3.1 Likelihood

Consider the current state of analysis for assessing the likelihood of nuclear war. In 2005, the office of Senator Richard Lugar published The Lugar Survey on Proliferation Threats and Responses (hereinafter, the Lugar survey), which addresses the risk of nuclear use (Lugar, Reference Lugar2005). Among the questions asked in the survey was, “What is the probability (expressed as a percentage) of an attack involving a nuclear explosion occurring somewhere in the world in the next ten years?” The distribution of replies from 79 respondents is shown in figure 2.

Figure 2 The Lugar survey, question 5.

What is most striking about figure 2 is the divergence of opinion. Responses span the full spectrum from 0 to 100%, with the mode occurring at 1–9%, but with only 18 respondents selecting that bin. From a classical statistics perspective, the true probability lies in only one unknown bin. The fact that most experts’ answers missed that value, whichever bin it lies in, means that most experts must necessarily be wrong. There are a number of possible explanations for this. One reason for the wide variation could be the lack of control of biases in the elicitation of the answers. Without bias control, experts can interpret and think differently about how to answer the question, resulting in wide variability. Even if biases are controlled, wide dispersion can still occur because of high uncertainty in the current state of knowledge. In any event, the most significant conclusion to be drawn from figure 2 is that there is no consensus on the answer to the question.

In other respects as well, the Lugar survey did not follow best practices in elicitation and analysis (Meyer & Booker, Reference Meyer and Booker2001; see also Ayyub, Reference Ayyub2001). While each survey respondent was presumably an expert in some aspect of nuclear policy, arguably no single person is truly an expert on all the factors that must be considered when answering broadly phrased questions such as that depicted in figure 2.Footnote ⁵ Additionally, the survey provides no information about the experts’ assumptions, reasoning, and uncertainties. Such information could, for example, be useful in understanding the apparently anomalous peak at 50–59% and the extremes of 0 and 100%. The cumulative impact of these and other deficiencies is that the survey falls short of what could be achieved by using best practices in expert elicitation.

Another exercise in characterizing the likelihood of nuclear war has been ongoing since 1947, when the Doomsday Clock first appeared on the cover of the Bulletin of Atomic Scientists (2019a). The setting of the clock is intended to represent how close the world is to nuclear war, metaphorically midnight. The clock was originally set at seven minutes to midnight and has been reset periodically every several (1 to 7) years. As shown in figure 3, the time of greatest danger – two minutes to midnight – was set in 1953 after US and Soviet hydrogen bomb tests, while the time of least danger, seventeen minutes to midnight, was set in 1991 after the START Treaty was signed and unilateral initiatives on both sides removed many nuclear weapons from “hair-trigger” alert (Bulletin of the Atomic Scientists, 2019b).

Figure 3 The Doomsday Clock, 1947–2004. The clock indicates then-current perspectives of the Bulletin of the Atomic Scientists on the dangers of nuclear war. Since 2007, dangers associated with climate change and developments in the life sciences have been added. Source: Public domain image via Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Doomsday_Clock_graph.svg.

There are multiple problems with taking the clock seriously as an assessment of the likelihood of nuclear war. In setting the clock, there could be motives beyond accurately characterizing the nuclear threat, such as to promote certain policies, especially with respect to arms control treaties, or simply to draw attention to the Bulletin of the Atomic Scientists. The process by which the clock is set is obscure, although brief summaries of the reasons for changing the clock’s setting have been provided (Bulletin of the Atomic Scientists, 2019b). No attempt has been made to define the clock’s scale, which is almost certainly nonlinear. Does ten minutes to midnight indicate half the probability of five minutes to midnight? And finally, the clock is unable to reflect the risks associated with short-duration, high-risk episodes, such as the Cuban missile crisis of 1962 and the coup attempt against Gorbachev in August 1991 (Pry, Reference Pry1999). Ironically, the former occurred during a period of declining risk, according to figure 3, and the latter occurred during the period of least risk.

Notwithstanding these points, the Doomsday Clock does seem to have captured the broad trends in the nuclear threat as it derives from the international political climate. Gaining a better understanding of the processes by which the clock has been set could prove useful in developing more scientific approaches. Unfortunately, the clock’s future utility as an indicator of the risk of nuclear war has been diminished since 2007 by the inclusion of climate change and harmful developments in the life sciences as additional harbingers of doomsday.

