Ukraine Post #8: Risk of Nuclear War

It seems worth going through the exercise of estimating the probability of nuclear war, and in particular the probability of it causing one’s death. If the probability gets high enough, one can strongly consider being elsewhere or otherwise doing something about it.

Note that all scoring rules and wagers are essentially useless here. You can look back and decide whether your reasoning was good, but saying ‘I was right’ is meaningless.

As a baseline to work from, this EA forum post presents multiple perspectives on nuclear war risk in terms of the danger of being in London, with the author of the post modeling risk as relatively high, versus some superforecaster predictions that modeled risk as relatively low. The forecasts are divided into steps.

1. Will there be a conventional exchange between NATO and Russia?
2. Will there be a nuclear exchange?
3. If there is a nuclear exchange will it hit London?
4. If it does will you have to get out?
5. If you don’t get out, will you die?
6. (Alternate path) Background risk of accidental nuclear war, which is higher when everyone is on alert.

If you multiply the odds of each step together, you get the level of danger from being in London. The level of danger in New York City should be similar.

Aside from the chances of the bomb killing you if it lands, these differences all point in the same direction, with two of them being on different sides of 50%. It is an interesting exercise to read the arguments, and to decide on one’s own opinion on each leg.

Probability of conventional war

There are two ways to get a conventional war. Russia could attack NATO and cause NATO to invoke Article 5 without an intervention in Ukraine, or NATO could decide to intervene in Ukraine.

We have a Metaculus market on whether a NATO country will invoke Article 5 by the end of the year and it is sitting at 5%. That seems reasonable.

I think there is a modest chance that Article 5 is technically invoked but there is nominal fighting, and there is a similar chance that NATO does something crazy and intervenes first for whatever reason. 5% here seems fine.

Dynamics of nuclear deterrence have changed

In the Cold War, both sides felt NATO had woefully inadequate conventional forces, and would need to resort to either lose or use nuclear weapons within weeks if the Warsaw Pact invaded Western Europe.

This has now reversed. Russia’s conventional forces have been exposed. Both sides now believe (correctly) that NATO has vastly superior conventional forces, and could easily repel a conventional Russian attack on NATO. At worst, Russia could make temporary gains in the Baltics.

Thus, I put the chances of NATO dropping the first nuclear weapon at epsilon. NATO has no reason to open Pandora’s box when it can win a conventional war.

I wouldn’t quite put the chance of Putin not knowing that NATO will never drop the first nuclear weapon at epsilon, but I remain very highly confident he knows this. Russia would have to use nuclear weapons first, knowing NATO would never use one first.

I would also put the chances of conventional NATO military invasion of Belarus or Russia, beyond at most necessary incidental incursions during a war over the Baltics or Poland, to be essentially epsilon, for the same reason. Russia is credibly threatening to respond to such attacks with nuclear weapons, even if ‘they started it’ and we have no interest in putting that to the test. Even in a hot conventional NATO/Russia war caused by a Russian invasion, I would expect us not to put troops even into Ukraine because we would not have to.

Putin thinks the West is weak. In some senses he is wrong, but in an important sense he is very right. One does not need to threaten the West with the mass destruction of its cities to make outcomes unacceptable to us. The only reason we would have the stomach to fight a hot war with Russia is if not doing so would break our commitments and thus the entire world order. Thus it is also unacceptable.

That is a very different situation than the Cold War. Only Russia might use the first nuclear weapon, they are under no threat of conventional invasion, and they know this, that NATO is not going to jump that gun even in a hot war. I don’t care what our official doctrine says, that’s ambiguity directed at China and even there it’s almost certainly a bluff (but that almost can make a big difference).

Russia still might choose to use a nuclear weapon, either to escalate-to-deescalate because Ukraine (or being able to claim a symbolic victory) was sufficiently existential, or because Putin thinks the West will simply fold.

Then there is the question of further escalation. Suppose Russia has used at least one nuclear weapon. Will it go strategic?

That depends on a lot of things, most obviously what we do in response. Even then, assuming the use by Russia was tactical and does not threaten to turn the tide of battle, I presume that we almost certainly don’t use our nukes on them at all nor do we conventionally strike at Russian territory.

Using a nuclear weapon in response, or even conventionally striking Russia, is not necessary. We can win a conventional war even if Russia uses some number of tactical nuclear weapons, and the diplomatic fallout would be immense especially if we did not answer in kind. Instead, I expect Russia to face additional conventional firepower combined with complete diplomatic and economic isolation, losing all the friends it has left with the possible exception of Iran. Our current sanctions may or may not pack sufficient punch, but the ultimate version of them really, really would pack quite a ton of punch. Russia would also be facing vastly superior conventional firepower, but we would have no desire to go to Moscow.

