3.1. Impacts on Most-Populated Target Country
If it is conservatively assumed that 34 million people die directly from the 100 nuclear bomb case, this is 6% of the population of the most populous nation’s largest 100 cities targeted [61
] and about 2.5% of the overall Chinese population. This represents a significant underestimate, as the impacts of the bombs on trade and the climate are not considered (as shown below) and thus the attack would kill a significant number of additional people. To demonstrate that such a death toll (and the best-case demographic shock determined by using the most populous nation) from a relatively small number of nuclear weapons would act as a deterrent for rational decision makers, the demographic shock is put into historic context. For example, when compared to past world wars the death toll is remarkable. World War I caused about 18 million deaths (of which about 9 million were civilians [62
]), so the 100 nuclear weapon case would kill more than 3 times more civilians than were lost in WWI. WWII killed about 71 million people in total (19 million military, 20 civilians, 15 million civilians in the Sino-Japanese war and 17 million from Hitler’s murders) [63
]. Thus, the 100 nuclear weapon case would kill about as many civilians as WWII. This loss of life can also be compared to the historical plagues to assess impact. The 1918 “Spanish” influenza pandemic, killed 50–100 million people, which was only 3 to 6% of the global population [64
] and would be considered roughly equivalent to the impact on the 100 most populous cities and all of China in a 100 bomb nuclear strike, respectively. Thus, the 100 nuclear warhead limit would be expected to create more than enough of a demographic shock to enable nuclear deterrence even in the most populous country in the world.
Other countries would be exposed to an even greater percent population shock and thus deterrent from 100 nuclear weapons. In both the future (because of the rise of urbanization [65
]) and for more developed countries, which are already more urbanized, this percentage of citizens killed in the target countries would be larger.
3.3. Impact on Wealthy Land-Rich Aggressor Nation: U.S. Case Study
The effects of a 100 nuclear weapon attack on the aggressor nation has significant uncertainty. This is because the likely results of a 20% drop in sunlight that could lead to a 19% drop in global precipitation would have a wide geographic diversity with respect to the impacts (e.g., some areas would receive far less precipitation). In addition, a few unfortunately timed frosts could wipe out a year’s harvest, whereas the same frosts bunched together at the end of the growing season would have a minimal impact on food production. Although there would be expected to be mass starvation in Africa and South Asia from even a 10% shortfall in food, the U.S. (and to a lesser degree Russia) could alter their eating habits to largely prevent starvation. There could be a dramatic reduction in food trade and higher prices for food. High food price would probably mean that Americans eat fewer fruits and vegetables, but also less meat, so the impact on nutrition in a country where more than a third of adults are obese [67
] is ambiguous.
The impact across America would also not be uniform. Currently, according to the U.S. Department of Agriculture, 12.3% (15.6 million) of U.S. households were food insecure at some time during 2016 [68
]. Food insecurity means that at times during the year, these households were uncertain of having, or unable to acquire, enough food to meet the needs of all their members because they had insufficient money or other resources for food. The poor are often food insecure, although it should be noted that half of those experiencing hunger had incomes above the poverty level [70
]. If the U.S. were an aggressor, the number of food insecure households would increase, but the majority of the impacts would fall on those existing food insecure households, pushing the 7.4% of households with low food security into the very low food security situation. Very low food security households, which already make up 4.9% of the U.S. households (6.1 million) have disruption in the normal eating patterns of one or more household members and food intake is reduced at times during the year because they had insufficient money or other resources for food. Most susceptible to food price shocks would be the 703,000 children (1% of the U.S.’s children), which live in households in which one or more children experienced very low food security. In addition to the risks of starvation, aspects of human development depend on food security [71
Thus, if the U.S. were the aggressor and in the best case scenario (as laid out by the assumptions in Section 2.2
) overall approximately 5% of the U.S. (one of the richest countries in the world) would be thrust into extremely precarious food insecure situations with only 100 bombs being detonated somewhere else in the world.
The mortality results of the Monte Carlo simulation are shown in Table 4
for the three cases of U.S. nuclear aggression: (1) current U.S. arsenal with a potential proposed increase in U.S. nuclear capabilities to reach 7000 nuclear weapons under the Trump administration’s goal to match Russia’s nuclear capabilities; (2) 1000 nuclear weapons and (3) 100 nuclear weapons. For the Cold War II arsenal, starvation deaths in the U.S. would be expected to be 5 million (there is some probability of no starvation, but some probability of much greater starvation). With 1000 nuclear weapons, the mortality is 140,000, and with 100 nuclear weapons, it is zero.
