Abstract

What is the best way to restore or uphold deterrence when an existing deterrent is perceived to have decayed? One common answer is that deterrers should simply add more of the ingredients that generally make for strong deterrents: more certainty that threats will be carried out, more capabilities to inflict severe punishments upon an adversary, and greater capacity to carry out threats with celerity (speed). This answer draws upon an intuitive quantitative logic that more is always better when it comes to dissuading an adversary from taking unwanted actions. In this article, however, we explain how following this quantitative logic can have the unintended consequence of worsening security relations and provoking war, especially under conditions of shifting power. Using proposals for the United States to provide ‘strategic clarity’ regarding its intentions to defend Taiwan against Chinese aggression as a case-study, we show how efforts to maximize the certainty, severity and celerity of threats can backfire in practice. In general terms, our conclusion is that scholars and policy practitioners must assess the viability of deterrents from a qualitative perspective. With specific reference to Taiwan, we find that strategic clarity would be unlikely to strengthen deterrence in the Taiwan Strait.

How should the United States deter China from invading Taiwan? This question has become central to debates over US foreign and defence policy, especially since Russia's invasion of Ukraine in February 2022. The new conventional wisdom is that deterrence in the Taiwan Strait has weakened, and that Beijing might be closer than ever to pursuing forcible unification.1 In this context, some prominent analysts have argued that the US must swap its longstanding policy of ‘strategic ambiguity’ for one of ‘strategic clarity’.2 Essentially, this approach amounts to leaders in Washington impressing upon their counterparts in Beijing that the US military would be certain to intervene on Taiwan's behalf in the event of unprovoked Chinese aggression. If China's leaders could be convinced that invading Taiwan would mean a major war pitting the US against China, the argument goes, then the chances of them ordering an invasion would drop precipitously.

The case for strategic clarity is rooted in a quantitative logic, which holds that the strength of deterrence at any given moment can be calculated by multiplying the probability of an aggressor facing costs by the severity of the costs being threatened. Analysts debate, for example, whether US commitments to Taiwan are ‘more’ or ‘less’ credible than they were in the past (and to what degree), as well as what level of Taiwanese and US forces might be necessary to convince Beijing that an invasion would be folly. Even if exact numeric values are not always assigned, the debate is squarely focused on the estimation of implied amounts of credibility, resolve and force size. Viewed from this perspective, strategic clarity would bolster deterrence because it promises more of everything that makes deterrence work.

Missing from this discussion on strategic clarity, however, has been a qualitative assessment of the deterrents that US leaders are being advised to level against China. For while quantitative reasoning is important when it comes to gauging the overall strength of deterrence, it is essential that any prospective move towards bolstering deterrence in the Taiwan Strait also be evaluated in qualitative terms. This means 1) exploring the precise actions that would be needed to actualize strategic clarity and 2) conjecturing how these moves would be perceived in Beijing. In this article, we argue that a qualitative assessment of strategic clarity casts significant doubt on whether the approach can be considered a practicable solution to the problem of Taiwanese insecurity. In short, we find that the available means of implementing strategic clarity invariably risk provoking China rather than assuring Chinese leaders that the United States remains committed to the political status quo.3 Our conclusion is that more is not always better when it comes to deterrence in the twenty-first century.

Upholding deterrence: quantitative versus qualitative logics

Deterrence is the act of ‘discouraging [an adversary] from taking unwanted actions, especially military aggression’.4 This is done by making threats to be carried out in the event of the unwanted action being taken. If an adversary can be made to anticipate suffering costs that outweigh the expected benefits of taking the unwanted action, then it becomes rational for the adversary to exercise restraint.5 Today, for example, Taiwan and its partners abroad (including the United States) have an interest in dissuading China from invading Taiwan. To discourage China from launching an armed attack, actors in favour of the status quo have made a series of explicit and implicit threats against Beijing that would be carried out in response to an invasion: military reprisals, economic sanctions, diplomatic punishments, popular resistance and so forth.6 So long as China fears the consequences of these threats more than it expects to profit from seizing Taiwan, deterrence can be said to exist. On the other hand, if Beijing comes to believe that seizing the island by force would result in more benefits than costs—that is, if the threats made against China pale in comparison to the expected value of Taiwan as a prize—then deterrence can be said to have evaporated.

What makes for a strong deterrent? The conventional answer is that the strength of any given deterrent is a function of its certainty (the likelihood of the threat being carried out), its celerity (the speed with which the threat could be executed) and its severity (the potential impact of the threat in terms of costs inflicted).7 However, none of these constituent elements of deterrence are fixed values. On the contrary, the overall strength of any given deterrent will tend to fluctuate over time.8 This can happen for a few reasons. First, a deterrer's capabilities might strengthen or weaken due to investment or underinvestment, which would alter an adversary's fear of suffering swift or severe punishments. Second, the underlying interests of the deterrer can shift, perhaps raising questions about the certainty of a threat being carried out. Third, the deterrer's adversary might become more or less powerful, or more or less committed to the resolution of a particular dispute on favourable terms, which would affect the perceived severity of the deterrer's threats (and perhaps their celerity and certainty of being carried out) even if nothing changes on the side of the deterrer.

If any of these dynamics unfold, then a deterrer must pay attention to the robustness of deterrence and invest in means of restoring deterrence if the conclusion is that deterrence has eroded rather than strengthened or remained static. How can deterrence be buttressed in response to perceived erosion? The quantitative approach reduces deterrence to its three stylized components—certainty, celerity and severity—and assumes that the health of deterrence is the product of these three values. By deduction, it follows that bolstering deterrence is just a matter of adding more of the essential ingredients: more resolve, more speed, more power—or some combination of the three.9 From this view, upholding deterrence is done through recalibration: the deterrer must ensure that sufficient quantities of hard-power capabilities and commitment are demonstrated to the adversary, such that the adversary remains persuaded (or can be persuaded anew) that an unwanted action must go untaken on pain of suffering certain, swift and severe consequences.

The quantitative logic of deterrence
Figure 1:

The quantitative logic of deterrence

a Even a low chance of facing extraordinarily high costs can have a deterrent effect.

