The complex stability of political equilibria

Introduction

Can Afghanistan’s leaders find a domestic political bargain that offers long-term hope for stable government and that will be robust enough to withstand emerging challenges after the withdrawal of international forces? Will the Obama administration’s pivot towards the Asia-Pacific come to be seen as a momentary preference or does it represent a sustainable long-term orientation for American foreign policy? Is the same region heading towards a clear concert of powers, an ugly competitive balance, or some unusual hybrid of the two? Will the international community be able to find a workable climate change regime based around some successor of the Kyoto process, or should it be careful to avoid a one-size-fits-all approach?

These are all important political questions in their own right. But they also have something in common theoretically: they all deal with the availability and sustainability of political equilibria whose stability is important for the fields of politics they come from. This article seeks to offer an overall theory of equilibrium that can apply to political life in all of these forms, each of which relies on a degree of cooperation between political actors to operate successfully. It also develops a multi-level understanding of the stability of these equilibria that applies to circumstances of stasis and relative simplicity as well as to situations of change and complexity.

The aim here is a general approach that examines and explains equilibrium in four main political arenas. The first, as suggested in the question about Afghanistan’s future, is governance equilibrium: the ways in which states organize and arrange themselves including their regime type. The second, as evidenced in the question about the Obama administration’s rebalancing strategy, is policy equilibrium: the ways in which states develop overall policy stances including on foreign relations and national security. The third arena, as suggested in the reference to the future of interstate relations in Asia, is power equilibrium: the ways in which states develop international forms of order based on the distribution of power between them. And the fourth, as indicated by the question about the future of multilateral cooperation on climate change, is institutional equilibrium: the way states coordinate to produce the regimes that help govern the relations between them.

For any theory of stability, there is no more important question than the treatment and explanation of change. Dealing effectively with change is a prerequisite for genuine stability. The equilibrium in question may be stable because of its ability to withstand change in the circumstances around it. Or the system of which this equilibrium is a characteristic may be stable because of its capacity to shift to another equilibrium when the change renders the existing equilibrium untenable. As a result, this article develops a multi-level understanding of stability, which is applied to the different types of political equilibrium. The first level – ‘preservation’ – is used to explain stability when it represents the continuity of a particular equilibrium. The second level – ‘transition’ – is used to explain stability when it refers to the capacity for one particular equilibrium to be replaced by another. While this second level engages a more active appreciation of change than some understandings of stability, which continue to focus on preserving the status quo, a third level is also found to be necessary. This third level – ‘oscillation’ – refers to situations of complexity where there may be ongoing movement between multiple equilibria. As noted below, this may be a rather controversial step because of the widespread assumption that stability involves convergence towards a single equilibrium.

A general understanding of equilibrium and stability that can apply in quite different political contexts remains relatively underdeveloped. One possible explanation for this situation is that the enthusiasm for general theory in the social sciences which blossomed in the 1950s is not nearly so apparent over half a century later. Another is that ‘equilibrium’ and ‘stability’ may be understood as products of a status quo materialist philosophy in an age when the academic world is more interested in theories of ideationally inspired change. But, as this article will argue, it is possible to develop a theory of the complex stability of political equilibria which does justice to the dynamism and plurality of world politics. The following analysis does so first by outlining a rather broad and inclusive understanding of equilibrium. It then focuses on the first two levels of stability (‘preservation’ and ‘transition’), each of which emphasizes the retention or adoption of unique equilibria. It next examines the third level of stability (‘oscillation’) which suits a complex world of multiple political equilibria. It then explains how these three levels might work in conjunction. Finally it examines some of the implications of this research for both future projections and historical assessments of international and domestic politics.

Understanding equilibrium

In political science possibly the best-known use of equilibrium is found in classical understandings of the balance of power between states. The idea of equilibrium as both emanating from and consisting of a balance of power can be found clearly in seventeenth-and eighteenth-century Western European thinking on interstate relations. ¹ It is also evident in American international relations thinking in the middle of the twentieth century, including in the influential work of Henry Kissinger which drew directly on that European tradition. ² These ideas included the especially simple but appealing notion of equilibrium as the balance between two relatively even but opposing forces, a balance which Hans Morgenthau, another advocate of the concept, regarded as precarious. ³ A somewhat similar notion attached itself to the ‘balance of terror’ and modern deterrence theory which followed the arrival of nuclear weapons. Here there was a corresponding tendency to emphasize the instability of these equilibria, given concerns that the balance between the sides might be too easily upset. ⁴ There was also some interest at this time in using the ideas of ‘balance’ and ‘balancing’ to denote equilibria in domestic politics. As David Easton observed in the early 1950s, the idea of balance also infused notions of what he described as ‘constitutional equilibrium’ within a state which often implied ‘power distributed in roughly equal proportions among the major elements in the system’. ⁵