The logic of nuclear escalation is completely different when one side has zero interest in escalation even in the face of extreme provocation, because they have faith that they don’t need to do it and would not benefit from it.

Yes, if they hit central London with multiple warheads we would likely have to hit back in kind, but that begs the question.

There is little or no risk Russia would feel the need to do a first strike as pre-emption, out of fear that they are about to get hit first instead or perhaps lose their capabilities.

What are the remaining potential reasons?

1. We need to worry about whether Putin will decide to go full outright nuclear apocalypse on his own, out of spite or other madness, and in turn whether his ministers and crews would cooperate with that if he tried.
2. We need to worry Putin somehow thinks he can ‘win’ via the widespread use of tactical nuclear weapons in a conventional sense, despite them having little utility in Ukraine. I don’t see how this works.
3. We need to worry Putin uses nuclear weapons as escalatory blackmail, expecting the West to fold. Perhaps he thinks if he keeps dropping nukes we will back down and give him whatever he wants, and he is willing to make that gamble such that he forces a nuclear response. But to back down in the face of nuclear blackmail would be the end of the world soon enough in its own way, so we can’t fold in the way Putin would like here. ‘The West actually folds in response’ beyond a cease-fire is so unlikely I’m not even considering it. But what we do maybe need to worry about is that Putin’s mafioso nature is so warped that if he drops a nuclear weapon and we don’t respond with one, he treats that as a green light to use more of them and/or directly test Article 5. In which case, either he is truly insane (which is case 1) or the intention is to back down if we do retaliate which we would at some point have to do.
4. We need to worry about a ‘escalate-to-deescalate’ move where the goal is a cease-fire aimed at keeping territorial gains, which only works if it doesn’t go strategic, and at most results in ‘all right you get your cease fire’ at the cost of complete and permanent isolation.

Note on defensive capabilities (can be skipped)

Dominic Cummings has written extensively lately about the historical logic of Cold War deterrence strategies, and our decision to intentionally be unable to defend against a Soviet nuclear attack. We adopted Schilling’s theory that by staying defenseless, we gave the other side hostages and thus created a stable strategic situation.

It turns out that a lot of our assumptions about Soviet thinking and deterrence dynamics were false. There were also numerous close calls. We were very lucky to survive the Cold War, in a ‘no time travelers allowed to go back before 1991’ kind of way.

I notice that in the new world, with its new dynamics, this more obviously nonsense.

What we need is for it to be clear to other nuclear states that the United States will be deterred from attacking because the cost of their retaliatory strike is unacceptable. Maybe not completely for those with a lot less than six thousand nukes, but quite a lot. Given our levels of risk tolerance, this is very much way over all our thresholds. The incentive this gives other nations to get nukes is unfortunate, but that ship has sailed. We expected during the Cold War for Russia to be deterred by the possibility that we might fight a nuclear war over Berlin. Thus, we do not need certainty that we can be devastated, or to maximize the pain. We merely need there to be the possibility that we would take unthinkable losses.

Whereas if the other state actually uses its full nuclear stockpile, now they both have really pissed us off and untied our hands, and are defenseless, with no chance that we would lose our second strike capabilities. And if they try to launch some nuclear weapons and they fail then that too leaves them fully exposed.

In that world, unless I am missing something, a probabilistically successful missile defense system is wonderful. Which describes every missile defense system. You never know if it is going to work until it is tested.

If you try to launch your nuclear weapons, you have to worry that it might not work, which would be the end. Total disaster. Imagine if Putin tried to use some of his nukes and we found out they hadn’t maintained them any better than his conventional army and they no longer work. Or that we can actually shoot them down. Or the crews refused to fire. Or they’ve been hacked and now we know it worked. Now suddenly maybe we do launch the bombers or march on Moscow.

Thus, as per Shilling’s logic, the uncertain situation helps in both directions. We remain deathly afraid of provoking a nuclear strike if we back the enemy into a corner, but the enemy is strongly deterred from actually launching without being backed into a corner, because they risk collapse of their deterrent.

Another argument was that if the Soviets saw us about to deploy a missile defense system they might attack us first. Cold War logic made that coherent. In today’s conditions it no longer seems coherent to me. Such things are continuous and probabilistic, there is no practical threat of anyone losing their deterrent value any time soon only some of their blackmail value. The blackmail move has already been tried. The cost of trying to stop the defense system from happening seems absurd in the modern world. The better argument is that others might then feel the need to expand their offensive capabilities to get around the defenses, and China is especially worrisome here, but again I see a probabilistic deterrent here as better on all sides – it is something they would absolutely use if under existential threat, but which is now that much riskier to use otherwise.