This is coherent logic. In the abstract, it is true that—all things being equal—a threat certain to be carried out should be more effective than one that is ambiguous; a threat that can be carried out quickly will have greater deterrent value than one that would be delivered slowly; and adversaries fear punishment from militarily powerful deterrers more than they fear weak ones. However, quantitative-inspired solutions to deterrent decay can be far less convincing when it comes to imagining their concrete implementation in qualitative terms. After all, moves to sharpen a deterrent's perceived certainty, celerity or severity are never as simple as the stroke of a pen or the making of a phone call. Rather, upgrades to deterrence must always be actualized via concrete policy changes designed to alter an adversary's strategic calculus. Such policies do not exist in a vacuum, and must also be evaluated in terms of their unintended consequences. To explore these unintended consequences, a qualitative approach is required.

In this article, we explore the generic phenomenon of moves intended to bolster deterrence having the specific unintended consequence of serving as provocations (accelerants to war) rather than stabilizing actions (actual deterrents). We posit that such an outcome will prevail in the following scenarios:

  1. If an adversary becomes convinced that the threats being made against it are incredible (unlikely to be followed through with) because the severity of the threats exceed the deterrer's underlying material interests;10

  2. If the policy change per se constitutes an overturning of the status quo from the perspective of the adversary, or else convinces the adversary that the deterrer is attempting to overturn the status quo in stages;

  3. If the deterrer seems set to accrue offensive, coercive or compellent capabilities via the implementation of a nominal deterrent, which would then create the conditions for a security dilemma or even push an adversary to consider preventive war;

  4. If moves to strengthen one arm of deterrence run counter to other means of deterrence that might be more promising; or

  5. If efforts at deterrence are likely to preclude political and economic cooperation with the adversary, the likes of which might otherwise have contributed to a more sustainable status quo.

To be clear, all of these scenarios are at risk of playing out whenever a deterrer attempts to buoy the strength of a decaying deterrent. But they are especially likely to unfold whenever attempts to restore deterrence are being undertaken under conditions of rapid or dramatic shifts in power. Whenever the distribution of power is undergoing significant change, leaders who are motivated by purely quantitative reasoning about deterrent strength are apt to be persuaded that the only way to restore deterrence is to make sizable or urgent investments in the certainty, celerity or severity of the threats being made against an adversary. As discussed, this makes logical sense when considered in the abstract. But considered in qualitative terms, sizable and urgent shifts in policy can easily serve as accelerants to war, via any of the five pathways outlined above.

The Taiwan case

In this section, we apply the logic developed above to the case of Taiwanese security. We interrogate proposals for the United States to exchange strategic ambiguity for strategic clarity to illustrate how quantitative and qualitative assessments of deterrent strength can produce wildly different conclusions about how best to uphold the status quo. The Taiwan case is useful for these purposes for two reasons: the ‘extreme’ incongruence between quantitative and qualitative logics of deterrence, which makes the Taiwan case an ideal ‘laboratory’ for testing our argument; and the obvious ‘intrinsic importance’ of the case given the prevailing conventional wisdom that war in the Taiwan Strait is an imminent possibility.11 We begin by explaining the content and context of strategic ambiguity before demonstrating how concrete moves to implement strategic clarity would be likely to trigger one of the destabilizing scenarios described above.

Strategic ambiguity: content and context

Strategic ambiguity is the policy of being intentionally vague about whether the United States would intervene militarily to defend Taiwan against Chinese aggression.12 It can be contrasted with strategic clarity, which is what the United States provides to its allies: an unambiguous guarantee to intervene militarily in the event of an armed attack by an aggressor. Usually, security guarantees from the US are codified in treaty form, such as the North Atlantic Treaty, the Inter-American Treaty of Reciprocal Assistance (also known as the Rio Pact), or the various bilateral treaties of alliance between the US and countries such as Japan, South Korea and the Philippines. From 1955 until 1980, the US maintained such a treaty of alliance with the government in Taipei (the Republic of China), which at that time the US recognized as the legitimate government of the whole of China, including both the island of Taiwan and the Chinese mainland.13

The US mutual defence treaty with the Republic of China was terminated in 1980, however, when the United States normalized diplomatic relations with the communist People's Republic of China. Since then, leaders in Washington have been intentionally vague about whether they would defend Taiwan against an invasion. Per the Taiwan Relations Act (TRA) of 1979, the US government is obliged to ‘maintain the capacity … to resist any resort to force or other forms of coercion that would jeopardize the security, or social or economic system, of the people of Taiwan’.14 However, this is not the same as a treaty of alliance. For more than four decades, the TRA and other statements by US officials have given officials in both Beijing and Taipei reasons to believe that the United States could and might intercede to repel an attack on Taiwan without the US having to say with certainty that its forces would mount such a response.

Strategic ambiguity has served America's interests well in the sense that it has helped to maintain peace and stability across the Taiwan Strait.15 On the one hand, even an uncertain threat that the US will defend Taiwan has likely helped to dissuade China from attacking the island. On the other hand, however, ambiguity about US intentions has also deterred Taiwan from taking provocative moves vis-à-vis China, such as a formal declaration of independence. In 2005, China passed the Anti-Secession Law after the re-election of Chen Shui-bian as president of Taiwan, amid concerns of an independence referendum. The law directed the Chinese state to seek ‘peaceful reunification’ but also stated that non-peaceful action would be taken if ‘the fact of Taiwan's separation’ was accomplished or if ‘possibilities for a peaceful reunification should be completely exhausted’.16 This is why strategic ambiguity is sometimes referred to as ‘dual deterrence’—because it serves to deter both China and Taiwan from overturning the political status quo through unilateral actions.

Today, however, a sizable number of analysts fear that strategic ambiguity has run its course. According to this view, circumstances have changed such that an unsure threat to intervene on Taiwan's behalf is no longer sufficient to deter Chinese aggression, which is correspondingly more likely because China's preferred option of peaceful unification is not going to plan. Only the guaranteed prospect of China fighting the United States is now enough to restore deterrence across the Strait. To be clear, the best available evidence from wargaming exercises suggests that the US has no easy pathway to victory in a war over Taiwan.17 Depending on circumstances, in fact, it is possible that the US military would lose a war over Taiwan in the sense that soldiers belonging to the People's Liberation Army (PLA) might occupy Taiwan before the US could intervene with sufficient force.

Advocates of strategic clarity acknowledge this—but they argue for strategic clarity regardless. Their argument is straightforward: no matter who would win a war over Taiwan in bare terms, the certain prospect of having to fight against the United States ought to be so terrifying for Beijing that no rational Chinese leader would order such an action.18 Of course, the costs and consequences of a US–China war have always been incalculably high: it is just that Chinese leaders have doubted whether such a war would inevitably follow an invasion of Taiwan. It is only by swapping ambiguity for certainty, then, that deterrence can be made stronger. This is quantitative logic par excellence—a wager that peace across the Taiwan Strait will be safeguarded, as long as the US can increase the certainty of severe threats being carried out swiftly.