The scenario of 1000 nuclear weapons has a mortality nearly 50 times deadlier than the 11 September terrorist attack that killed 2996 people, the worst terrorist attack in U.S. history [72
]. This is an important reference point for comparison as the U.S. spent more than $
7.6 trillion on defense and homeland security (more than $
635 billion for homeland security alone) by 2011 after the 11 September terrorist attacks in 2001 [73
]. This shows the willingness of the U.S. to invest in the security of its own population. It should be noted that this level of expected U.S. citizen starvation was developed following the most conserving course of food distribution. Specifically, this analysis assumed that all those that would eventually starve would be cut off from food immediately (severe rationing). This is very unlikely to be the case, as people slated to starve would have access to some food initially and there would be some benevolent sharing as hunger progressed throughout society. Furthermore, there would likely be aggression (e.g., stealing of food, fighting for food, killing for food, etc.) as more and more people were thrust into worsening food insecurity situations. The latter stages become difficult to model as aggression for food causing mortality would have both a negative (murder) as well as positive (more food for survivors) effect on overall mortality. Current agent-based simulations used by the Department of Defense [74
] should be extended past the immediate effects of nuclear strikes to determine the best policies to prevent widespread American deaths from nuclear autumn scenarios. Using extreme measures such as the rapid scale-up and use of alternative foods (e.g., natural gas fed edible bacteria, mushrooms grown on trees, etc.) could in theory prevent all American starvation [48
]. It should also be pointed out here that until nuclear stockpiles are drawn down to prevent each individual nation from causing nuclear winter (or autumn) single-handedly, significantly more resources need to be devoted to the studying and dissemination of information about alternative food to provide an insurance for the greatest number of human survivors.
In addition to the likely loss of life and security from food deprivation there would be other negative effects including disruption of the economic system, reduction of medical supplies and personnel, high levels of pollution (e.g., aggravating existing levels of premature death from other sources such as coal pollution [78
]) psychological stress, increased diseases and epidemics, and enhanced UV radiation causing increased rates of skin cancer [81
]. It is possible that global stock exchanges collapse, potentially losing $
69 trillion in value, ~$
28 trillion in the U.S. [84
Food prices would increase dramatically. If there were a 10% global agricultural shortfall, it has been estimated that grain prices would triple [85
]. Wheat flour had a price of 1.15 USD/kg retail in 2015 [86
]. Other grains are generally more expensive than wheat. Global grain production is ~2.7 billion tons (Gt)/year [87
]. If all grain were as inexpensive as wheat, the increased global annual expenditure on grains would be 6 trillion USD. This is conservative because other grains are generally more expensive than wheat. Other foods are significantly more expensive per kilogram than grains, so the percent increase in price would be smaller, but the absolute increase in price would likely be similar. Total calorie production of grains is approximately half of all food production [88
]. This means the global food expenditure would increase at least 12 trillion USD per year. Though the U.S. is only 5% of the global population, it consumes more than 10% of the food grown, because of its high consumption of meat and other animal products. Since impacts could last a decade, the total food expenditure impact on just the U.S. would be more than 12 trillion USD. Also, loss of food trade would mean that the U.S. would not be able to import tropical crops such as tea, coffee, coconut, papaya, rubber and chocolate.
In addition, it should be noted, besides the direct negative effects of a 10% global food shortage [53
], there are also highly likely indirect negative effects on the aggressor nation including the fact that food shortages are likely to cause increased conflicts and refugees as has been shown in both North Korean refugees entering China [89
] and Kurdish refugees in Turkey [90
]. Refugees entering the U.S. in higher numbers illegally and increased conflict throughout the globe are also counter to U.S. interests.
Thus, it can be conservatively concluded that even in the U.S., the country with the highest capacity to absorb the indirect effects of limited nuclear attacks on another country, the use of more than 100 nuclear weapons is counter to the interests of the nation.
3.4. Pragmatic Limits in the Context of Nuclear Deterrence
This study is a synthesis of the work done in the catastrophic risk communities [46
] and those skeptical of nuclear deterrence theory [91
]. It provides a more quantitative analysis than that offered by Baum [46
]. It must be noted that the general issue of nuclear deterrence is highly contentious and complex [94
]. Baum’s proposal to replace nuclear weapons with bioweapons to enable deterrence while eliminating the risk of nuclear winter, for example, was attacked from all sides in the debate [96
] including those that think there is not solid evidence for nuclear deterrence as a whole [99
]. Lewis, in particular, points out the nuclear deterrence community functions isolated from reality as if in a snow globe [100
], yet the more conventional argument that nuclear deterrence reduces the probability of war is used to justify current nuclear arsenals that do indeed exist. Then there are also those such as Alexi Arbotov who argue the entire arms control process is falling apart and more important priorities are to salvage the most critical parts [101
Critics of this analysis will point out that using death toll for a short hand estimate of deterrence over simplifies the issue as decision makers and thus both states and non-state entities can act irrationally [102
]. While this is obviously the case, policies by rational actors themselves should be rational and using demographic shocks with historical examples as was done above provides an effective short hand for determining the actions of a rational actor. Frankly speaking, there are no policies that can offer defense against a nuclear power willing to commit suicide. Thus, it is assumed here that although having nuclear weapons may deter others from attacking (with all the caveats and lack of consensus acknowledged in the nuclear deterrence debate), it does not guarantee this. Having multiple nuclear weapons would be expected to increase this deterrent effect, but it would be expected to saturate, while the losses to the potential aggressor continue to rise rapidly (e.g., increasing from 1000 nuclear weapons by a factor of 7 means expected mortality of the aggressor of ~40 times as much). Therefore, in the vicinity of 100 nuclear weapons, adding further weapons likely increases the costs more than the benefits, so it does not appear to be rational.