Several individuals have also estimated the likelihood of interstate nuclear war or nuclear terrorism. Selected estimates are summarized in Table 1. Most are subjective judgments, such as Kennedy (Sorensen, Reference Sorensen1965), Bundy (Reference Bundy1988), Allison (Reference Allison2004), Perry (Kristof, Reference Kristof2004), Albright (Hegland & Webb, Reference Hegland and Webb2005), and Garwin (Garwin, Reference Garwin2007) without a formal underlying analysis, while others are based on a quantitative analysis, such as Hellman (Reference Hellman2008), Bunn (Reference Bunn2007), and Mueller (Reference Mueller2008).

Table 1 Individual estimates of the probability of nuclear war.

Arguably, the most compelling assessments are those of crisis managers who experienced a nuclear close-call firsthand: President Kennedy and his national security advisor, McGeorge Bundy. Not long after the Cuban missile crisis, Kennedy told Ted Sorenson, special counsel to the president, that during the crisis he believed that the chances that the Soviets would go to war were between one in three and even, while Bundy, reflecting 26 years after the crisis, came to the dramatically lower estimate of up to 1 in 100. Of course, the crisis occurred over a half-century ago, and even with the additional information now available, it is hard to estimate its risks retrospectively. For example, depending on one’s interpretation of the probabilities associated with the incident in which a nuclear-armed Soviet submarine was forced to surface, and the risks one should attach to other “close-call” incidents during the Cuban crisis (Sagan, Reference Sagan1993), one could argue for either Kennedy’s estimate or Bundy’s. Moreover, neither Kennedy nor Bundy knew at the time they made their estimates that the Soviet submarine had come close to launching a nuclear torpedo, but they could have imagined this and other scenarios as part of their risk estimates, so it is unclear whether either of them would have raised or lowered their estimates if they had known at the time of their estimates everything we know now.

Of course, beyond the question of what the actual risk was at the time of the Cuban crisis is the problem of the relevance of that information to the assessment of future risks. More recently, Martin Hellman assessed the risk of a future “Cuban-missile-type” crisis that results in nuclear use as between 2 in 1000 and 1 in 1000 per year. Note that this is only one of two estimates in Table 1 that provide a range of values, a useful approach to addressing uncertainty. Hellman also points to a dearth of analyses of the risk of deterrence failure and proposes that “several prestigious scientific and engineering bodies undertake serious studies to estimate its failure rate.”

Not surprisingly, a number of estimates in the first decade of this century have focused on the probability of nuclear use by terrorist organizations. Of the subjective estimations, Richard Garwin’s estimate of 20% per year against a US or European city is the highest. Assuming that this probability remains constant over the period, it equates to a probability of approximately 90% within a decade. In the middle of the range of subjective estimates are Graham Allison and William Perry, who independently judge this probability to be 50% within a decade. At the low end is David Albright, who estimates it to be less than 1% over 10 years. These subjective assessments span almost the complete range of possibility from near 0 to 90%.

Two nuclear terrorism estimates in Table 1 are based on quantitative analysis. Matthew Bunn estimates 29% within the next decade, and John Mueller estimates less than 1 in 1 million per attempt. This large difference in estimates is not an encouraging indicator that quantitative analysis will facilitate convergence on a consensus estimate, but at least it provides valuable information regarding the basis for each estimate.

In summary, the principal insights I take from the estimates in Table 1 are the same as for the Lugar survey: (1) they differ widely, and (2) they are all of questionable validity because they do differ widely and because they are fundamentally either intuitive or based on simple, perhaps simplistic, analysis. Also, subjective judgments appear to gravitate to either 1 or 50% as an estimate, which suggests that the resolution of human intuition is relatively coarse on this question.

3.2 Consequences

Nuclear risk assessment must consider the entire spectrum of potential consequences of all levels of nuclear war, ranging from a single detonation in a remote area to a large-scale nuclear exchange. These consequences must include all types of harm, including fatalities and injuries to humans, damages to infrastructures and the environment, and harm to militaries, economies, and other social structures. Assessments must consider not only the short-term harms but also harms that extend through time to future generations, likely centuries into the future.