Problems one and two: incredible commitments and unavailable commitment devices

This approach to deterrence suffers from serious problems when placed in context. First, a threat to fight a war against China—a defensive war, fought over 6,000 miles away from the continental United States at a time of China's choosing—would be challenging to make credible. Strategic clarity is, in essence, a promise to fight a war against China that 1) might turn nuclear; 2) would almost certainly result in enormous military losses and economic devastation, even if it did not turn nuclear; 3) would not easily be won, and might very well be lost; and 4) would leave the United States in a perilous security environment even if China were denied victory, narrowly defined. Can such a promise be made in a way that others will find fully believable? There are obvious reasons for scepticism, especially given that Chinese decision-makers view Taiwan as a core (vital) national interest, whereas they regard the issue as a secondary interest for the United States.19 Instead, declarations of strategic clarity might well be interpreted by China as a bluff from the American ‘paper tiger’, and would invite brinkmanship from Beijing in order to test US resolve.20

Proponents of strategic clarity admit that a war against China would be ‘disastrous’21 even if the United States won, but it is incumbent upon them to go further and explain how US leaders could be made to follow through on such threats. After all, if Beijing does not believe that the United States would carry out threats to fight against China, then strategic clarity would become a dud deterrent. For the most part, however, mechanisms to make strategic clarity appear credible to China have gone underdeveloped. This is no accident or oversight, but rather a reflection of the fact that the usual commitment devices used to strengthen extended deterrence are unavailable to the United States in the Taiwan Strait.

For example, formal defensive pacts are one of the most common ways of strengthening the credibility of a defensive arrangement.22 If two governments are willing to make public and legally binding guarantees to one another, then this strengthens the perception of their commitment to each other's security. This is because, while agreements can always be broken, it is usually at least somewhat costly for leaders to abrogate international commitments, especially those that enjoy broad political support at home. Yet the United States cannot sign a mutual security agreement with Taiwan, because the US government does not recognize Taiwan as a sovereign state. For such a treaty to be barely possible in a legal sense, let alone credible in politico-military terms, the US would first need to recognize Taiwan as a sovereign member of the community of nations. This cannot be done, because it would provide China with an immediate casus belli.

Nor can the United States station a large contingent of conventional or nuclear forces on the island of Taiwan, which is another common form of strengthening extended deterrence. In places such as Japan, South Korea and western Europe, US garrisons serve as ‘tripwires’ to bolster confidence that a sitting US president will follow through on past promises to defend an ally. The logic is that, if an attack happens and US forward-deployed forces are killed by an invading force, there would be considerable political pressure at home for the United States to repel the invaders, if for no other reason than to avenge fallen Americans.23 Again, however, the US cannot establish tripwire forces in the case of Taiwan, because doing so would cross the red line specified in China's 2005 Anti-Secession Law and would almost certainly precipitate an immediate attack on Taiwan by China. Establishing a base on Taiwan, moving nuclear weapons there once again, or permanently interposing naval warships in the Taiwan Strait cannot be said to strengthen deterrence if these actions are also liable to cause a war. To argue otherwise is to do extreme violence to the concept of deterrence.

It is more feasible that the United States could unilaterally change its policies and laws regarding Taiwan in an effort to create ‘audience costs’.24 For example, it could be written into law—or stated in some sort of public declaration—that the United States regards itself as bound to defend Taiwan in the event of an armed attack by China. The proposed Taiwan Invasion Prevention Act (introduced into the US Congress in 2021) comes close to doing this. If passed, the act would ‘provide a standing authorization for use of military force to defend Taiwan in the event of a Chinese invasion’.25 But while unilateral declarations of America's intention to defend Taiwan might have the effect of tying the hands of future US leaders without requiring a change in how the United States regards Taiwan's political status, even these could easily be interpreted by China as overturning core elements of the US' ‘One China’ policy, which, again, would run the risk of precipitating an invasion rather than discouraging one.26

Another way that states have historically tried to enhance the credibility of extended deterrence is to ‘sink costs’ towards the end of protecting a client.27 In the case of Taiwan, this would involve the United States spending enormous amounts of time, effort and money preparing for the defence of Taiwan as a way of proving to China that the US is serious about its commitments to the island. Of all the commitment devices available to the US and Taiwan, the sunk-costs approach is probably the strongest and most realistic. However, that does not mean it is strong enough to make strategic clarity credible—or that it is without other problems.

For one thing, it will be challenging for the United States to use high levels of defence spending to make costly signals regarding its intentions vis-à-vis Taiwan, because the US already spends so much on defence that China might be forgiven for believing defence spending is a consumption good for the US political class—that is, something that America's elected representatives positively want for its own sake. For another, even a massively augmented forward presence in east Asia would not, in China's eyes, guarantee a US intervention to defend Taiwan. This is because the prospect of the United States fighting a war with China is so obviously grave that Chinese leaders will have grounds to suspect that their US counterparts might decline to intervene, no matter how many forces had been pre-positioned in east Asia. Also, in operational terms, the more the United States comes to rely upon forward bases, the more of the US military China would be able to destroy in a first strike (thereby actually reducing the quality and quantity of forces that the United States could count upon in a prolonged war). This means that even if China could be made to judge that the United States intended to fight for Taiwan, the very actions that made this commitment credible could also undermine the US' ability to win a long war.28 We expand on this logic in the next section.

Problem three: simplifying China's operational calculus

What will happen if the United States continues to surge forces into east Asia as a means of convincing Chinese leaders that they cannot expect to win a war over Taiwan at an acceptable cost? Proponents of such a build-up argue that China will be deterred from attacking Taiwan. But there is another possibility: that China might perceive a narrowing window of opportunity for such an attack. In other words, if the US joined a declaration of strategic clarity with concrete moves (augmented forward deployments, particularly to Taiwan) designed to make strategic clarity credible, then this might well incentivize China to invade Taiwan before those moves were completed. Paradoxically, then, it might be better for Taiwanese security if China can maintain a low chance of seizing Taiwan militarily—an unattractive ‘outside option’ that China's leaders do not want to exercise as their best option—than for China to perceive itself being pushed into a world with a vanishing chance of seizing Taiwan by force, in which case it might become rational for China to strike, no matter how bad the odds and how costly the endeavour.