Within the social sciences more generally, as Cynthia Russett has noted, the concept of equilibrium is most specifically (and measurably) defined in economics. ⁶ Here the notion of balance is also an important inspiration to conceptions of equilibrium – for example, in the idea of a market equilibrium where there is a balance between supply and demand. ⁷ But especially significant is the argument that this equilibrium is the place where we can expect the system to come to rest, and to return to rest following a disturbance. The system’s tendency to maintain itself around a particular resting place encourages predictions about the behaviour of self-interested economic actors, and allows economists to theorize these workings. As Franklin Fisher notes in regards to these equilibrium positions, ‘The plans of agents (usually derived from the solution of individual optimization problems) are taken together, and certain variables – usually prices – are assumed to take on values that make those plans mutually consistent.’ ⁸ A given system is regarded as determinate if it tends towards a unique equilibrium and indeterminate if it does not. Indeterminacy, which may mean a multiplicity of potential equilibria with no obvious ranking between them, is correspondingly problematic for orthodox economic thinking.

The notion of an equilibrium as a unique resting place can be interpreted in an imaginative fashion to examine social behaviour. Thomas Schelling, for example, developed the idea of an equilibrium as a resting place at which expectations and behaviour can be coordinated. ⁹ As a result, (and with creative insights from game theory) equilibria can be treated as consistent patterns of behaviour which stand out from the background. These patterns of behaviour offer a sense of continuity: they are focal points which offer clear choices and thus resolve the potential indeterminacy of processes which might otherwise suggest a paralysing multitude of potential outcomes. As H. Peyton Young observes, ‘A convention is an equilibrium that everyone expects.’ ¹⁰ These equilibria can be understood in qualitative behavioural terms rather than in the quantitative material terms one might expect from some of the treatments of equilibrium in neoclassical economics.

This article takes a similarly broad approach to the concept of equilibrium (although, as the reader will discover, it regards multiple equilibria situations as opportunities to be exploited rather than as problems to be resolved). It deals with four types of qualitative political equilibrium which encompass both the power and policy aspects of domestic and international political life. The first is ‘governance equilibrium’. Here a given country’s regime type (democracy, autocracy or some other) might be viewed as an equilibrium which is retained in line with domestic and international conditions. For example, the division of federal power in the United States might be seen as an equilibrium representing a consistent pattern of behaviour and expectations over more than 200 years. The fact that it produces a balance between the three, as emphasized by Morgenthau, ¹¹ is somewhat coincidental to this analysis. Instead it is more closely connected to Easton’s notion of general political equilibrium, where ‘constitutional democracy would be just a particular kind of equilibrium’ and ‘where the theoretical model’ could even be a dictatorship if ‘none of the elements would find any inducement to alter its position’. ¹² In other words it is a steady state, although this particular term may encourage a static view of political equilibria which this article is keen to avoid.

The second type is ‘policy equilibrium’. Here we might observe what would seem to be a consistent tendency within the policy stance of a particular country. It might be argued, for example, that independent India has had a Nehruvian foreign policy equilibrium which has proved particularly challenging to alter (or which reappears even when other equilibria are being promoted). Another example might be Canada’s consistently strong commitment to multilateral institutions.

The third type is ‘power equilibrium’. Here a particular constellation of power between states may prove persistent over a substantial period – for example, the bipolar power structure of the international system during the Cold War period dominated by United States and the Soviet Union. Another example might be the longstanding multipolar concert of power in post-Napoleonic Europe. It is possible that such an equilibrium may also take the form of an effective imbalance of power, such as the operation of American unipolarity in the post-Cold War international system.

The fourth and final type is ‘institutional equilibrium’. Here, the free market norms supported by the World Trade Organization, for example, may constitute an equilibrium of an institutional sort. As both Robert Keohane and Oran Young suggest, institutions can be informal as well as formal. ¹³ This means that the stability of an institution can often be regarded as the stability of a given set of rules rather than the survival of an organization. In turn, as Hedley Bull argues, these rules contribute to international political order which itself is based on the operation of institutions. ¹⁴ Within Southeast Asia, the norms of non-interference and consensus undergirding the Association of Southeast Asian Nations (ASEAN) since its inception in 1967 might be regarded as representing an institutional equilibrium in a particular regional setting.