We should also acknowledge, if only for the sake of completeness, that something positive might come out of some nuclear usages. In particular, limited nuclear use might reinforce the nuclear taboo, which is seen as increasingly fragile (Tannenwald, Reference Tannenwald2018). Of course, as Hahn and Scouras (forthcoming) observe, “The greatest challenge to this norm will occur when nuclear weapons are used. There is a presumption that once violated, the norm against use of nuclear weapons cannot endure. But, this presumption is not based on a body of research; it is possible that the response to first use could act to reaffirm the relevance of the norm, so that a single violation would not necessarily irreversibly undermine its existence. In fact, norm theory suggests that the response to the norm violation is pivotal in determining the ultimate impact of the initial violation.” An extension of this thinking holds that norms, in general, cannot endure indefinitely without periodic violations that provide tangible reminders of their value. In any event, this area is highly speculative, and no one seriously advocates limited nuclear use as a mechanism to reinforce the nuclear taboo.

Our knowledge base on nuclear effects is extensive in some areas but meager in others.Footnote ⁶ It is not an exaggeration to say that, as a whole, it is woefully inadequate to support a comprehensive consequence assessment. There are several reasons for this state of affairs. First, while the United States has conducted over 1000 nuclear tests and spent billions of dollars on nuclear effects research, the great majority of this effort focused on fulfilling Cold War military requirements. In support of nuclear mission planning, the United States sought high-confidence estimates of the effects of nuclear weapons of various designs with different outputs on targets of varying characteristics primarily in the Soviet Union. Post-attack planning for damage assessment and the possible need for subsequent attacks also demanded confidence in determining target damage. These imperatives led to a focus on the nuclear damage mechanisms of air blast, cratering, ground shock, and similar phenomena. As a result, our knowledge base is relatively good on these nuclear effects.

Second, somewhat less attention was paid to those phenomena that were inherently hard to predict or whose effects were delayed. In the former category is fire initiated by the thermal radiation of nuclear explosions. The US Defense Nuclear Agency, now the Defense Threat Reduction Agency, tried hard to model this phenomenon, but only very recently has this effort showed signs of potential payoff. In the latter category is fallout. While fallout modeling was a research focus, and we now have good models of fallout production and propagation, the vagaries of weather, the uncertainties related to population evacuation and shielding, and other variables are impediments to confident prediction of the effects of fallout.

Third, some phenomena were discovered late, and by surprise, in the nuclear test program. For example, an unexpectedly large EMP was observed in the Starfish Prime atmospheric nuclear test in 1962. Further high-altitude testing was prohibited by the 1963 Treaty Banning Nuclear Weapons Tests in the Atmosphere, in Outer Space, and Under Water, which relegated future research to the domain of modeling. Starfish Prime also resulted in the unanticipated gradual destruction of all commercial satellites in low-earth orbit due to pumping the Van Allen radiation belts with electrons.

Fourth, the physical consequences to the infrastructures that sustain societies – power, water, finance, transportation, etc. – has never been a focus of nuclear weapons effects research. However, the Department of Homeland Security has funded the National Infrastructure Simulation and Analysis Center (https://www.sandia.gov/nisac-ssl/), an effort by Sandia National Laboratories, Los Alamos National Laboratory, and Pacific Northwest National Laboratory to model the interdependencies among these infrastructures, albeit with limited success. Nonphysical societal effects (e.g., social, psychological, political, and economic effects) are even more difficult to assess and have never been adequately investigated.

Arguably, the two phenomena most in need of further research are nuclear winter and EMP. Nuclear winter has the potential to pose even greater harm to life on earth than all the more immediate damages due to blast and prompt radiation. A small research community continues to model nuclear winter in various nuclear war scenarios with ever-more sophisticated models. But controversy over the many uncertainties associated with the inputs to these models and the underlying physics, as well as possible antinuclear biases of some of the researchers, have impeded acceptance of nuclear winter predictions. As a result, the Department of Defense simply does not consider nuclear winter in its policy formulation or military planning. In fact, it argues that by making nuclear war even more horrific, nuclear winter is a positive contribution to deterrence. Similarly, the consequences of EMP may be catastrophic, but we simply do not know whether a nuclear attack will bring down the electric grid or otherwise cause great damage to the electronic systems that power our economy, military, and society (Frankel, Scouras, & DeSimone, Reference Frankel, Scouras and DeSimone2015).

