## Saturday, September 22, 2012

### Polarity and War

Over at IntrotoIR, J raises some excellent questions about the work I discussed in my previous post, many of which have to do with the relationship between polarity and war onset.  I was going to respond to him in the comments on his blog, but I realized that I had a lot to say in response to his excellent questions, and readers of this blog might be interested in those comments.

Let me begin by observing that there's a big difference between what is strictly assumed by the mathematics of a formal model and what is assumed by the analyst who uses the model to tell a story.  The argument put forth by an analyst when using a model almost always involves assumptions that are entirely separate from (thought not in contradiction to) those of the model itself.  That is the case in the paper I am writing with Scott and Kyle as it is with most every paper that contains a formal model.

Our model doesn't actually say anything about what form the intervention provided by C and D takes.  All it does is assume that A is more likely to prevail if D "intervenes" than if D does not, and B is similarly more likely to prevail if C intervenes.1 Thus, the model could apply equally to proxy wars like the Iran-Iraq War as well as situations where the major powers directly intervene and come into combat with one another as a result, as seen in the Korean War and the world wars.

The next step of the project, which we haven't yet undertaken, will look at the likelihood of interstate wars expanding to include direct military intervention by major powers.  It would be no less appropriate, though, for us to look at whether outside powers provide material or financial support without deploying troops to the battlefield.  And it would be no less appropriate to look at foreign intervention, of whatever form, into civil wars.  The model has much broader implications than we're going to explore in the paper.

Similarly, the model does not require that C and D be major powers.  We are focusing on the most powerful states in the system because we think the model allows us to say some interesting things about old debates on that front, but the model could easily be used to study conflicts (interstate or civil) where there is an expectation of neighboring states intervening, but not of the great powers doing so.

All the action in the model comes from the relative difference between the outcome A expects to receive when B is likely to receive support from C versus the outcome A expects to receive when B is unlikely to receive support from C.  One thing that influences this is parity between C and D (it's not the only one -- just one that we've chosen to highlight).  When D is much stronger than C, it is very unlikely that C will intervene, because C expects D to do so as well and D's contribution will more than offset C's.2  Since any intervention by D would mean that C will have expended resources without substantially altering the expected outcome, and given that D is likely to intervene in such cases, we typically won't expect C to intervene, regardless of the cost.  And given that C has a powerful material incentive to stay out of the conflict under such conditions, the fact that B has more information than A about C's cost of intervening becomes pretty irrelevant.  A and B will have pretty similar expectations for how the conflict would unfold, and that makes it easy for them to reach an agreement.

When C is much stronger than D, we get a pretty similar story, if for a slightly different reason.  C is willing to intervene under a very broad range of conditions.  D's behavior is almost irrelevant to C, because C can dramatically alter the expected outcome, irrespective of whether D also chooses to intervene.  For this reason, though B has a better sense than A of precisely how costly it would be for C to intervene, they both expect that it is pretty likely that C will intervene.  Having pretty similar expectations about the likely outcome of the conflict, they are likely to reach an agreement.

It is only when C and D are relatively equal in capabilities that B's insight into the likely cost of intervening for C creates a real challenge.  Under such conditions, C's ability to alter the expected outcome of the conflict is moderate.  As a result, the cost of intervening in the conflict will weigh heavily in C's decision of whether to intervene or not, and B's private information about C's cost of intervening becomes very important.

That's what drives everything we have to say about the relationship between the systemic distribution of capabilities and war onset.  A and B are only influenced by B's inside knowledge about C when the thing that B knows is likely to make a difference to the outcome of any conflict between A and B.  And that's most likely to be true when C and D are relatively evenly matched.

Note that the model really only concerns itself with the expected contributions (be they direct or indirect, military or financial) of the two states that are most likely to intervene in the conflict.  In many cases, those states will be major powers, but it won't always be.  IF it is major powers that we're concerned with, what really matters is whether C's ability to alter the outcome of the conflict is moderate (in which case B's private information poses a real challenge to the negotiations between A and B).  When C's ability to alter the outcome is low, it doesn't matter whether it is low because D (and E, and F, and so forth) could easily offset C's contribution or because A is herself a major power or whatever.  When C has the ability to alter the outcome of a military contest between A and B, irrespective of the likely decisions of D (and E and F and so on), it again doesn't really matter to A that B technically has information that she does not about C's cost of intervening because A knows that C will intervene in such cases even when the cost of intervening would otherwise be prohibitive.  And, knowing this, A's expectation of how the conflict would unfold has relatively little uncertainty in it, and the prospects for a peaceful agreement between A and B are quite good.

Thus, the logic behind our argument about war onset implies that unipolarity should be more peaceful than bipolarity.

If we were to extrapolate from this argument, we might reasonably conclude that multipolarity is expected to be more peaceful than bipolarity because C's ability to alter the expected outcome of a conflict will often be negligible when there are multiple other powers who could offset her contribution -- at least, provided that the major powers all have similar spheres of influence and there really is an expectation that each and every  one of them is likely to contemplate intervening in any given conflict.  Insofar as some conflicts, even in multipolar systems, will only be of interest to two of the major powers, the outcome will resemble that expected until bipolarity.

For that reason, our model probably can be said to provide a better explanation of the patterns we've seen historically than I suggested in my post.  To the extent that the frequency of war seems to be roughly increasing over time (see the first graph in my original post), much of that increase comes from the Cold War, which is the only real instance of bipolarity over the last 200 years.

I'm reluctant to read too much on this, however, since I'm extrapolating beyond anything we can actually rigorously derive from our model when I say that multipolarity ought to be more peaceful than bipolarity, with respect to the impact of the distribution of capabilities among the great powers on the likelihood of conflict among other actors.3  Without a 5 or 6 player game, which would be a nightmare to solve, I don't think it would be appropriate for us to do more than speculate about multipolarity briefly in our conclusion.  I'd rather focus on empirical evaluation of patterns that emerge from the model we actually have solved.

If forced to speculate about the likelihood of war in the future under various assumptions about what the distribution of capabilities among the major powers is going to be, though, I'd say that I'm not really sure what the impact of transitioning from unipolarity to multipolarity would be, but I'm reasonably confident that a return to bipolarity would bring an increase in the overall frequency of wars across the globe, even if it was unlikely that the two great powers themselves would come into direct conflict with one another.

1.  That is, a war with A and D against B gives A the best expected outcome and a war with A against B and C gives A the best prospects -- whether a purely bilateral war is expected to produce an outcome that is better for A than a war that involves both C and D depends on the actual capabilities of each state.

2. The relationship between C's ability to alter the outcome of the war and D's ability to alter the outcome of the war is actually weaker than I'm implying here.  I'm speaking as if these patterns are stronger than they are for rhetorical effect.  Even in the context of our simplified model, things are substantially more complicated.

3. Multipolarity might well exacerbate uncertainty among the major powers about their relative capabilities and this might encourage conflict directly between the major powers, relative to conditions of bipolarity.  This might be true even if multipolarity discourages conflicts among minor powers and non-state actors.  Put differently, the claim that bipolarity was responsible for an increase in the overall frequency of war during the Cold War relative to the eras that preceded and followed it need not be seen as contradictory to the claim that major power war is less likely under bipolarity than multipolarity.  There's a lot to sort out here.  A thorough evaluation of the effect of polarity would need to consider the impact of the systemic distribution of capabilities on far more factors than I have considered here.