The first and second levels of stability

The various types of political equilibrium considered in this article can be stable (or unstable) in three ways or levels. The first level (‘preservation’ stability) is associated with the retention of a particular equilibrium. Here the stability of the equilibrium refers to its ability to remain intact. As Russett’s book shows, two notions of equilibrium come into play in the social sciences at this point. ¹⁵ One is a mechanical understanding as seen in a pendulum which tends to return to a particular position following a disturbance. The other understanding is organic, seen in the self-regulating homeostatic properties of blood sugar levels in non-diabetic people. The organic variant in particular suggest that for genuine stability to operate the equilibrium needs to be able to withstand significant shocks and disturbances and to do so without generating major harm to those actors who depend upon it. In other words the mere existence and persistence of the given equilibrium is not a sufficient condition for stability. A second condition of harm avoidance is also very important. ¹⁶

This style of thinking about stability has clear applications to the social world. With reference to the work of Vilfredo Pareto and Lawrence Henderson in the early decades of the twentieth century, Russett observes that ‘Equilibrium in society meant simply this: any small change in the state of the system would engender a reaction tending to restore the original state as unmodified as possible.’ ¹⁷ This fits in well with the first level of stability discussed in this article (equilibrium preservation) which can be applied to each of the four types of political equilibrium under consideration. For example, in governance equilibrium a first-level stability question could involve the sustainability of the Chinese Communist Party’s authority (and control) in Beijing against the backdrop of ongoing economic and social change, internal migration and the limited legitimacy of socialist dogma. Another would be the sustainability of democratic governance in East Timor as that still rather recently independent country struggles against significant social, economic and political pressures.

In terms of policy equilibrium, the first-level idea of equilibrium preservation can be detected in the existing work on the stability of foreign policy. For instance Goldmann explains ‘foreign policy stability’ as the tendency of a policy to resist change. ¹⁸ One potential example is the continuity of New Zealand’s strong support for nuclear disarmament which has a strong domestic constituency and which has survived changes in government at the domestic level as well as changes in the international system. The solidity of this policy is such that the United States has been willing to restore significant aspects of security cooperation with New Zealand without expecting that non-nuclear position to change. Another example could be the United Kingdom’s consistent quest for a strong alliance relationship with the United States, which has survived numerous changes of government in both countries and the shift from the Cold War period to the post-Cold War era. Of course this same example suggests that a corresponding quest for such a strong alliance relationship was not nearly as stable in New Zealand’s Cold War experience.

A similar logic applies to power equilibrium. An important first-level question to be asked here in the contemporary international system concerns the future of American primacy: if some observers are right, this equilibrium may not be as stable in the early twenty-first century as it was in the early post-Cold War period. ¹⁹ There are also regional examples of power equilibria: one is the ongoing balance in South Asia between India and Pakistan, which demonstrates that stability does not require symmetry. Finally, in terms of institutional equilibrium we might look at efforts to preserve the Nuclear Non-Proliferation Treaty as the central element of the international non-proliferation regime despite the challenges which have been posed by the development, testing and accumulation of nuclear weapons by both India and Pakistan, the small nuclear weapons programme of North Korea and Iran’s involvement in the nuclear fuel cycle. Or we might wonder what the collapse of the Doha Round of international trade negotiations in 2006 meant for the stability of the free trade norms supported by the World Trade Organization, or what the paralysis at Copenhagen in 2009 has meant for the hopes of organized restraint on carbon emissions.

This first-level understanding of stability risks confirming the suspicion that to utilize ideas of equilibrium in the social sciences, and especially in political science, is to buy into a very conservative outlook which places a premium on preserving the status quo. It can be observed, however, that the organic versions of first-level (‘preservation’) stability do in fact incorporate and recognize the reality of change. A homeostatic process adjusts constantly to the external change around it, but manages to retain its own essential characteristics. Even so, a more unequivocal means of addressing the issue of change is still required, especially when that change exceeds the bounds of tolerance which the existing equilibrium can manage. This is provided by the second level of ‘transition’ stability where a single equilibrium is exchanged for another. Here we are not evaluating the stability of a particular equilibrium as in first-level stability. Instead the focus shifts to the system’s ability to make a major adjustment: is it able to locate an alternative equilibrium in a time of major change which offers a better fit to those new circumstances?

This second level stability is reminiscent of W. Ross Ashby’s work on adaptive systems as part of the new science of ‘cybernetics’. ²⁰ This work took inspiration from the adaptation which learning systems such as the human brain were capable of demonstrating. In a subsequent systems-based account of political processes, Morton Kaplan adopted Ashby’s concept of ‘ultrastability’ wherein ‘Periods of transitional adjustments, either in the behavior of individuals or in social systems, may represent attempts to find new patterns of stable behavior after the old patterns have proved unstable for some reason’. ²¹ It is an easy translation to view these patterns of behaviour as equilibria.

Similar thinking, although in a different context, can be found nearly two decades later in the biologist C. S. Holling’s influential discussion of ‘domains of attraction’ in ecological systems where ‘the important point is not so much how stable they are within the domain, but how likely it is for the system to move from one domain into another and so persist in a changed configuration’. ²² Here Holling’s interest is in the preservation of the given species in an overall sense rather than its capacity simply to maintain itself at a particular population level. In other words the emphasis is on the stability of the system (which he calls ‘resilience’) rather than the stability of a particular equilibrium value (which he calls ‘stability’). Holling’s work also connects us back to the argument made above that a stable system needs to be one where no major harm is done to those who depend upon it.