The best defence of strategic clarity when considered in these terms is that, even if the US' adoption of strategic clarity forced China to contemplate striking US forces first as part of an overall invasion plan, such calculations would raise China's expected costs of an invasion to such an extent that deterrence would be re-established. But, in fact, a declaration of strategic clarity would not necessarily worsen China's strategic position. On the contrary, the luxury of being more certain about how the United States would respond to an armed attack on Taiwan would simplify Chinese policy. Let us consider the following three scenarios, which imagine how China might deal with the presence of US forces in east Asia under different levels of certainty about the United States' intentions to intervene.

First, there is a scenario in which Chinese leaders have full confidence that the United States would stay out of a war over Taiwan. In these circumstances, it follows that Beijing would not attack forward-deployed US forces and would instead seek to secure the continuance of America's non-belligerent status, no matter how many US military assets were deployed in east Asia. This is China's best-case scenario.

Second, there is a scenario in which Chinese leaders are uncertain about a US response. Under such conditions, strategists in Beijing would face a conundrum. Choosing to attack US forward-deployed forces in a pre-emptive strike would deliver some early operational successes, perhaps akin to the Japanese attack on Pearl Harbor, but would also provoke a major power war in the process. Yet if they took a risk by wagering that the United States would not intervene on Taiwan's behalf, Chinese strategists would forgo the chance to achieve operational successes (missed opportunities that could prove costly in the event that the United States decided to intercede) but would preserve hope of securing the best-case scenario of keeping America out of the war. Of course, attacking the US when the latter would otherwise have been inclined against intervention would be the definition of foolish. However, not attacking and then facing a major US intervention would be the worst of all cases; US forces would disperse from vulnerable locations (warships sailing into the high seas, fighters moving to an agile combat employment posture), and the United States could sink many high-value Chinese naval assets (especially ferries and roll-on/roll-off vessels) in a synchronized surprise attack that integrated navy, air force and army assets and drew on the US' tradition of ‘shock and awe’ warfare. One version of China's Science of military strategy explains how dangerous this situation would be to China, given its theory of victory in war: ‘If one loses at the beginning of a conflict, then it will become very difficult to reverse this passive situation. Therefore, the first battle is incredibly important for winning the initiative in warfare.’29

Third, there is a scenario in which Chinese officials have high confidence that the United States would intervene on Taiwan's behalf. In this case, leaders in Beijing would have no reason to bring about the worst-case scenario outlined above. They would, instead, feel justified in launching a surprise attack against the US in hopes of doing enough damage to delay America's effective entry into the war. The bulk of America's forward-deployed forces would first be disrupted—their ‘system of systems’ degraded and dazzled—and a few symbolic American assets (aircraft carriers) sunk in order to undermine US morale, disrupt the US ‘operational centre of gravity’, and prove that China has successfully exploited the contemporary revolution in military affairs.30 The strategic bet here would be that after a series of Chinese successes, US leaders would decide to cut their losses, or else conclude that the United States would recover too slowly to mount a defence of Taiwan.

Chinese invasion decision-making: three scenarios
Figure 2:

Chinese invasion decision-making: three scenarios

One implication of articulating China's hierarchy of best-case and worst-case outcomes is that there is not much difference between China estimating, say, a 65 per cent chance of US armed intervention, or an 85 per cent chance. In either case, China would be likely to proceed with a first strike against US forward deployments in order to ensure operational success. The most propitious scenarios for the United States—by far—are those in which Chinese leaders are uncertain about US resolve or believe that the United States has determined not to intervene on Taiwan's behalf. These scenarios preserve the possibility that Beijing will err on the side of caution, declining to launch pre-emptive attacks on US forces even as an invasion of Taiwan proceeded apace. Under such circumstances, the United States could choose to stay out of the war (if its leaders decided this was in the US' national interest) or else could intervene with the benefit of America's forward-deployed military assets being firmly intact, seizing the initiative and eliminating the PLA's high-value assets. Under any scenario where China's answer to the question of whether America will intervene is ‘yes’ or ‘probably’, Chinese forces would almost certainly follow their own doctrine, which calls for a massive first strike against adversarial logistics and communication hubs.31

Under today's policy of ‘strategic ambiguity’, China might estimate that US entry into a war over Taiwan is more likely than not, but Chinese leaders would almost certainly categorize the chance of a US intervention as below the level of ‘high confidence’. Changing US declarative policy would nudge Chinese assessments of US intentions closer to ‘high confidence of intervention’. Although this might seem like it would consequently reduce the likelihood of war by making China more cautious, our argument is that strategic clarity would also encourage China to default to its optimal operational approach of a first strike, which paradoxically reduces operational risk by ensuring that the worst-case scenario—of a synchronized and overwhelming US armed intervention that catches Chinese forces in the middle of the Taiwan Strait—does not occur. To decision-makers, the costs of a prolonged great power war often feel uncertain and distant.32 In contrast, the costs of operational failure, in this case failing to land powerful formations on Taiwan, loom large. The operational level of war should not be allowed to trump the strategic, but it often does.33

The history of the First World War can offer some instructive lessons here. In some ways, the United States today may appear to China as Russia appeared to Germany in 1914. Back then, German leaders were faced with the problem of how to successfully fight a war against France and Russia simultaneously—a conundrum that became existential once Russia began to mobilize for war. German strategy had been formed around the idea of quickly defeating France and then turning to Russia before its mobilization could be completed. But what this meant was that Russian mobilization in July 1914 started the countdown for Germany's window of success; Berlin had to move quickly against France, and could not delay in case it became vulnerable to a joint attack by France and Russia.34

Today, China would also want a short war over Taiwan (bringing about the speedy conquest of the island), but it must know from the example of Russia's invasion of Ukraine, if from nothing else, that the United States will probably enjoy some forewarning of Chinese invasion plans, and thus may begin elements of military mobilization, such as sending fleets towards Taiwan. But China cannot load and disembark roll-on/roll-off vessels full of soldiers and military equipment with American attack submarines, F-35s and destroyers in the vicinity, because this would risk catastrophe (a ‘million-man swim’).35 Even under conditions of US strategic ambiguity, then, any sort of sustained mobilization for war by the United States could be perceived by China, as Germany perceived Russian mobilization in July 1914: as the beginning of the war, even if no shots had yet been fired. Knowing this, Chinese leaders would feel significant pressure to play their cards first and to launch an overwhelming attack at the moment of peak US vulnerability. Once US forces had been degraded, China would then turn to its true strategic objective, Taiwan. This would of course be the opposite course of action to that taken by Germany in 1914: Germany planned to secure its true objective first (defeat France) and then fight Russia to a standstill second, as a necessary but unfortunate consequence of the first action. The difference is not fundamentally strategic but technological: because the United States has the military capabilities to stop China from attaining its primary objective (with a US first strike), it would be incumbent upon China's leaders to neutralize the US threat before (or at the same time as) moving on Taiwan, if those leaders perceived that an American intercession on Taiwan's behalf was very likely.

