Russia has invaded Ukraine.

Mar 6 JDN 2459645

Russia has invaded Ukraine. No doubt you have heard it by now, as it’s all over the news now in dozens of outlets, from CNN to NBC to The Guardian to Al-Jazeera. And as well it should be, as this is the first time in history that a nuclear power has annexed another country. Yes, nuclear powers have fought wars before—the US just got out of one in Afghanistan as you may recall. They have even started wars and led invasions—the US did that in Iraq. And certainly, countries have been annexing and conquering other countries for millennia. But never before—never before, in human historyhas a nuclear-armed state invaded another country simply to claim it as part of itself. (Trump said he thought the US should have done something like that, and the world was rightly horrified.)

Ukraine is not a nuclear power—not anymore. The Soviet Union built up a great deal of its nuclear production in Ukraine, and in 1991 when Ukraine became independent it still had a sizable nuclear arsenal. But starting in 1994 Ukraine began disarming that arsenal, and now it is gone. Now that Russia has invaded them, the government of Ukraine has begun publicly reconsidering their agreements to disarm their nuclear arsenal.

Russia’s invasion of Ukraine has just disproved the most optimistic models of international relations, which basically said that major power wars for territory were over at the end of WW2. Some thought it was nuclear weapons, others the United Nations, still others a general improvement in trade integration and living standards around the world. But they’ve all turned out to be wrong; maybe such wars are rarer, but they can clearly still happen, because one just did.

I would say that only two major theories of the Long Peace are still left standing in light of this invasion, and that is nuclear deterrence and the democratic peace. Ukraine gave up its nuclear arsenal and later got attacked—that’s consistent with nuclear deterrence. Russia under Putin is nearly as authoritarian as the Soviet Union, and Ukraine is a “hybrid regime” (let’s call it a solid D), so there’s no reason the democratic peace would stop this invasion. But any model which posits that trade or the UN prevent war is pretty much off the table now, as Ukraine had very extensive trade with both Russia and the EU and the UN has been utterly toothless so far. (Maybe we could say the UN prevents wars except those led by permanent Security Council members.)

Well, then, what if the nuclear deterrence theory is right? What would have happened if Ukraine had kept its nuclear weapons? Would that have made this situation better, or worse? It could have made it better, if it acted as a deterrent against Russian aggression. But it could also have made it much, much worse, if it resulted in a nuclear exchange between Russia and Ukraine.

This is the problem with nukes. They are not a guarantee of safety. They are a guarantee of fat tails. To explain what I mean by that, let’s take a brief detour into statistics.

A fat-tailed distribution is one for which very extreme events have non-negligible probability. For some distributions, like a uniform distribution, events are clearly contained within a certain interval and nothing outside is even possible. For others, like a normal distribution or lognormal distribution, extreme events are theoretically possible, but so vanishingly improbable they aren’t worth worrying about. But for fat-tailed distributions like a Cauchy distribution or a Pareto distribution, extreme events are not so improbable. They may be unlikely, but they are not so unlikely they can simply be ignored. Indeed, they can actually dominate the average—most of what happens, happens in a handful of extreme events.

Deaths in war seem to be fat-tailed, even in conventional warfare. They seem to follow a Pareto distribution. There are lots of tiny skirmishes, relatively frequent regional conflicts, occasional major wars, and a handful of super-deadly global wars. This kind of pattern tends to emerge when a phenomenon is self-reinforcing by positive feedback—hence why we also see it in distributions of income and wildfire intensity.

Fat-tailed distributions typically (though not always—it’s easy to construct counterexamples, like the Cauchy distribution with low values truncated off) have another property as well, which is that minor events are common. More common, in fact, than they would be under a normal distribution. What seems to happen is that the probability mass moves away from the moderate outcomes and shifts to both the extreme outcomes and the minor ones.

Nuclear weapons fit this pattern perfectly. They may in fact reduce the probability of moderate, regional conflicts, in favor of increasing the probability of tiny skirmishes or peaceful negotiations. But they also increase the probability of utterly catastrophic outcomes—a full-scale nuclear war could kill billions of people. It probably wouldn’t wipe out all of humanity, and more recent analyses suggest that a catastrophic “nuclear winter” is unlikely. But even 2 billion people dead would be literally the worst thing that has ever happened, and nukes could make it happen in hours when such a death toll by conventional weapons would take years.

If we could somehow guarantee that such an outcome would never occur, then the lower rate of moderate conflicts nuclear weapons provide would justify their existence. But we can’t. It hasn’t happened yet, but it doesn’t have to happen often to be terrible. Really, just once would be bad enough.

Let us hope, then, that the democratic peace turns out to be the theory that’s right. Because a more democratic world would clearly be better—while a more nuclearized world could be better, but could also be much, much worse.