The idea of moving from one stable equilibrium to another also has parallels with the theory of punctuated equilibrium in evolutionary thinking, which also came into prominence in the 1970s. While admitting to several versions, an attempt by Somit and Peterson to distil a common approach suggests that ‘at its most basic, punctuated equilibrium involves two key propositions: first, that species undergo long periods of little or no evolutionary change; second, that these lengthy intervals of stasis (i.e. equilibrium) are broken (i.e. punctuated) by relatively rapid speciation events’. ²³ Here there is a tendency to differentiate between long periods of stability (i.e. stasis) and short, intense moments of change during which a new equilibrium is located.

Frank Baumgartner and Bryan Jones have utilized this theory in their examination of the American political system which ‘displays considerable stability with regard to the manner in which it processes issues, but the stability is punctuated with periods of volatile change’. ²⁴ This approach, and the useful survey of related domestic policy applications by Peter John, ²⁵ tends to suggest a dichotomy between stability and change. Yet if volatility is part of the transition from one stable equilibrium to another we may be less inclined to regard it as inherently destabilizing. The welcoming of change as a possible sign of overall stability (rather than instability) has some interesting applications in the governance category of political equilibrium. For example, the political volatility which accompanied the post-Suharto era in Indonesian politics (after the collapse of that veritable political dynasty under the additional pressure of the 1997 Asian financial crisis) may be interpreted as a necessary part of the successful transition from an authoritarian governance equilibrium to a democratic governance equilibrium. By contrast, the absence of change in the Suharto era, while at the time often seen as a sign of stability, including by Western powers, was eventually a sign of its systemic instability.

We might also apply the idea of transition stability to a circumstance when no previous governance equilibrium appears to have existed. An example here might be the initial agreement of a social contract where a polity is rescued from the situation which Thomas Hobbes famously described as consisting of ‘no Society; and which is worst of all, continuall feare, and danger of violent death; And the life of man, solitary, poore, nasty, brutish, and short’. ²⁶ Yet even in this Hobbesian world there may well be patterns of behaviour which, while unpleasant, could be regarded as constituting an equilibrium of sorts. (This may not satisfy, however, the avoidance of harm, which is the second requirement for stability.) Moreover while the initial establishment of the contract might be a form of transition stability, its ongoing maintenance might be considered simply as a case of first-level stability. Indeed, the combination of a social contract’s establishment and its maintenance over time is a central theme in the evolutionary game theory of Robert Axelrod where the equilibrium consists of a mutual strategy of cooperation. ²⁷

Second-level ‘transition’ stability can also apply in the three other types of political equilibrium. One example from policy equilibrium could be the shift from Australia’s forward defence strategy of the 1950s and 1960s to the defence of Australia logic which was more in keeping with changed external circumstances (the reduction of British and American regional commitments) and which also had a good fit with Australia’s own evolving worldview. There is just a chance that after a period of extensive expeditionary commitments since the 9/11 attacks on the United States, Australia’s defence policy in an era of austerity will find that defence of Australia policy equilibrium a comfortable resting place. One might also argue that after the Second World War, Japanese security policy found a new ‘pacifist’ equilibrium which represented a conjunction of external and internal (constitutional) trends. In the early twenty-first century, as that existing equilibrium is increasingly questioned, Tokyo’s task now is to look for some sort of normalized security policy equilibrium. It might be asked here if we are simply talking about the movement between successive foreign policy strategies. But ‘strategy’ implies a deliberate choice to pursue a particular approach. ‘Equilibrium’ implies that there is somewhat less choice here – these are positions shaped by internal and external influences effectively beyond the control of the state actor which occupies something of a mediating position between them. It suggests a natural resting place as much as it does a deliberate strategy.

In power equilibrium there are many potential examples of transition stability where one equilibrium is exchanged for (or surpassed by) another. One obvious and still fairly recent case is the transition from a bipolar Cold War distribution of power to a unipolar situation, which may itself prove to be a relatively brief phase en route to a new multipolar distribution in which China and India are increasingly prominent. Such an understanding might be questioned on the basis that, because it seems to include any possible change in the international distribution of power, the overall system is always going to be stable by this measure. (And if stability includes all circumstances and excludes nothing it may have no explanatory value.) However, the transition from a bipolar to a more unipolar world order did occur relatively peacefully and this would seem to suggest that the avoidance of harm condition has also been satisfied. Whether the shift toward a more multipolar world will have that same feature is yet to be determined, and will depend to a considerable degree on the extent and intensity of Sino-US strategic competition.