As a result of this limited state of knowledge of the consequences of nuclear war, a comprehensive consequences assessment is simply not possible. The best we can do is estimate lower bounds on consequences and recognize that the true consequences of nuclear war may be significantly higher.

4.1 Nonproliferation

It might seem obvious that the fewer the number of nuclear states, the safer we are, and indeed that appears to be the consensus view in the national security community. The main argument is that with fewer nuclear states, there are fewer pathways to nuclear war. This may be true, but it is not the whole story. The United States benefits from both the British and French nuclear arsenals in deterring Russia from nuclear and large conventional attacks in Europe. This is not primarily because of our allies’ arsenals themselves, but because they provide independent decision authorities that Russia must consider when contemplating an attack.

It is not entirely clear why the development and possession of nuclear weapons by Japan or South Korea, for example, would not similarly contribute to international security, especially because further proliferation in northeast Asia is unlikely to be provoked. More generally, Kenneth Waltz has argued that the more states that have nuclear weapons, the safer the world will be from nuclear war (Sagan & Waltz, Reference Sagan and Waltz2012). His argument is consistent with the historical experience that demonstrates that nuclear weapon states have shown great forbearance in engaging in direct combat with each other.

In any event, proliferation is also dangerous because new nuclear states pose special risks that established nuclear states do not. One such risk arises from the fact that they have little or no experience with nuclear diplomacy and crisis management, which could lead to reckless posturing or behavior. We may have witnessed this dynamic in the 2018 war of words between US President Donald Trump and North Korean Supreme Leader Kim Jong Un.

Another source of proliferation risk arises from the reactions – especially threats of preventive war – of established nuclear states to nascent nuclear states. Preventive war was considered – and rejected – by the United States to counter a prospective nuclear Soviet Union and by the Soviet Union to counter a nascent nuclear China. More recently, to counter the prospective threat from “rogue” states, President George W. Bush emphasized the need for preemptive attack options in our deterrence strategy.

4.2 Counterterrorism

After the attacks of September 11, 2001, fear that a terrorist organization would succeed in stealing, building, or buying a nuclear weapon or weapons dominated nuclear concerns. The thought was that such organizations were immune to the logic of deterrence, because they did not present targets of value in the way that states do. Hence, counterterrorism strategy focused on preventing substate actors from acquiring both weapons and nuclear materials. These efforts have been largely successful – so far – although more can and should be done. Terrorist organizations are unlikely to have given up their nuclear ambitions. More recently, we have begun to understand that deterrence still has a role to play against terrorism. But the focus of deterrent threats must be the countries that harbor terrorist organizations, either willfully or through neglect or incompetence.

4.3 Deterrence

Deterrence of a nuclear first strike depends on the fear of a retaliatory strike, which, in turn, depends on the nuclear capabilities of the victim of the first strike. Here I summarize two studies that illustrate the complexity of assessing the relationship between nuclear capabilities and deterrence. These studies address (1) the importance, or irrelevance, of nuclear parity, and (2) how many weapons are enough to underwrite deterrence.

4.3.1 Nuclear parity

The imperative to achieve nuclear superiority – or, at a minimum, nuclear parity – drove the Cold War arms race to dizzying heights, as illustrated in figure 4 (data through 2010 are from Norris & Kristensen, Reference Norris and Kristensen2010, and data after 2010 are from Kristensen & Korda, Reference Kristensen and Korda2010–2019). Yet, the United States has also voluntarily tolerated a significant imbalance in nuclear weapons during the last decade of the Cold War and the first post-Cold War decade, and China has embraced a minimum deterrence posture. As we look ahead, we must consider the potential for both further negotiated arms reductions and the opposite – abandonment of strategic arms control – as well as continuing growth in the Chinese arsenal and vertical and horizontal nuclear proliferation in other states. Facing this highly entropic future, how should nearly three-quarters of a century of nuclear experience inform US policy with respect to the nuclear balance with Russia and other adversarial nuclear states?

Figure 4 US and Soviet/Russian nuclear arsenals over time.