Others have thought about these questions a lot more than I have, and I am sure all of this is in some sense terribly naïve. But then again, from what I can tell, past decisions on these questions did not have a sounder basis, and also are the people currently making these decisions thinking about such issues at all? Dominic Cummings frequently points out that no one in government takes nuclear security seriously, and then points out this means they take nothing seriously. It also has direct bearing on questions like this.

Certainly improving mitigation capabilities such as bomb shelters and emergency supplies seems clearly good. During the Cold War, the logic was that doing such things might make the Soviets think we thought that a nuclear war was thinkable, so we should avoid it. At this point, that logic is obvious nonsense. If we had better protections and thus a nuclear war killed 50 million Americans instead of 100 million while potentially creating nuclear winter, frying our electronics and leaving massive radioactive fallout, would that suddenly make it thinkable for us? If we also had a backup system that wouldn’t be fried and still had cell phones and computers, would that make it thinkable? If we had ALLFED’s emergency foodstuffs ready to go?

No. Obviously not. But it would make nuclear blackmail somewhat less effective, and if the worst did happen it would make it less bad. Logic no longer reverses itself, and we should look to cost-benefit. We depend on the world and on ‘regular order’ far too much to not be well-deterred from existentially messing with nuclear states. Being even more vulnerable makes threats and escalations more attractive, and increases risk that things go wrong, while also increasing the negative consequences of things going wrong. There is much talk in Russia that the West will lose because they are not willing to risk nuclear war, which in turn is causing that very risk to rise.

That does not mean that any given mitigation plan is worth its cost. As always, one must talk price.

Probably a lot of that is wrong and perhaps stupid, but it is at least thinking about the situation at all, which is something I otherwise do not see.

Back to the original question at hand.

Probability of nuclear use

What is the probability it goes nuclear? Well, how would it go nuclear? An accident is one possibility, but if it is not an accident, what happened?

I would presume that Russia is attacking NATO, and NATO is defending itself, as noted above without substantially invading Russia. Using a nuclear weapon offensively against NATO while not under attack, if NATO stayed out of Ukraine and Belarus as well, goes against all stated policies and all reason and I put this probability as rather low. Even if Putin wanted to do it, I’d put a large probability that he was refused, especially if he tried to go strategic.

But it might be different if Russia attacked NATO and then NATO sent forces into Ukraine, so the question is whether NATO would do that in response, and then whether Russia would use a nuke in that situation. I don’t think Ukraine would like it if NATO still wouldn’t enter Ukraine with its troops, but that is what I expect would happen for exactly this reason. I’d only give at most a ~25% chance that we’d take that risk, although we would step up military aid short of this.

Given the probabilities here, I obviously agree with this expected path. That is especially true given I would expect Ukraine to win anyway, since we are siphoning off much of Russia’s strength while increasing our levels of aid, and nuclear weapons are of little practical use in Ukraine.

So let’s say in the 75% of cases where we stay out Russia has a 5% chance of using a nuclear weapon anyway because if they attacked at all Putin might be nuts and be allowed to go nuts, and a 50% chance they use it if we do go into Ukraine given the evidence of the attack on NATO. So that’s about 17% chance, conditional on a war, that Russia uses the first nuclear weapon.

I will note that I don’t buy that risk is evenly distributed throughout the year. If Russia is going to launch an attack I think it more likely happens sooner.

5% times 17% is 0.85% (85bps) of risk of first use, plus the background risk of accidental use that is not covered above, but that goes on a distinct track since it could cause unintentional escalation to the strategic level, or could be something less dangerous than an intentional launch.

Probability nuclear use becomes strategic

So what we need to worry about isn’t stepwise nuclear escalation and whether we can do things like trade cities. We have to worry that Putin launches one nuke, we don’t give in, so he launches another, then another, or a lot of them. If it’s the first scenario, he skips to full apocalypse at the start.

I’m going to go with 25% chance that Putin is crazy enough to go all the way, conditional on him willing to drop the first nuclear weapon.

In all these scenarios, there is also a substantial chance that Putin tries to use the nukes and is told no. I realize this could be called wishful thinking. I certainly wouldn’t rely on it, but in terms of probabilities, trying to launch strategic nukes while not under direct attack (no matter what he might call an intervention in Ukraine) and without enemy nuclear use seems like it’s only maybe 50% to get carried out. I’m going to combine ‘Putin is not allowed to launch one nuke’ into this 50%.