Finally, there are also institutional examples that suggest the plausibility of transitional stability. In recent times, the same group of 18 countries can be found in the expanded membership of the East Asian Summit and the ASEAN Defence Ministers Meeting Plus group. These members include the ten ASEAN countries plus eight others: China, Japan, South Korea, India, New Zealand, Australia and, more recently, the United States and Russia. This consolidated grouping seems to have taken at least some of the running from older and more inclusive economic and security groupings such as the Asia Pacific Economic Cooperation (APEC) forum and the ASEAN Regional Forum. This transition is far from complete, in part because these older bodies have not been disbanded and because America’s renewed interest in Asia-Pacific multilateralism has given APEC a little more energy. But there does still appear to be some sort of evolution taking place in the Asia-Pacific’s organizational future. A less formal example (in which institutions refer as much to practices as to organizations) may involve the rise of norms of humanitarian intervention in global affairs to challenge the pre-existing institutional equilibrium around non-intervention. Here the jury may still be out, not only in terms of whether that transition has properly occurred, but also whether it can do so without major harm being done to the actors in the system. At the time of writing the international community’s response to the events associated the Arab Spring, including the violence in Syria, are part of this test.

Level three: the stability of multiple equilibria

The first and second levels of stability rely on the assumption that at any given time there is a unique equilibrium. The aim is either to hang on to the original unique equilibrium (preservation stability) or to replace it with another unique equilibrium (transition stability). But it is unlikely that reality conforms to these rather reassuringly simple pictures. First of all, most equilibria are likely to be dynamic in and of themselves, even if they are unique. As James Rosenau argues in an obvious application of organic views of the world to political processes, ‘Like any other type of organism, the political entity is never quite the same from one moment to the next, and yet it is never entirely different either.’ ²⁸

The same might be said for any one of the four types of political equilibrium. In terms of governance equilibrium, a ‘descent’ by Afghanistan into a polity which is increasingly dominated by rivalries between local power brokers (including warlords and the Taliban) after the withdrawal of Western forces in 2014 might be interpreted as a return to the default (and pre-existing) power equilibrium for that country. But for a range of internal and external reasons this equilibrium will not be identical to its earlier variants. There may also be something eerily familiar in the non-liberal tendencies of Vladimir Putin’s Russia, and some of the formal institutions of state power have at least some resemblance to their forebears. ²⁹ But we should not expect this to be a straightforward return to an older autocratic equilibrium because of internal and external changes, however much Putin seeks to take inspiration from earlier examples of strong Russian leadership.

In terms of policy equilibrium, a good example here may be Washington’s policy of containment. While this served as a steady equilibrium for a long series of Cold War decades, containment was an adjustable mechanism, not least because the United States’ understanding of international communism altered as the years went on. China’s apparent interest in a hierarchical regional system may be another such example. Such an interest may persist even if Beijing does not and cannot seek a carbon copy of the imperial tributary system.

In terms of power equilibrium, the international system at time t + 1 may be just as recognizably unipolar as it was at t, but this does not mean it will be identically so. There were differences, for example, between the still novel American unipolarity of 1991 (George H. W. Bush’s New World Order), and its more assertive cousin in 2002 (George W. Bush’s doctrine of ‘pre-emption’, which was in reality a logic for preventive war). And while international relations scholars may be able to draw some interesting parallels between the global multipolarity which may already be upon us and the experiences of the nineteenth and early twentieth centuries which involved the jostlings of a world of many great powers, they are wise to avoid drawing too many direct ‘back to the future’ lessons. ³⁰

Finally, the evolution of particular institutions provides weighty support for the same thinking. Here the European Union serves as an interesting example. Few would doubt its uniqueness as Europe’s dominant institutional equilibrium. But the European project’s fluctuating fortunes, from steady progress to grandiose hopes and then to the recent despair born of financial crisis, indicates the variability built into this one example. Moreover the connections between the modern EU and the principles behind the establishment of the European Coal and Steel Community, the product of the very early days of European integration, are also impossible to ignore. To continue the quotation from Rosenau, ‘political organisms are always both constant and evolving, always both adhering to past precedents and forming new patterns’. ³¹

There is a second and even more significant reason why the assumption of a singular equilibrium (common to stability levels one and two) is unlikely to hold. Even if a particular equilibrium is dynamically adjusting and adapting as we have just seen, or if a transition is occurring from one dynamic equilibrium to another, there are reasons to question whether political systems will be characterized by just one equilibrium at any given time. We should instead be expecting to see multiple equilibria in many of these situations. This is a familiar situation for economists who have grappled for many years with the existence of multiple equilibria in ‘non-cooperative’ games: despite the terminology these are not games where cooperation is impossible, but instead where there is no outside authority to enforce cooperation – a situation which resembles what Bull calls the anarchical society in international politics. ³²

The existence of multiple possible equilibria is a problem for economists because there is no unique equilibrium around which behaviour can be coordinated. As George Malaith notes, a number of explanations have been developed as to how a unique Nash equilibrium can be found in these situations. ³³ (In a Nash equilibrium no party benefits by changing its strategy in the knowledge that the other players are sticking to theirs.) These explanations include Schelling’s focal point theory noted earlier in this article. But what if the very multiplicity of equilibria was regarded as unavoidable and unresolvable? Would this make stability impossible?

