The world is a complicated place. Even if we limit our attention to the world’s countries—and in so doing, ignore other vital actors like non-governmental organizations, firms, political parties, and many others—we have nearly 200 entities to study. As it happens, those entities care about a lot of things: resources, policies, regimes, and so on. They also interact with one another in many ways: trades, wars, declarations, sanctions, alliances, threats, summits, votes. And, these countries interact over time and space and context. In other words, studying international relations (IR) is tricky, in no small part because of the world’s inherent complexity.

This is also why IR is so much fun.

My job as an IR theorist is to try to develop lenses—particularly in the form of mathematical models—to help see the world more clearly. Just like a cinematographer uses a different lens for a long shot than she would for a close-up, so too do IR scholars use different lenses for different types of analysis. In IR, the most common lenses are designed for close-ups. We often reduce our analytic attention to two countries, a single issue, and only one or two forms of interaction. In so doing, we can seize upon some of the most pressing questions in international relations: Why do countries fight? Why do they trade? How do competing industries within a given country influence trade policy?

This shared commitment to close-ups has taught us a lot about these forms of association, but they’ve also stripped away some of the world’s beautiful complexity. In contrast, the lenses I develop are designed to capture the world’s grandeur: the models include all the world’s countries, along with all the world’s issues, and multiple means of interaction. Compared to most extant models out there, my approach ignores a lot of the fine details, but it also gains a lot of perspective.

In particular, I study how countries engage in simultaneous exchange and conflict. The former takes the form of global markets, while the latter takes the form of war. The model incorporates lots of information about the world: each country’s endowment of resources, and their preferences over all the issues, and their production, militarization, and battlefield technologies. Using all this information, the model then predicts each country’s wealth, power, final consumption levels, and wars with one another. The idea is to get a “birds-eye” view of the world—a wide shot, rather than a close-up.

But what I hadn’t been able to do, up to this point, is figure out what change, evolution, and dynamism look like in the mathematical worlds I construct. When viewed on this grand scale, does the international system evolve slowly and continuously, or does it necessarily require abrupt changes, disruptions, revolutions? From a mathematical point of view, I didn’t even know how to look at the problem for a few years.

This past spring, I had one of those eureka moments and realized that an answer wasn’t too far away. So, over the course of a coffee-fueled weekend, I began and finished a new research note entitled “Smooth International Systems.” The paper’s results suggest that the world is indeed capable of evolving smoothly when its underlying factors do. For example, if the world’s resources increase or decrease slowly over time, then so too do trade and war, wealth and power, conflict and exchange. The same goes for technologies and preferences.

In general, I view this as a positive result: “discontinuous,” abrupt change gets a bad rap, often under the names of “revolution,” “revolt,” “volatility,” or “instability.” If the world cannot change smoothly, then international institutions can’t design robust policies, since any small (and inevitable) deviations from a proposed plan will lead to significant changes in the outcomes. Volatility also hinders the ability to amend policies on the fly, since it rules out some candidate compromises.

Now, that isn’t to say all good things go together. For starters, many of us would tolerate an abrupt change if it led us to a fantastic outcome—how beautiful would it be to wake up tomorrow to a world without war, with stable financial institutions, without bloodshed? My paper indicates that this scenario is tough to pull off from the birds-eye view, but that we have hope to design policies to take us there over time.

I also can’t say much about what happens if disruptions happen in the world’s underlying inputs (the resources, the preferences, and the technologies). While resource endowments do evolve slowly, other factors don’t: notably, production technologies, militarization technologies, and battlefield technologies are all subject to rapid change. If that happens, my result has little to offer for guidance.

Finally, the research note is a bit abstract, and it’s natural to wonder what the “real-world” punchline is. One nice thing about abstract models is that they help us to see exactly what assumptions were made and how they were used to drive the analysis. In this case, the assumptions are very weak, meaning that the results hold in a wide variety of contexts. What is more, if these smoothness results weren’t true even in a mathematical utopia, then they surely wouldn’t hold up in the real world!

Nevertheless, it is heartening to know that the model that I’ve developed over the years is indeed capable of providing some insight about the nature of change in the international system. Our brains are hard-wired to think the most about discontinuities like the wars, revolutions, and bubbles mentioned before. But most of the time, most of the world is not subject to these abrupt discontinuities. I hope my work can help us to learn more about the calm changes, and also to learn how to avoid the not-so-calm ones through the design of robust policies.

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Robert Carroll is an assistant professor in the Department of Political Science. He studies international relations. 

 

 

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