At the least, this suggests that, if US leaders ever do determine to adopt strategic clarity, they should be confident that other deterrents are in place while the US is modifying its force structure to avoid creating an imperative for Chinese pre-emption, per the scenario described above. More generally, US policy-makers should reflect on the strategic worth of ambiguity: the less certain China is of how the US will respond, the less likely it is that Chinese action would begin with a first strike on US forces, enabling a more decisive US response, were America's leaders to determine that it was in the national interest to fight. A decisive US move that destroyed Chinese high-value assets in the Taiwan Strait would result in Chinese operational failure. Risk of such operational failure reduces the likelihood of a Chinese invasion.36 Paradoxically, strategic clarity reduces this operational risk by guaranteeing a Chinese first strike. In contrast, strategic ambiguity presents China both with strategic risk (of a long war with the US) and operational risk (of victory denial in the Strait).

Problem four: too many eggs in one basket

The problems outlined above—that strategic clarity could be interpreted as a bluff, that attempting to make strategic clarity more credible would provoke the very war that US policy is meant to avert, and that simplifying the Chinese leadership's calculus is not necessarily in the interests of the United States—should be more than enough to make the policy unattractive to US policy-makers. But there are more problems with strategic clarity than just these three, including the possibility that strategic clarity, if ever implemented without provoking a major war, would rule out (or at least seriously undermine) the creation of other deterrents by regional powers, including by Taiwan itself.

The insight here is that deterrence is always at its most credible and most durable when it is waged by actors who have the most to lose.37 It therefore makes little sense for Taiwan to stake its survival as an autonomous political entity on the willingness of a third party to intervene on its behalf—especially not when most analysts agree that Taiwan could, if it wanted to, develop an independent capacity to fight for its own security. This might involve credible plans to mount a vigorous military defence of the island that involved fully embracing urban warfare, preparing for a costly insurgency in the event of a military collapse, implementing a ‘scorched earth’ policy as the PLA advanced, and coordinating economic sanctions by Taiwan's allies and partners.38 It might also involve new ideas, such as developing the ability to disable Chinese satellites and gaining access to resilient satellite communications networks. The more Taiwan comes to rely on the United States for its defence, however, the less likely it will be to make these hard calls.39

Problem five: the militarist trap

Finally, it is worth pointing out that an American shift to strategic clarity would bring about an irrevocable deterioration of US–China relations. From China's perspective, bringing Taiwan (back) under the US security umbrella would signal a return to pre-1970s relations. Chinese leaders could have no confidence that the United States was agnostic about a potential China–Taiwan union at some point in the future. This would make war across the Taiwan Strait more likely, not less. In the meantime, essential cooperation between the US and China would become impossible.

America's political leaders should not dismiss the costs of losing China as a negotiating partner. It is widely accepted, for example, that progress on climate change and other environmental challenges cannot be sustained without the active participation of China.40 Climate targets would be missed, as China would invest more in coal, the one source of energy to which it has abundant domestic access (meaning the costs of a US-led blockade would be reduced), even as the US imported fewer Chinese batteries or solar panels, slowing its own energy transition. The argument that China would remain equally committed to slowing global warming regardless of American actions is not plausible: avoiding catastrophic defeat in war in the 2020s and 2030s will always be of a higher political priority than avoiding the generation of higher temperatures in the future.

The same is true for global economic growth, poverty reduction, sustainable development in the global South, arms control and multinational cooperation to guard against a future global pandemic along the lines of COVID–19. Any hope of China using its leverage to rein in North Korea's nuclear programme would also evaporate, as would the already slim prospects of China helping to promote peace in eastern Europe.41 At home, pushing US–China relations into the abyss of Cold War-like competition would mean vastly expanded military budgets, heightened prejudice against Chinese immigrants and Chinese Americans (and other Asian Americans), and an array of economic costs that would come along with ‘decoupling’ and ‘de-risking’. In short, the United States and the rest of the world need a strong US–China relationship—but moving to strategic clarity regarding Taiwan would preclude even the most elementary bilateral negotiations.

Proponents of strategic clarity often insist that a policy of military clarity could be implemented in conjunction with renewed diplomatic efforts to reassure the Chinese leadership about the United States' commitment to a peaceful resolution of the China–Taiwan dispute. In this view, strategic clarity need not come at the cost of bilateral cooperation; the Taiwan issue can be fenced off from other areas of mutual concern. But this is wishful thinking. If, for example, the US government followed advice to ‘reestablish U.S.–Taiwan Defense Command,’ as one prominent proposal has argued,42 the US–China relationship would be reduced to a fierce competition devoid of any rules or boundaries. China would conclude that the US was determined to prevent China–Taiwan unification under any circumstances, and, by extension, that the US was an implacable foe of China.

One objection to this argument is that strategic clarity could be framed in such a way that exempted the United States from having to defend Taiwan, if ever Taiwan's government was judged to be responsible for having provoked an invasion—for example, by declaring independence from China, or launching an armed attack of its own. In theory, such a caveat might reassure China's leaders that the US remained committed to the status quo (and open to the possibility of peaceful cross-Strait unification), thus preserving the political space for wide-ranging bilateral cooperation. However, while this suggestion makes some theoretical sense, it would be hard to implement in practice. Certainly, it would be challenging to make compatible with any of the commitment devices described above. Would a US garrison on Taiwan or a naval detachment in the Strait really stand by and watch as Taiwan's citizens were killed, simply because the US government had determined that Taiwan was at fault? When considered in this light, it is obvious that strategic clarity cannot be adopted with caveats. If it is implemented at all, it will mean a defensive commitment in all circumstances.