This somewhat heretical question is encouraged by complexity theory, a branch of thinking which examines non-linear processes where the relationships between initial conditions and their global results can be difficult to predict, but where there is nonetheless a tendency towards emergent patterns of organization. As J. Barkley Rosser explains, complexity theory leads us to expect that many systems will tend towards multiple equilibria. ³⁴ These multiple equilibria may also occur simultaneously. This poses a challenge for theories involving cooperation because it would then not be clear (at any particular time) exactly where coordination could be arranged.

The concept of ‘multistability’, which can also be traced back to the work of Ashby, ³⁵ comes into play here. Within cell biology, for example, the existence of ‘bistability’ has been recognized for some time. This sort of system ‘toggles between two discrete, alternative steady states, in contrast to a monostable system, which slides along a continuum of steady states’. ³⁶ But there is also increasing interest in multistability where ‘multiple equilibrium states, or “attractor states” may co-exist in high-dimensional state space’. ³⁷ There is a corresponding interest in economics where ‘multistability’ equates to the ‘coexistence of many distinct attractors’. ³⁸ It could be argued that this multistability is problematic because it makes it difficult to ascertain the dynamics of the situation: this is certainly the case for the consideration of this concept in economics. But we might also argue that for any political process to be stable in a complex environment it will need to have a good fit with multiple possibilities. To borrow the language of Erica Jen, there is a requirement for ‘robustness’ here. ³⁹

Rather than a complete and clear shift from unique equilibrium a to unique equilibrium b as envisaged in second-level ‘transition’ stability, we might expect a pattern of ongoing oscillation between multiple equilibria a, b and c. It would be wise, therefore, for any political actor in such a process to maintain multiple strategies so as to keep their options open. Stability no longer rests on identifying a unique political equilibrium which needs to be retained or found, but instead on understanding the pattern of oscillation which is involved in a complex system. This judgement takes advantage of the idea of emergent organization within complexity thinking: the capacity for patterns to develop even when the system appears chaotic.

Examples of third level ‘oscillation’ stability can be suggested for all four types of political equilibrium under consideration in this article. For example, stable governance for Indonesia might actually oscillate between liberal and more guided democratic arrangements, and between Jakarta-centred and provincial arrangements. A similar picture might apply to post-2014 Afghanistan where any hopes for political stability may need to anticipate a variety of concentrations of authority. In terms of policy equilibrium, a stable foreign policy pattern for the United States might be one which oscillates successfully between the Wilsonian, Hamiltonian, and other traditions which Walter Russell Mead has observed. ⁴⁰ By contrast, a foreign policy fixed on just one of these traditions might be unable to cope with the change in international and domestic politics. A stable order in the Asia-Pacific may be one which oscillates between a great power concert, moments of US leadership and a balance of power in which China is increasingly prominent. A stable institutional setting for dealing with regional economic integration might be one which oscillates effectively between progress towards a plurilateral Trans-Pacific Partnership (involving the United States), ASEAN+1 cooperation where China is more prominent, and other forms.

Combining the three stability levels

Continuing oscillation is likely, however, to be regarded as a sign of instability by those reared on first-level stability thinking which focuses on the determinacy of a single equilibrium position. But the first and third levels of stability (equilibrium ‘preservation’ and ‘oscillation’) might actually combine in some instances. Malaith points to the existence of different ‘strategy profiles’ (which we might translate as different mixes of multiple equilibria) wherein there is one particular profile to which the system tends. That stable equilibrium profile still allows for what we would call oscillation because it consists of a combination of strategies: ‘The important feature is that behavior within the population need not settle down to a steady state, rather it can “drift” between the different patterns within the “evolutionary stable” set.’ ⁴¹ And we should probably expect oscillation as a natural part of most political processes. John Maynard Smith suggests that oscillation is common when games are asymmetric: i.e. when the roles and payoffs of the participants are not identical. ⁴² Most political situations can be regarded as asymmetric games because symmetry is the exception rather than the rule, if it ever really exists at all.

