I have enjoyed the recent exchange between Kroenig and Sechser & Fuhrmann (see here, here, and here).  One interesting point that came up regards the role of conventional military capabilities in determining crisis outcomes.  Kroenig says that the MCT data S&F analyze must be flawed because their results indicate that conventional military capabilities don’t matter whereas we have good reason to believe that the strong do what they will while the weak suffer what they must.  S&F reply that there’s nothing odd about their non-finding because this is precisely what bargaining models predict.  They are essentially correct about that, but I think they fail to appreciate what this very argument implies about their findings regarding the impact of nuclear weapons.

The dependent variable in S&F’s study is whether a challenging state’s compellent threat met with some measure of success.  That’s not necessarily what we’re interested in if we want to evaluate the coercive value of nuclear weapons.

Suppose we have two similar crises: one involving a powerful challenger and one a weak challenger.  In the first case, war between the challenger and the defender is expected to end with the challenger in control of 80% of some disputed territory.  In the second case, war between the challenger and the defender is expected to end with the challenger in control of 20% of the territory.  Suppose further that both challengers are uncertain about how important the issues involved are to the defenders.  For the sake of simplicity, let’s assume in each case that there’s a 50% chance that the defender would consider war so costly that he’d feel as though he lost an additional 10% of the territory and a 50% chance that the defender is so resolved that he views the costs of war as being equivalent to losing merely 1% of the disputed territory.

Our first challenger knows that if she demands anything up to 81% of the territory, the defender will give in regardless of whether he is the more or less resolved type.  Our second challenger knows the same to be true of a demand for 21% or less of the territory.  If the first challenger demands more than 81% but less than 90% of the territory, there is a 50% chance that the defender will give in.  If the second challenger demands more than 21% but less than 30%, there is similarly a 50% chance that the defender will give in.  If the first challenger demands more than 90%, or the second challenger more than 30%, war will occur for a certainty.

Suppose that both challengers value the disputed territory enough that they’d rather risk war in hopes of securing the larger set of concessions.  Finally, suppose that the stronger state’s demand for 90% of the territory is rejected (resulting in a war in which the challenger acquires 80% of the territory) but the weaker state’s demand for 30% is accepted.  Can we conclude form this that strong states are less able to get their way?  Of course not.  And that problem doesn’t go away if you increase the sample size.  If we had 500 crises just like the first, half of which ended with the 90% demands being accepted, and 500 crises just like the second, half of which ended with the 30% demand begin accepted, we’d have systematic evidence that the compellent threats issued by strong states do not meet with success more often than those issued by weak states, but we’d still be unable to infer that conventional military capabilities confer no bargaining advantage.

I don’t think the world is this simple, and the precise numbers above were chosen purely for the purposes of illustration.*  But the point is, recent work on crisis bargaining implies that we cannot evaluate the coercive power of nuclear weapons this way.  States whose compellent threats meet with success more often might well be states who are less willing to bear the costs of war, or might be states who face less uncertainty.  There are a variety of reasons why strategically chosen demands might be more or less likely to be accepted that are independent of a state’s bargaining strength.  Without taking account of the size of the demands, we can’t say anything about the coercive value of either conventional military capabilities or nuclear weapons.

For example, US attempts at compellence often fail.  This might mean that its massive capabilities and vast nuclear arsenal confer no advantages…but it might also mean that the US is so wealthy, and so secure, that it is willing to push its adversaries to the brink with its demands, knowing full well that those demands are not certain to be accepted.

The best way to sort these things out would be to analyse the relationship between marginal changes in the distribution of benefits, on the one hand, and marginal changes the distribution of military capabilities and the distribution of nuclear weapons on the other.  Of course, no one has a good measure of the distribution of benefits, so we can’t do that.  (I suspect that means we’re dealing with a fundamentally unanswerable question, but that’s what the cranky game theorist always says.)

To sum up, S&F are absolutely right that bargaining theory does not lead us to expect a clear relationship between conventional military capabilities and the likelihood of any given compellent threat meeting with success.**  But if we think that states choose the size of their demands strategically, that also means that we can’t evaluate the impact of nuclear weapons on coercion the way either Kroenig or S&F seek to.  What we really want to know is who gets what, not whether their endogenous demands are likely to be accepted.

*I really, really don’t.  As I’ve said before, and will doubtless say again a million times, I analyze simple models because I think they offer useful, albeit partial, insights.

**Depending on the specific assumptions of the model, parity is often be associated with a greater willingness to tolerate rejection with one’s choice of demands.  Thus, there could be a non-monotonic relationship between the distribution of capabilities and the likelihood of acceptance.