Commentary

# How not to estimate the likelihood of nuclear war

As Russia retaliated for Ukraine’s destruction of the Kerch Bridge by launching strikes on energy facilities and civilian targets in Kyiv, commentators returned to the question of whether events were escalating, and whether the world was inching closer to the brink of nuclear war. Probability estimates by these observers have, unsurprisingly, mushroomed as well.

On the high end, these estimates ranged from 10-20 percent to an overly precise 16.8 percent to 20-25 percent for “some analysts.” Some of these headline-grabbing estimates are likely inflated to create a sense of urgency and put pressure on policymakers to take action, rather than to showcase the ability to carefully craft probability estimates. The difference between estimates may simply reflect the prominence of each nuclear scenario in each analyst’s mind.

Here, we lay out the debate over the probability of nuclear use, outlining flaws in current estimates. We offer an alternative approach that focuses on thinking broadly across multiple scenarios and minimizing the rewards of using nuclear weapons, to minimize the possibility of nuclear war.

## Can you put a number on the likelihood of nuclear use?

Predicting the future is hard, and estimating the probability of future events is no exception. Estimating the probability of future events like ones that have occurred many times before is already difficult enough, since — in a complex world — it is difficult to determine which factors decreased or increased the probabilities for past events. For example, the possible causes of Russia’s attacks on Ukrainian civilians span across international, domestic, and psychological explanations.

Trying to estimate the probability of nuclear use is just as difficult — if not more so.  Nuclear scholar and Russian forces expert Pavel Podvig argued along these lines in Newsweek and on Twitter, publicly asserting that nuclear strikes are so rare, it is impossible to calculate their frequency and therefore meaningless to translate that frequency into a probability. Director of the Global Catastrophic Risk Institute Seth Baum noted that Podvig was critiquing frequentist approaches to calculating, which infer how likely an event is to happen based on a sampling of past similar events. He argued that instead, Bayesian approaches – which rely on subjective probabilities that get updated when new information is presented – could be a more helpful way of thinking across multiple different nuclear scenarios, as Baum himself has done in a working paper. Superforecasting, when ordinary people cultivate their intuitive sense for prediction, and which relies in part on good Bayesian updating, is one such approach to nuclear scenarios; Baum’s co-author and superforecaster Robert de Neufville argued in March that there was a 4% chance of at least one fatality from nuclear use by July 1, 2022.

What’s going on here? Is Baum correct that Bayesian approach is the right way to think about nuclear use? And is this war of the nerds helpful in understanding how to avoid nuclear war?

Podvig and Baum are correct that frequentist approaches are definitely not useful here. Estimating the likelihood of a future nuclear war based on how often past nuclear wars occurred is not appropriate, given how rare past nuclear weapons use is.

Bayesian approaches are useful for thinking about adjusting one’s own subjective estimate of probability, but not for informing the actual probability of Putin deciding to use a nuclear weapon. What’s more, there is no way of adjudicating between subjective estimates, and consequently no way of coming up with a combined estimate overall. Even people with the same information may have wildly different guesses: Former U.S. President John Kennedy estimated the odds of nuclear war during the Cuban Missile Crisis to be between one in three and one half, but former U.S. National Security Advisor McGeorge Bundy thought it was one in 100.

Even approaches that attempt to deal with this problem of competing subjective estimates, such as a team of superforecasters working together, cannot work here, since they rely heavily on good estimates of the base rate of an event occurring, which is similarly difficult. As RAND economist Alain Enthoven said to a senior Air Force general, “General, I’ve fought just as many nuclear wars as you have.” Moreover, there is no one in the Kremlin turning the dial up or down, creating an objective change in the probability of nuclear weapons use.

We are also likely to overestimate the likelihood of nuclear war when those estimates are informed by public behavior, because we can’t see the private behavior that would decrease our estimates. Russian leaders have good reasons to make multiple public threats. By increasing other countries’ perception that Russia is willing to use nuclear weapons, the Kremlin increases Russia’s bargaining leverage (although this can also create a commitment trap, where a country that has threatened to use nuclear weapons could be forced to do so in order to remain credible). This means that when numerous threats are made over time, subjective estimations of the probability of nuclear war act as a ratchet, even when the exact same statements are repeated. These estimations cannot take into account unobserved private efforts that are being made to decrease the chance of war.

While we tend to think of nuclear escalation as a ladder, it can be more like an escalator or a vortex, or even a roller coaster. What looks like a terrifying downhill rush towards nuclear war may be balanced out by private counters that slow momentum and return it to level ground: The anticipation of the danger of nuclear use leads actors to try to overcome it. Such recalibrations may be better carried out privately. As U.S. Secretary of State Jake Sullivan noted, “We have communicated to the Russians what the consequences would be, but we’ve been careful in how we talk about this publicly, because from our perspective we want to lay down the principle that there would be catastrophic consequences, but not engage in a game of rhetorical tit for tat.”

It is a mistake for analysts to ascribe a statistical probability for the likelihood of nuclear war, instead of a relative claim (such as “very” or “more than yesterday”). They should also be accompanying estimates with their confidence in the estimate. Yet, many foreign policy experts appear to be far too confident in their assessments. Making a useful probability assessment is impossible under conditions of uncertainty, when we are lacking information about the variety of possible outcomes or the probability of those outcomes.