Critics can also point out that nuclear weapons may also be used in counter-force applications (e.g., attacking enemy nuclear weapons), reducing the blowback as many nuclear weapons are stored outside of major population centers and thus away from sources of fuel needed to significantly block the sun. Nuclear weapons can certainly be used in that way, but it is clear that this use case would provide less of a deterrent effect than targeting population centers, which also provide the most climate forcing. Finally, critics could argue that they have to assume that a significant fraction of their stockpile could be destroyed in a first strike and therefore need some form of redundancy. To eliminate the need for redundant nuclear warheads, which could bring about an unacceptable toll on domestic interests if they were ever used it is necessary to deploy these 100 warheads on survivable platforms such as submarines or airplanes. It should, however, be pointed out that additional future work is needed to determine the potentially destabilizing effect of first strikes, survivable platforms and missile defense combined with counter-force strikes.3.5. Pragmatic Limits Compared to Existing Stockpiles
The pragmatic nuclear limit should be set at 100 warheads or less for China, India, UK, Pakistan, Israel and North Korea for both the potential impact of a 10% food shortfall as well as the risk to a high percent of death within their populations because of the inability to feed themselves without trade and industry.
For the cases of France, Russia and the U.S. these same limits should also be adhered to primarily for the former issue of increased food prices causing significant hardship to large swaths of their populations and resultant starvation many times worse than historical terrorist attacks. The U.S. values are given above; however, in France 11% of the adult population is food insecure [103
] and in Russia about 12% of the population has inadequate food now [104
]. This again would indicate these people would be in severe risk of starvation with significantly increased food prices unless radical changes were made to their economic system. In truly horrific cases, Russia risks returning to widespread cannibalism as occurred during Stalin’s reign [105
]. These risks are obviously against the best interests of Russia as a nation.
To visualize the necessary reductions from the best-case aggressor nation the total number of nuclear warheads in the U.S. stockpile are shown plotted as a function of time and compared against pragmatic nuclear weapons limits along with their date of origin in Figure 1
. It should be noted that this plot is on the log scale on the y-axis for clarity. As shown in Figure 1
, the Strategic Arms Reduction Treaty (New START) nuclear arms reduction treaty between the U.S. and the Russian Federation [106
] is inadequately aggressive at arms reduction to make reach the pragmatic safety limit by more than order of magnitude.
The results of this study indicate a massive draw down of nuclear weapons is necessary for a country to reach the pragmatic limit of 100 in the case of both the U.S. and Russia. To put these numbers into perspective, a single U.S. submarine carrying 144 warheads of 100-kt yield could generate about 23 Tg of soot [41
] creating far more damage to U.S. interests than the conservative model used here. For France and China their nuclear stockpiles should be reduced to a third, the UK would need to reduce their stockpile by more than half and both Pakistan and India should make cuts of 15 and 25%, respectively. Israel and North Korea should also limit their stockpiles to under 100 nuclear weapons as they are among the most susceptible to widespread starvation from the effects of nuclear explosions outside of their borders.
This study has shown 100 nuclear warheads is more than enough to act as a nuclear deterrent even when faced with the most populated nation on the earth as an enemy. At the same time, using more than 100 nuclear weapons by any aggressor nation (including the best positioned strategically to handle the unintended consequences) even with optimistic assumptions would cause unacceptable damage to their own society. Based on the demographic shock this damage represents and the likely outcome on the stability of the society this would be considered unacceptable damage in all but the most extreme situations. Thus, the use of government funds to manufacture, store and upkeep nuclear weapons in excess of 100 is not pragmatic. Clearly stated: Efforts to create or maintain nuclear arsenals with more than 100 weapons does not appear to be rational. Similarly, it can be concluded increasing the size of the mega arsenals of Russia or the U.S. [107
] is counterproductive to either nation’s self-interest and national security. Policies to accelerate individual country’s efforts to reduce their stockpiles to a pragmatic limit should be encouraged. The primary weaknesses of this study, which are overly optimistic conservative assumptions, can be addressed in future work by carefully selecting more likely assumptions and using sensitivity analysis on them to provide more granular results. In addition, with the pragmatic limit set for an individual country in this study, more work is necessary once the stockpiles have dropped to those limits to determine how to share the fraction of nuclear weapons allowed under the world nuclear weapons limits previously determined by Robock and Toon [45