To be clear, strategic clarity from the United States would also have significant implications for Taiwan–China relations. Rightly or wrongly, China is likely to assume that a US policy of strategic clarity enjoyed the blessing of leaders in Taipei. They would conclude that Taiwan had become a protectorate of the United States in all but name, and that the government of the island was set against peaceful unification for all time. The political and economic status quo across the Taiwan Strait—which most ordinary Taiwanese profess to support—would be in tatters, and the Chinese military threat will have been heightened, and not lessened. There is some evidence that Taiwan's citizens understand this dynamic, with opinion polls revealing that Taiwanese sometimes view US proclamations of ‘support’ as unwelcome interventions that jeopardize the island's security.43 Even if war could be averted in the short term, the damage done to cross-Strait relations in social, economic and diplomatic terms would be enormous. Given that around 40 per cent of Taiwan's exports go to China (including Hong Kong), it cannot be ignored that China has significant economic leverage over Taiwan that could be brought to bear if China ever determined that Taiwan had chosen the path of permanent separation. In other words, a US decision to adopt strategic clarity would carry significant implications for Taiwan—worsening its immediate security environment, raising the risk of war and calling into question the island's most important economic relationship. It is therefore shortsighted to treat strategic clarity as an unalloyed good for Taiwan.

Conclusions

Under conditions of shifting power, it is not always clear how decaying deterrents can be kept in good repair. This is a problem for US foreign policy, in particular, given that the United States assumed a large number of defensive commitments (formal and informal) in the post-1945 era, almost all of which now depend upon US leaders being able to deter their adversaries from sparking regional or global conflicts. How can the various extended deterrents levelled against China, Russia, North Korea, Iran and myriad non-state actors be upheld, in an era when the United States is suffering from relative decline and strategic overstretch? Quantitative reasoning suggests that the answer is simple: the US merely needs to clarify its intention to defend allies and partners, forward deploy its military such that its armed forces can respond quickly to international instability, and boost the aggregate size and strength of its hard-power assets.

Using Taiwanese security as a case-study, we have argued that this quantitative logic makes some sense—but only in the abstract. In the case of Taiwan, exchanging strategic ambiguity for strategic clarity would create far more problems than it would solve. In truth, the United States is ambivalent when it comes to securing Taiwan in the shadow of China's rise: US leaders want Taiwan to remain free from coercion by China, but not to the extent that they are certain to fight a devastating war over the island's political status. Strategic ambiguity is therefore appropriate, because it accurately reflects the fundamental irresolution at the heart of US policy toward Taiwan. Strategic clarity, on the other hand, would appear to outside observers—not least in China—to outstrip the true strength of America's interest in Taiwan's security and de facto political independence. All of the barely conceivable options for making such a US security commitment to Taiwan seem more credible are, upon close inspection, fraught with danger, and ought not to be tried, at least in the short term. In any case, as we have argued, certainty is not a panacea, and would actually make China's strategic calculations simpler, and more dangerous. To deter China from invading Taiwan in the short and medium term, policy-makers must look elsewhere.44

These problems with strategic clarity are broadly instructive for scholars and policy-makers who focus on deterrence. What the Taiwan case shows is that an effective deterrence policy in the twenty-first century needs to mix reinvigorated (and multilateral) constraints on adversaries' freedom of action, with positive inducements for would-be aggressors to act with restraint. What this means practically is that anyone who desires to avoid war in the Taiwan Strait or elsewhere should not just look to increase the likely costs of wars of aggression, but must also avoid decreasing the value of the status quo.45 The pressing danger today is that China's own actions, its domestic economic condition, and the increasing costs being imposed on its modernization by the emerging tech war will create a situation where Chinese leaders perceive themselves to already be operating in the domain of losses, despite no military force having yet been directed against Taiwan.46 This is the opposite of stable deterrence, and implies that wide-ranging policy changes—in east Asia, but also elsewhere—are in order. If such strategic rethinking is to occur, it must be rooted in qualitative assessments of individual deterrents as well as quantitative estimates of the overall strength of deterrence.

Footnotes

1

See, for example, Oriana Skylar Mastro, ‘The Taiwan temptation: why Beijing might resort to force’, Foreign Affairs 100: 4, 2021, pp. 58–67, https://www.foreignaffairs.com/articles/china/2021-06-03/china-taiwan-war-temptation; Mike Gallagher, ‘Taiwan can't wait: what America must do to prevent a successful Chinese invasion’, Foreign Affairs, 1 Feb. 2022, https://www.foreignaffairs.com/articles/china/2022-02-01/taiwan-cant-wait; Michael Beckley and Hal Brands, Danger zone: the coming conflict with China (New York: W. W. Norton & Company, 2022). (Unless otherwise noted at point of citation, all URLs cited in this article were accessible on 22 Jan. 2024.)

2

Richard Haass and David Sacks, ‘American support for Taiwan must be unambiguous: to keep the peace, make clear to China that force won't stand’, Foreign Affairs, 2 Sept. 2020, https://www.foreignaffairs.com/articles/united-states/american-support-taiwan-must-be-unambiguous; Richard Haass and David Sacks, ‘The growing danger of U.S. ambiguity on Taiwan: Biden must make America's commitment clear to China—and the world’, Foreign Affairs, 13 Dec. 2021, https://www.foreignaffairs.com/articles/china/2021-12-13/growing-danger-us-ambiguity-taiwan.

3

On this point, see also Bonnie S. Glaser, Jessica Chen Weiss and Thomas J. Christensen, ‘Taiwan and the true sources of deterrence: why America must reassure, not just threaten, China’, Foreign Affairs 103: 1, 2024, pp. 88–100, https://www.foreignaffairs.com/taiwan/taiwan-china-true-sources-deterrence.

4

Michael J. Mazarr, Understanding deterrence (Santa Monica, CA: RAND Corporation, 2018), p. 1, https://www.rand.org/pubs/perspectives/PE295.html.

5

Richard Ned Lebow, ‘Deterrence’, in Myriam Dunn Cavelty and Victor Mauer, eds, The Routledge handbook of security studies (Abingdon and New York: Routledge, 2009), pp. 393–402 at p. 393.

6

See Michael J. Mazarr, Nathan Beauchamp-Mustafaga, Timothy R. Heath and Derek Eaton, What deters and why: the state of deterrence in Korea and the Taiwan Strait (Santa Monica, CA: RAND Corporation, 2021), pp. 41–56 and 61–81; and Jared M. McKinney and Peter Harris, Deterrence gap: avoiding war in the Taiwan Strait (Carlisle, PA: US Army War College Press, 2024), pp. 9–26.