Because all targeted states would suffer enormously in a nuclear war regardless of the nuclear balance, nuclear crisis management is the default mechanism through which the nuclear balance affects states’ behaviors, and nuclear crisis outcome is the primary measure of the value of nuclear superiority. Scholars and strategists debate the importance of relative nuclear capabilities as well as myriad other factors, including political stakes, resolve, risk tolerance, the conventional military balance, and domestic politics. Multiple factors are often at play in any particular crisis, and there are important relationships among them. The key policy-relevant question for the United States is, Are nuclear-superior states more likely to prevail in nuclear crises?

Perspectives on this question underlie national security policies regarding, inter alia, arms control, triad recapitalization, nonstrategic weapon deployments, nuclear proliferation, nuclear crisis management, and cross-domain and extended deterrence. Over the next decade, these perspectives will be reflected in decisions on implementing the 2018 Nuclear Posture Review, strategic arms control after the New START Treaty, the future (if any) of the INF Treaty or a possible successor treaty, and the fate of the Comprehensive Test Ban Treaty. They will also impact US crisis management strategy vis-à-vis North Korea and nonproliferation policy vis-à-vis Iran.

Recent research has incorporated quantitative analysis into traditionally qualitative investigation. However, there are concerns about the appropriateness of these studies’ statistical methods. One important result of a recent analysis is displayed in figure 5 (Rooker & Scouras, Reference Rooker and Scouras2019). Based on historical data on nuclear crises compiled by Matthew Kroenig (Reference Kroenig2013), the probabilities of winning a nuclear crisis are plotted for both the side with the superior and the side with the inferior nuclear arsenal. Both probabilities are highly uncertain, reflections of the small data set and the importance of variables other than the nuclear balance. Notwithstanding these uncertainties, the probability of winning is significantly lower with an inferior arsenal. These results suggest that (1) even the side with the superior arsenal should not confidently expect to win a nuclear crisis, and (2) if a nuclear state anticipates nuclear crises in its future and wishes to win, it should strive to avoid nuclear inferiority.

Figure 5 Uncertainty in the probability of winning a nuclear crisis.

To summarize, the importance of the nuclear balance vis-à-vis our principal adversary has been the subject of intense but unresolved debate since the Soviet Union acquired nuclear weapons some seven decades ago. Though nuclear superiority has not always swayed crisis resolution, it has mattered in at least some crises. Thus, we cannot ignore the possibility that it will matter in some future crises – perhaps even the next crisis. Given profound uncertainties about the implications of asymmetries in nuclear arsenals, it would seem the most prudent approach is to hedge against the possibility of dire consequences of nuclear inferiority. Nevertheless, the contrary view that the United States would be safe even after unilateral deep cuts in nuclear arsenals cannot be dismissed out of hand.

4.3.2 How much is enough?

Even after we answer the parity question, we still have the related question about how many nuclear weapons we need. Figure 6 shows US nuclear warheads under the New START Treaty (see chapter 2 of Cimbala & Scouras, Reference Cimbala and Scouras2002, for a more detailed discussion of this graphical representation). Five states of these forces are arrayed along the x-axis. The total number of warheads is equivalent to arsenal size. It includes both deployed and nondeployed warheads. Available warheads, which exclude nondeployed warheads, are those that realistically could be used in a nuclear war. But not all available warheads are on alert, ready to be launched within minutes of a presidential order, or are based in a survivable posture to be launched at any time. On day-to-day alert, fewer than half of the available warheads could be launched rapidly or are survivable. Then, we must consider whether the United States launches intercontinental ballistic missiles on tactical warning (LOW) or rides out an attack (ROA). Riding out the attack will further decrease the warhead count. Finally, we must factor in the system reliabilities and probabilities of penetrating Russian defenses. At the end, we are left with the number of warheads that we – and Russia – can reasonably anticipate would detonate in a US retaliatory strike on Russian targets. It is this quantity – arriving warheads – not arsenal size or any of the other intermediate quantities that underwrites deterrence.

Figure 6 Measures of effectiveness for nuclear weapons.

In Figure 6, we see four scenarios with different numbers of arriving weapons. The lowest level is defined as assured retaliation. I argue that our focus should be on this number as the single best measure of our nuclear forces’ contribution to deterrence. Although it might not be the most likely of the four scenarios, it is still probable enough, relative to the others, that we must plan for it. Furthermore, while we may be able to control whether or not we ride out an attack or launch on warning, there is great uncertainty in what we will actually do. Thus, we should not count on launching on warning. And finally, whether we are on generated alert as opposed to day-to-day alert is actually a decision that our attacker will make, because the timing of any attack would be up to them.

