Bargaining or Breakthrough?

By Matthew Kocher

The Imperial German Chief of Staff Erich von Falkenhayn is said to have intended to bleed the French white at the Battle of Verdun. The French held at Verdun, and in that sense Falkenhayn’s attrition strategy can be said to have failed. Nevertheless, it was based on some reasonable assumptions: Germany had a manpower advantage over France, both in total numbers and rate of growth. Germany also consistently killed enemy soldiers at higher rates than they killed Germans. Moreover, attrition strategies are sometimes effective: casualties build and build, with no apparent benefit to either side until, suddenly, one side’s resolve or resources are exhausted.

In his excellent working paper, Harvard graduate student Jeff Friedman identifies a general class of cumulative causal processes that differ from the more common (or more commonly recognized) class of repeated causal processes. He calls them “breakthrough problems.” In repeated processes, the effects of a policy are consistent in each time period; long-run consequences can be reliably judged from short-term effects. Breakthrough problems are different. A consistently applied policy may fail to work period after period until suddenly its accumulated effects produce a major change.

Friedman’s insight has important implications for the way we think about war. The dominant theoretical approach among political scientists over the past decade and a half is based on the so-called ‘bargaining framework,’ in which warring parties go through a series of discrete stages, each of which conveys important information about the strength and determination of the other side. Once the two sides’ beliefs about the likely costs and outcome of the war converge sufficiently, they should be able to conclude a bargain that ends the war and gives each side what they would likely have won (or lost) without paying the additional costs of fighting on.

But, what if war works more like a breakthrough problem than a bargaining problem? Fighting might not convey much useful information at all. In fact, Friedman shows formally that in breakthrough problems rational actors can become increasingly optimistic about the likely success of their strategy as time passes without success. This sounds a little crazy when you first think about. But, Friedman points out that if you are in the middle of a breakthrough problem, much of the total cost of getting to a breakthrough is already sunk (so you shouldn’t care about it), and your remaining cost until the breakthrough is achieved keeps falling. That’s a reasonable basis for optimism.

Friedman applies this insight to a dataset he built about the American Indian Wars. This is a nasty business, but he makes a reasonable case for thinking of these wars as breakthrough problems in which all tribes eventually gave in once English or American forces imposed enough damage on them. The strategic problem is that the English and Americans had little objective basis for judging which tribes could sustain a large amount of damage and which would give in quickly. In the small number of instances in which the tribes held out for many years, this attrition strategy might appear irrational. But, if these wars were truly breakthrough problems, then the English and Americans were right (in purely instrumental terms) to be optimistic year after year that their approach would eventually work. With the benefit of hindsight, we know they were correct.

What about Falkenhayn? Let’s assume for the sake of argument that WWI battles, and the war overall, were breakthrough problems (after all, the Entente did eventually achieve a breakthrough). At Verdun, German optimism over months and months of unprecedented slaughter achieved nothing more than a pitiful few kilometers of territory. Ultimately, it was German resolve to continue the offensive that buckled.

To my mind, all this suggests a central role for uncertainty in the analysis of war, something the bargaining framework has largely banished. Falkenhayn appears to have faced uncertainty over not only French strength and determination, but also that of his own army and political system. If that’s correct, then rationality may yield less in the way of understanding war than the most recent generation or two of political scientists have tended to think.

Friedman apparently has quite a bit more to say about breakthrough problems in his Harvard dissertation. I’ll be interested to see how far down the rabbit hole he goes.