7

Glenn H. Snyder, ‘Deterrence and power’, Journal of Conflict Resolution 4: 2, 1960, pp. 163–78 at p. 167, https://doi.org/10.1177/002200276000400201. See also Thomas C. Schelling, The strategy of conflict (Cambridge, MA: Harvard University Press, 1960); Thomas C. Schelling, Arms and influence (New Haven, CT: Yale University Press, 1966).

8

McKinney and Harris, Deterrence gap, pp. 27–36.

9

For illustrative examples of such thinking being applied to Taiwan, see Andrew F. Krepinevich, Jr, ‘How to deter China: the case for archipelagic defense’, Foreign Affairs 94: 2, 2015, pp. 78–86, https://www.foreignaffairs.com/articles/china/2015-02-16/how-deter-china; Mike Gallagher, ‘State of (deterrence by) denial’, The Washington Quarterly 42: 2, 2019, pp. 31–45, https://doi.org/10.1080/0163660X.2019.1626687; Elbridge Colby, The strategy of denial: American defense in an age of great power conflict (New Haven, CT: Yale University Press, 2021).

10

There is some evidence that conveying resolve might be especially difficult for democracies like the United States. See, for example, Joshua D. Kertzer, Jonathan Renshon and Keren Yarhi-Milo, ‘How do observers assess resolve?’, British Journal of Political Science 51: 1, 2021, pp. 308–30, https://doi.org/10.1017/S0007123418000595.

11

Stephen Van Evera, Guide to methods for students of political science (Ithaca, NY and London: Cornell University Press, 1997), pp. 79–81, 86–7.

12

Nien-chung Chang-Liao and Chi Fang, ‘The case for maintaining strategic ambiguity in the Taiwan Strait’, The Washington Quarterly 44: 2, 2021, pp. 45–60 at p. 46, https://doi.org/10.1080/0163660X.2021.1932088.

13

Richard C. Bush, At cross purposes: U.S.–Taiwan relations since 1942 (Armonk, NY: M. E. Sharpe, 2004), chs 3 and 4.

14

Public Law (United States) 96–8—Apr. 10, 1979, 93 Stat. 14, https://www.congress.gov/96/statute/STATUTE-93/STATUTE-93-Pg14.pdf.

15

Chang-Liao and Fang, ‘The case for maintaining strategic ambiguity in the Taiwan Strait’.

16

‘Anti-Secession Law’, Xinhua News Agency, 14 March 2005, accessed via Interpret: China, Center for Strategic and International Studies, https://interpret.csis.org/translations/anti-secession-law.

17

See, inter alia, Mark F. Cancian, Matthew Cancian and Eric Heginbotham, The first battle of the next war (Washington DC: Center for Strategic and International Studies, 2023); Stacie Pettyjohn, Becca Wasser and Chris Dougherty, Dangerous straits: wargaming a future conflict over Taiwan (Washington DC: Center for a New American Security, 2022); Justin Katz and Valerie Insinna, ‘“A bloody mess” with “terrible loss of life”: how a China–US conflict over Taiwan could play out’, Breaking Defense, 11 Aug. 2022, https://breakingdefense.com/2022/08/a-bloody-mess-with-terrible-loss-of-life-how-a-china-us-conflict-over-taiwan-could-play-out; Valerie Insinna, ‘A US Air Force war game shows what the service needs to hold off—or win against—China in 2030’, Defense News, 12 April 2021, https://www.defensenews.com/training-sim/2021/04/12/a-us-air-force-war-game-shows-what-the-service-needs-to-hold-off-or-win-against-china-in-2030.

18

Haass and Sacks, ‘American support for Taiwan must be unambiguous’; Haass and Sacks, ‘The growing danger of U.S. ambiguity on Taiwan’.

19

Shanbo Shao, ‘Zhong mei zai taiwan wenti de hexin fenqi’ [The core disagreement between China and the United States on the Taiwan issue], Aisixiang [Love Thinking], 18 June 2022, http://www.aisixiang.com/data/134761.html; Zhengrong Liao, ‘Meiguo dui hua weishe yu taiwan wenti’ [US deterrence against China and the Taiwan Issue], Aisixiang [Love Thinking], 21 Aug. 2023, http://www.aisixiang.com/data/145512.html. A vocal group of US-based analysts agree with this basic assessment of interests. See, for example, Charles L. Glaser, ‘Washington is avoiding the tough questions on Taiwan and China: the case for reconsidering U.S. commitments in East Asia’, Foreign Affairs, 28 April 2021, https://www.foreignaffairs.com/articles/asia/2021-04-28/washington-avoiding-tough-questions-taiwan-and-china.

20

Jianping Ruan and Ye Ruqi, ‘“Zhanlue mohu” haishi “zhanlue qingxi”? Meiguo “yi tai zhi hua” de zhengce zhenglun yu shijian luoji’ [‘Strategic ambiguity’ or ‘strategic clarity’? The policy debate and practical logic of the US policy of ‘using Taiwan to contain China’], Aisixiang [Love Thinking], 20 Oct. 2023, http://www.aisixiang.com/data/146937.html; Xiao Tianliang, ed., The science of military strategy, transl. by China Aerospace Studies Institute (Beijing: National Defense University Press, 2020), ch 7, https://www.airuniversity.af.edu/Portals/10/CASI/documents/Translations/2022-01-26%202020%20Science%20of%20Military%20Strategy.pdf.

21

Haass and Sacks, ‘The growing danger of U.S. ambiguity on Taiwan’.

22

Matthew Fuhrmann and Todd S. Sechser, ‘Signaling alliance commitments: hand-tying and sunk costs in extended nuclear deterrence’, American Journal of Political Science 58: 4, 2014, pp. 919–35, https://doi.org/10.1111/ajps.12082.

23

Recent work on deterrence has cast some doubt on the deterrent value of tripwire forces. See, for example, Brian Blankenship and Erik Lin-Greenberg, ‘Trivial tripwires? Military capabilities and alliance reassurance’, Security Studies 31: 1, 2022, pp. 92–117, https://doi.org/10.1080/09636412.2022.2038662; Oriana Skylar Mastro, ‘Reassurance and deterrence in Asia’, Security Studies 31: 4, 2022, pp. 743–70, https://doi.org/10.1080/09636412.2022.2140598; and Paul Musgrave and Steven Ward, ‘The tripwire effect: experimental evidence regarding U.S. public opinion’, Foreign Policy Analysis 19: 4, 2023, https://doi.org/10.1093/fpa/orad017.