These considerations may help ameliorate the old coordination problem: in the absence of a single equilibrium, how and where can expectations and behaviour converge to produce some sort of agreement, convention or order? For if we expect multiple equilibria, but if we also have a sense of the set (or pattern) of multiple equilibria in play, at least some coordination should be possible. For example, two governments may be able to enjoy a stable bilateral relationship not because they each settle on a single consistent policy equilibrium and know the single policy equilibrium that the other is sticking to as well. (This could well be expecting too much: both may wish to keep options open.) Instead if both sides know that each of them will wish to keep options open but also have a reasonable idea of the mix of options likely to be favoured, some measure of coordination may still be possible.

We might find this operating in the bargaining strategies which are being used as Iran and North Korea are engaged by other members of the international community on the future of their respective nuclear programmes. Coordination may be possible here around a mix of equilibrium policies including deterrence and rewards, disarmament and accommodation. Stability comes here not from an absolute answer (a single bargain which is struck) but from an implicit agreement that the mix of approaches is heading in a generally acceptable direction, or at least a direction that is better than the worst possible outcome. Of course, in the case of Iran in particular, it is not clear that there is any likely mix of equilibria which may achieve that.

There might also be useful combinations of levels 2 and 3 (‘transition’ and ‘oscillation’) stability. Even if we are seeking to identify a transition from one unique equilibrium to another, it might also be best to think in complex stability terms: looking into the future we may not be aware which single outcome from a range of possible alternative equilibria might be decided on, and which one we can get the other parties to converge around. For example, looking at Indonesia’s governance equilibrium today, we might be tempted to conclude that there was a clear transition from the autocratic equilibrium of the Suharto era to today’s more democratic system. But looking forwards as the Suharto dynasty was crumbling in the mid 1990s, the picture was not nearly so clear. It could easily have gone in one of many different and much more depressing directions. Some analysts were certainly not as confident as we might expect looking back from the situation we have now. ⁴³ As C. F. Kurtz and D. F. Snowden argue in general terms, ‘Once a pattern has stabilized, its path appears logical, but it is only one of many that could have stabilized, each of which would also have appeared logical in retrospect.’ ⁴⁴ We need to be ready for a range of possible equilibria which might display different levels of fitness to the internal and external dynamics around them.

The process of transition itself may also consist of multiple steps, as transient equilibria are found along the way. For example, one study of North Korea’s gradual process of economic reform suggested in 2006 that ‘The process in North Korea will move forward and backwards and fluctuate frequently in search of temporary points of equilibrium, before reaching a relatively stable economic and political plateau.’ ⁴⁵ The task confronting North Korea is especially difficult because of the lack of a historical equilibrium which resembles where it may well be heading. Precedent is important here, not because future equilibria will be carbon copies of the past, but because they provide part of a set of optional dynamic equilibria from which either a single choice may be made (as in transitional stability) or between which the system may oscillate or drift (as in complex stability). However, precedent is not always a useful guide if the external and internal changes which have subsequently occurred are so great that even a revised version of that earlier equilibrium can no longer fit. This may be part of the challenge facing those who seek refuge in earlier political equilibria as a way of dealing with the perplexing changes of modernity. Attempts to reassert tribal systems of governance (or a theocratic system) as single equilibria may be recipes for even weaker statehood than the modern system they seek to replace. By the same token having a (dynamic) tribal political equilibrium as part of a wider equilibrium set, alongside rather than instead of the modern system, may prove part of a more robust set. Perhaps that is one way of depicting the reality of politics in Papua New Guinea or Solomon Islands.

Finally, on some occasions it may be possible for a political system to make a transition from one of Malaith’s ‘evolutionary stable set’ of equilibria to another stable set in response to the emergence of one or more new serious equilibrium candidates. In power equilibrium, for example, this may be necessary because of the emergence of a new great power. In institutional equilibrium it may involve the rise of a new organisation or norm. And the coordination issue here is similar to that previously discussed – coordinating with the new set of equilibria. This might be stretching the allowable boundaries too far for some theorists. For example, it may well violate the thinking behind ideas of ‘collective’ and ‘evolutionary’ stability in evolutionary game theory. Axelrod admits that ‘There may be many evolutionary stable strategies’ because in some situations ‘there is no single best strategy’. ⁴⁶ But the introduction of new equilibrium candidates which then coexist with the pre-existing ones might be considered destabilizing because a stable strategy is one which can ‘resist invasion by mutant strategies’.