So, what level of assured retaliation do we need? In fact, this has been subject to debate throughout the nuclear age. During most of the Cold War, we focused on being able to achieve high damage levels to military, economic, and leadership targets in the Soviet Union. And as our arsenals grew, so did our target lists. The prevailing view was that deterrence required us to be able to utterly destroy the Soviet Union as a functioning entity in a retaliatory strike under the worst plausible circumstance. As a point of reference, to Secretary of Defense Robert S. McNamara, this meant being able to destroy one-third of the Soviet population and one-half of its industry (McNamara, Reference McNamara1967).

Today, other views are gaining traction. At this point, there appear to be two main intellectual camps among deterrence analysts, one cautioning against going to lower levels and the other advocating at least some additional nuclear arms reductions. There are important distinctions within the group that advocates for further reductions. Some call for modest bilateral reductions under a negotiated treaty, although that seems improbable at least for the next several years. Others call for a US minimum deterrence posture, independent of the size of the Russian arsenal. Proponents of minimum deterrence argue that far fewer weapons (arsenals numbering in the hundreds) are sufficient to deter Russia. They point to China, and to a lesser extent the UK and France, all of which have adopted variants of minimum deterrence postures.

4.4 Residual risk and risk acceptance

It is clear that we cannot reduce nuclear risk to zero unless we eliminate all nuclear weapons from the earth, and perhaps not even then. And while President Obama was a strong advocate for “global zero” as a long-term objective, no other nuclear state seems to have seriously embraced this vision.

But there is also a possible serious downside to reducing nuclear risk to zero. Citing the absence of great-power wars since 1945, some proponents of nuclear weapons have emphasized their importance in saving lives by reducing the frequency and intensity of conventional wars between great powers. To support their viewpoint, they often point to a singular analysis of wartime fatalities from the year 1600 to the present. While the original graph of the results of this analysis was circulated in the defense community in the mid-1990s, it has evolved over the decades, with the most recent variant (shown in figure 7) appearing in the 2018 Nuclear Posture Review report. It indicates that wartime fatalities have been lower in the nuclear era than during any previous time since 1600, implicitly crediting the advent of nuclear weapons for these saved lives.

Figure 7 Wartime fatalities as a percentage of world population, as appears in the 2018 Nuclear Posture Review report.

Ice et al. (forthcoming) analyzed this graph and found that it is fatally flawed. In particular, it is irreproducible from information provided by the Department of Defense Historical Office, the cited source of data; it uses dubious analytical methods (among them, concatenation of incompatible databases and erroneous normalization by world population); and it presents results in a profoundly misleading manner, primarily due to varying histogram bin widths.

A more rigorous analysis results in the graph in figure 8 (Ice et al., forthcoming). All the cited flaws of the preceding histogram have been rectified. In particular, wartime fatalities are shown on an annual basis, which enables more insight into the aperiodic nature of wartime fatalities and entails less bias. This graph indicates that the incidence of annual wartime fatalities after World War II (as a percentage of world population) is comparable to that of many earlier times. Also, periods of diminished fatalities typically follow major wars; for this reason alone, we cannot conclude with certainty that nuclear weapons are the source of the current relatively quiescent period. Finally, we observe a clear trend in the intensity of major wars. Projecting this trend to the future reminds us what we already know – that nuclear war will be unprecedented in its human toll, potentially exceeding the fatalities of all previous wars combined. There is simply no basis in this analysis to conclude that nuclear weapons will continue to deter either nuclear or large-scale conventional war.

Figure 8 Recalculated annual wartime fatalities as a percentage of world population.

Finally, it is important to understand that statistical analysis – done correctly – can at most show a correlation between the advent of nuclear weapons and a change in wartime fatalities. Proving a causal relationship would require a complex multidisciplinary analysis. Understanding the potential for nuclear weapons to prevent great powers from waging conventional war is a worthy pursuit that deserves a thorough and rigorous analysis. Basing vital national security decisions on irreproducible, misleading, and logically flawed reasoning is a dangerous practice.