony and results in ambiguity.

Fourth, as is drilled into any first-semester statistics student, correlation does not prove causation. It is true that vast increases in arms expenditures preceded World War I. French and British spending on armaments doubled, and German spending increased tenfold. But, non-defense spending increased even faster. Furthermore, nations that never got into World War I, such as Sweden and Switzerland, also vastly increased their arms spending.

Fifth, and most important, we now have access to the minutes of German cabinet meetings leading up to World War I, and we now understand that Germany knowingly risked a general European war but hoped for a limited one. That is, the war was neither accidental nor unforeseen. In short, the increased armaments did not change or drive policies of the regimes amassing them. WWI was not accidental, unforeseen, or caused by the preceding arms race.

Sixth, in subsequent debates, only one of the four possibilities commonly receives any credence—that arms races lead to war. The other three are ignored or downplayed. In this vein, the Fall 1960 Canadian Army Journal reported that:

Computations made on an electronic computer by a former president of the Norwegian Academy of Sciences, aided by historians from England, Egypt, German and India, have produced some astounding figures on the frequency and severity of wars. Included in these findings is the fact that since 3600 B.C., the world has known only 292 years of peace. During this period there have been 14,531 wars, large and small, in which 3,640,000,000 people have been killed. The value of the destruction would pay for a golden belt around the earth 156 kilometers in width and 10 meters thick. Since 650 B.C. there have been 1656 arms races, only 16 of which have not ended in war. The remainder have ended in economic collapse.

It may be true as is commonly said that there have only been 292 years (or some similar small number) of total peace—but most wars were local and most of the world was at peace at any given time. Even World War II left South America and most of Africa untouched (although some troops from both did participate, primarily those from British and French colonies). If instead of counting countries at war one counted the number of states at peace each year, war would appear rare. For example, since 1815, approximately 150 states never have been at war and approximately 50 experienced only one or two brief ones.

The real interest of this article is in the way arms races were defined, identified, selected, and assessed—none of which is explained in the one paragraph article printed above in its entirety. My inquiry directed to the Norwegian Academy requesting a reprint or source for the original research resulted in a handwritten reply on a Post-it note attached to the original letter (Figure 12.2). The editor of the Canadian Army Journal declined explanation. No better reason for skeptical reading, replicating research, and the importance of verification and falsification emphasized in Chapter 1 could have come to light!

In a modification of arms race theory, Michael Intriligator (2000) proposed taking greater account of economies of scale and changes in technology. As Lewis Richardson anticipated, “Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians' stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.”