Yet even here there may be an answer in research findings outside of political science. As Ulf Dieckmann and Michael Doebeli explain, the theory of adaptive dynamics, which seeks to emphasize ecological diversity, offers the concept of ‘invasion fitness’ in biological populations which appears to allow for ‘polymorphic’ stability: i.e. the stability of many equilibrium shapes. ⁴⁷ One such study of seed sizes concluded that when competitive asymmetry increases, ‘evolutionary stable polymorphisms with progressively larger numbers of different seed sizes become possible’. ⁴⁸ There is some hope, therefore, for the idea of a changing but still stable set of multiple equilibria. This may counter the argument by Bryan Skyrms that polymorphism is a ‘problem’ and a ‘pitfall’ in evolutionary game theory because of the multiple equilibria it suggests. ⁴⁹

Ideas of a single best fit in evolutionary game theory and of self-interested optimization in economics tend to assume the sort of ongoing improvement which may be out of place in some political settings. Allowing for the potential to oscillate between ‘new’ (or ‘better’) and ‘old’ (or ‘worse’) equilibria may be a more realistic approach in our discipline. Hence while the approach taken in this article requires a theory of stable political equilibria to incorporate a theory of political change, it does not share the emancipatory objectives common to some other theories where change is often welcomed as carrying the potential for an increasingly free and freeing politics.

Political consequences: looking forwards and backwards

One of today’s most important political questions is the extent to which difference can be tolerated, including forms of domestic political organization in other states and their approaches to international norms and institutions. What are the limits for us in terms of what might count for order? The common realization from years of nation-building efforts in various places that there is no single model to be shored up is one sign of the importance of this question. Is stability here more than the stability of a single preferred equilibrium? Are we willing to allow different equilibria in different societies which fit different internal and external conditions? And how much effort should go into supporting a particular constellation of power in international relations? Are some Asia-Pacific countries putting too much of their hope on the longevity of America’s strategic power? I say ‘too much’ here not because Chinese regional dominance is on the horizon, but because there will continue to be oscillation between alternative power distributions depending on the issue and location: some may favour American leadership, others Chinese leadership and so on. How much effort goes into trying to stabilize a single policy equilibrium – i.e. a free trade policy – when a more pluralistic strategy may have a better chance of sticking and may in the end produce better overall outcomes?

A complex understanding of stability may also have some significant implications for our appreciation of the past. We are tempted looking back to see one era based around one equilibrium replaced by another. This is to some extent reinforced even by the notion of learning and adaptive systems and by aspects of evolutionary game theory where a single Nash equilibrium is eventually selected. But complexity should inform our appreciation of what has gone before as well as of the possibilities in front of us.

For example, in the realm of power equilibrium, it is commonplace to argue that the bipolar order of the Cold War was superseded by a unipolar order based on American primacy which in turn may give way to a multipolar system. Indeed that very argument has been made in this article. But what if that bipolar system was just one of a number of equilibria in that Cold War period? At times, especially in Asian affairs, there was a tripolar distribution of power involving the United States, the Soviet Union and China. In his examination of Australia’s options after America’s difficult and draining years in Vietnam, Hedley Bull suggested that Canberra should in fact rely on a quadrilateral equilibrium which also involved the Soviet Union, China and Japan. ⁵⁰ Even if that Asian equilibrium did not come to pass, it is more than likely that there was some sort of oscillation between the bipolar and tripolar distributions of power in Asia. This mean that the stability of the Cold War rested not just on the stability of the bipolar balance (i.e. of a single ‘power’ equilibrium). It also depended on the extent to which this set of multiple equilibria (a set including bipolarity and tripolarity) proved a good fit to the internal and external conditions which helped shape it.

Conclusion

Recognizing the complex stability of multiple equilibria is not without its challenges. One of the appeals of a single equilibrium model is that all actors remain on the same page: indeed it could be argued that they focus on the same single letter in the same word in the same sentence on that same page. This is not so much about the optimization of collective interest around the single best equilibrium, an issue which is examined by Jon Elster. ⁵¹ Instead it is more about the practical appeal of consistency and simplicity. Transition stability means shifting to a different, but still unique, letter. But complex stability means we have to be aware simultaneously of a number of letters on different parts of the page. Complex stability seems to undermine the obvious analytical appeal which comes from treating a single equilibrium as a unique bargain: the idea that we may have to deal with multiple simultaneous bargains over the same issue does not seem to stick quite so well. And some situations may require single stable equilibria for the system to work at all without complete chaos and mutual harm. One non-political example is the convention of driving on the right-hand side of the road in the United States: although there are opposite conventions elsewhere, as H. Peyton Young observes, ⁵² they are still singular within those countries. (Even so, if we are international travellers we need to be aware of the differences.)

But if we regard politics as an inherently messy business, we might be attracted to complex stability not because it seeks to narrow down the range of possible outcomes to an analytically neat and powerful unique point, but because it narrows them down to a realistic selection of likely (but non-unique) steady states. In other words, we do not have to abandon the search for patterns in politics. But in doing so we can still take account of the constant jostling between alternative positions which is the essential, and perhaps unchangeable, stuff of political life domestically and internationally. The question really is whether we can be satisfied by realizing that this jostling never stops.