24

James D. Fearon, ‘Domestic political audiences and the escalation of international disputes’, American Political Science Review 88: 3, 1994, pp. 577–92, https://doi.org/10.2307/2944796.

25

Gallagher, ‘Taiwan can't wait’.

26

Even if they did not provoke Chinese aggression, unilateral undertakings—alone— would not be very strong commitment devices. There is doubt about whether audience costs actually tie the hands of future leaders, and history is replete with examples of states not following through on pledges to defend another nation. See Daryl G. Press, Calculating credibility: how leaders assess military threats (Ithaca, NY: Cornell University Press, 2005); Jack Snyder and Erica D. Borghard, ‘The cost of empty threats: a penny, not a pound’, American Political Science Review 105: 3, 2011, pp. 437–56, https://doi.org/10.1017/S000305541100027X; Marc Trachtenberg, ‘Audience costs: an historical analysis’, Security Studies 21: 1, 2012, pp. 3–42, https://doi.org/10.1080/09636412.2012.650590.

27

James D. Fearon, ‘Signaling foreign policy interests: tying hands versus sinking costs’, Journal of Conflict Resolution 41: 1, 1997, pp. 68–90, https://doi.org/10.1177/0022002797041001004.

28

Oriana Skylar Mastro, ‘Biden says we've got Taiwan's back. But do we?’, New York Times, 27 May 2022, https://www.nytimes.com/2022/05/27/opinion/biden-taiwan-defense-china.html.

29

Tianliang Xiao, ed., The science of military strategy (Beijing: National Defense University Press, 2015), p. 228 quoted in Roy D. Kamphausen, ed., Modernizing deterrence: how China coerces, compels, and deters (Washington, DC: National Bureau of Asian Research, 2023), pp. 141–58 at p. 149.

30

Academy of Military Science, The science of military strategy (Beijing, Military Science Press, 2013), transl. by China Aerospace Studies Institute, 2021, p. 161; Xiao, ed., The science of military strategy, p. 389; Guangqiang Peng and Youzhi Yao, The science of military strategy, English edn (Beijing: Military Science Publishing House, 2005), p. 464.

31

Academy of Military Science, The science of military strategy, p. 143; Xiao, The science of military strategy, p. 192; Headquarters, US Department of the Army, Chinese tactics, ATP 7-100.3 (Washington DC: Army Publishing Directorate, 2021), https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN34236-ATP_7-100.3-001-WEB-3.pdf, secs 1–33; 1–38; 7–1; Toshi Yoshihara, ‘Chinese views of future warfare in the Indo-Pacific: first strikes and U.S. forward bases in Japan’, in John H. Maurer and Erik Goldstein, eds, The road to Pearl Harbor: great power war in Asia and the Pacific (Annapolis, MD: Naval Institute Press, 2022), pp. 162–82.

32

William Mulligan, ‘Armageddon: political elites and their visions of a general European war before 1914’, War in History 26: 4, 2019, pp. 448–69, https://doi.org/10.1177/0968344517736082; Marion Wullschleger, ‘Far from Armageddon: Austria–Hungary's officers and their visions of a general European war before 1914’, War in History 29: 3, 2022, pp. 563–83, https://doi.org/10.1177/09683445211029333.

33

S. C. M. Paine, ‘Japan caught between maritime and continental imperialism’, in Hal Brands, ed., The new makers of modern strategy: from the ancient world to the digital age (Princeton: Princeton University Press, 2023), pp. 415–39.

34

Christopher Clark, The sleepwalkers: how Europe went to war in 1914 (London: Allen Lane, 2012); Sean McMeekin, July 1914: countdown to war (New York: Basic Books, 2014).

35

Denny Roy, Return of the Dragon: rising China and regional security (New York, NY: Columbia University Press, 2013), pp. 199–200.

36

Academy of Military Science, The science of military strategy, pp. 23, 143.

37

Mazarr, ‘Understanding deterrence’, p. 3.

38

Joel Wuthnow, Derek Grossman, Phillip C. Saunders, Andrew Scobell and Andrew N. D. Yang, eds, Crossing the Strait: China's military prepares for war with Taiwan (Washington DC: National Defense University Press, 2022); Jared M. McKinney and Peter Harris, ‘Broken nest: deterring China from invading Taiwan’, Parameters 51: 4, 2021, pp. 23–36, https://doi.org/10.55540/0031-1723.3089.

39

See Peter Harris, ‘Deterring a Chinese invasion of Taiwan: upholding the status quo’, Defense Priorities, 16 May 2022, https://www.defensepriorities.org/explainers/deterring-a-chinese-invasion-of-taiwan.

40

Robert Falkner and Barry Buzan, eds, Great powers, climate change and global environmental responsibilities (Oxford: Oxford University Press, 2022).

41

See Huiyao Wang, ‘From wars to global warming, the world is crying out for collective action’, South China Morning Post, 12 Nov. 2023, https://www.scmp.com/comment/opinion/article/3240925/wars-global-warming-world-crying-out-collective-action.

42

Gallagher, ‘Taiwan can't wait’.

43

Alastair Iain Johnston, Tsai Chia-hung and George Yin, ‘When might US political support be unwelcome in Taiwan?’, Brookings, 5 April 2023, https://www.brookings.edu/articles/when-might-us-political-support-be-unwelcome-in-taiwan.

44

See, for example, Glaser, Weiss and Christensen, ‘Taiwan and the true sources of deterrence’; McKinney and Harris, Deterrence gap.

45

Glaser, Weiss and Christensen, ‘Taiwan and the true sources of deterrence’; Kayse Jansen, ‘How competition undermines deterrence’, Master's thesis, Missouri State University, 2021.

46

Xi Chen and Tengfei Ge, ‘An analysis of the United States' deterrence by denial strategy against China’, transl. by Interpret: China, 16 Sept. 2022, https://interpret.csis.org/translations/an-analysis-of-the-united-states-deterrence-by-denial-strategy-against-china.

Author notes

Peter Harris would like to thank Lyle Goldstein and Matthew Mai for comments on an earlier draft. Robert Lawrence also provided useful suggestions. The views expressed are those of the authors only, and not those of any institution to which they are affiliated.

This work is written by (a) US Government employee(s) and is in the public domain in the US.