If we instead are so foolish to respond to Russia’s first use with our own use or a strategic conventional attack on Russia itself, I don’t like our chances for de-escalation after that and presume Putin would probably be allowed to proceed, but I see this as rather unlikely. What would even be the point? Still, we can be this kind of stupid and I want to be appropriately uncertain here, so maybe 20% chance, and after that the 65% chance things go all the way.

Thus, a 13% (20%*65%) chance of escalation via us being stupid, and a 10% chance (80%*25%*50%) via Putin being crazy and allowed to strike, adding up to 23%, so that’s an 0.2% (23%*0.85%) chance of Putin attempting escalation within a year.

Chance of getting out

This seems underspecified. At what point on the risk curve is this person deciding to leave? What is their trigger? If they leave now, their chances are very very good.

Presumably the trigger that makes sense here is the start of the conventional war between Russia and NATO. The other trigger is the first nuke.

If it’s the first trigger, then I think the chances of a person who wants to get out getting out are very good, unless actual everyone tries to leave at once, in which case it’s a capacity question and a how-long-did-it-take-to-escalate question. If you’re informed on the level of making these plans I think you’re a strong favorite to get out and the 25% risk seems fair. There is still some chance that escalated quickly.

If you wait until the first nuclear weapon, that’s different, because a lot of the risk is that the others fly very quickly and also yes at this point the streets are going to be mobbed disaster-movie style. A 70% risk seems fair here.

There is also the question of what it means to ‘get away.’ A random location in the UK is better than an apartment in London, and a random rural area in America is better than New York or Washington, but how much better? I ask because I do not know, and this ties into the last question.

In practice few of us know what our threshold would be, so for simplification purposes I am going to split the difference and call this a 50% shot, for an 0.1% chance of being there when the nuke hits.

Chance of dying

Here is where their forecasts align, but they do not adjust for the fact that someone who is considering these questions can adjust their behavior even if they are stuck in London or New York. If it is worth considering leaving, it is worth having a plan for where to take shelter and packing an emergency bag, and knowing what to do. I haven’t studied in detail, but I know what the very basics are, and assuming I got an alert soon after the missiles launched and I was at home, I know I would be able to make it reasonably deep into a subway tunnel along with the rest of the family. Given the chances there are six thousand other nukes, to me this is not obviously worse than being in a random town in Kansas with no plan, although it is obviously worse than a town in Kansas plus a properly stocked properly constructed bomb shelter, and obviously worse than hiding out some place safe in the southern hemisphere. But where are you going to go, Detroit?

A lot of people won’t even do the basics, so I am going to say that you can at least knock this down to a coin flip and a 50% shot, and also even if you leave your chances of survival are very much not 100%, especially if you are still in the UK or continental USA. So at most, we are talking about an 0.05% risk (5bps), or 1 in 2000, over the next year.

There are a few places where I am guessing my estimates are high or I could give reasons to lower the answer, but model uncertainty is also a thing. I’m going to let those basically cancel out here.

That puts me in between the two estimates above. For the next month, I would say there is about a basis point (0.01% or 1bp) of risk. The longer things go on without escalation, the less likely that escalation is imminent, a lot of war is Lindy.

Comparing this to the two estimates above, the existing two estimates are 0.2bps (0.002%) and 3.7bps (0.037%).

This should make us some combination of happy (we are in the middle of two well-intentioned estimates) and also somewhat suspicious (that I went looking for a ‘reasonable’ conclusion on some level). It should also be a clear mix of reassuring (in some sense risk is not so high) and also utter terror (in another sense risk is really super-frighteningly high).

Practical bottom line

This is about the annual risk of death for someone who is 56 years old, so it is no joke, but it also clearly does not rise anywhere close to the level where I would be willing to seriously consider not living my life.

I am not in the ‘I do not want to survive a nuclear war’ camp. I very much would want to survive and for my family to survive, but I would acknowledge that the utility available would be much reduced, which is a further discount on effective practical downside risk from being in the wrong place and thus dying.

What I find most interesting is that the logical pathways I am thinking about seem distinct from those either of the other two forecasts were thinking about. The conflict’s exact details and paths of escalation seem important to me, more so than questions like where everyone is aiming missiles or our general ‘skills at de-escalation.’ It seems hard for things to actually go nuclear or go fully strategic now in a crisis like this, in a way that it doesn’t retrospectively feel hard when thinking about the cold war even knowing it did not happen. The strategic dynamics are very different. Still possible, certainly, but hard.

If you told me a strategic nuclear war happened in 2022 anyway, my presumption would be that it was not an accident or a situation that slowly got away from everyone. Rather, it would be that it happened either because Putin actively decided he would start a global thermonuclear war rather than face defeat at the hands of Ukraine or because we were stupid enough to interfere in Ukraine directly and things escalated from there.