Scott E. Page
Department of Economics, Pappajohn Building, University of Iowa, Iowa City, IA 52242-1000, USA.
Children and adults play with dominoes differently. Children stand the dominoes adjacent to one another, paying no attention to the number of dots on any particular tile. They then push over the first domino and watch the rest topple in sequence. More advanced children create patterns of topples. A single row might split into distinct paths that later cross. In contrast, adults play a strategic game. And, although this game relies on simple rules, it supports rather sophisticated strategies. Novice players learn to leave themselves an out. Advanced players employ more subtle tactics. They may try and force opponents to take certain actions or to signal information inadvertantly about what tiles they hold. Ironically, the way that adults play with dominoes also creates dynamic patterns. These dynamics differ in two respects. First, they occur less quickly than in the children's version of play, and second, the adult patterns rarely could have been predicted from the initial distribution of tiles.
I mention dominoes because the "domino theory" is one of the few popularised models in international relations, aside from the Prisoner's Dilemma. The domino theory of international relations is essentially the children's version. Tip one, and they all fall down. In this ambitious new book, Robert Jervis proposes that scholars consider the adult version of the game, that they study strategic behaviour in a systems framework. I agree. According to Jervis, a complex systems approach will help us to understand the evolution of micro-level strategies and their emergent macro-level patterns. This approach will force recognition that the whole exceeds the sum of its parts, that feedbacks can be positive or negative, and immediate or delayed, that the mapping linking incentives to outcomes need not be linear, that not only the state of the world but how we got there might matter, and finally, that when choosing one of the two equally compelling paths (in the words of Robert Frost - two roads in the yellow woods), we often alter the environment that created the paths.
And yet, lest we all trip over ourselves singing the praises of complex systems theory, we must first ask: is there any theory in complexity theory? Or, to borrow a phrase from Michael Cohen, is complexity theory just a festival of bad metaphors? If you pose these questions to an arbitrary social scientist, you will undoubtedly receive one emphatic yes and an equally emphatic no. I just cannot predict the order in which you will receive those two responses.
Unfortunately, for those of us interested in those two questions, this book does not produce any new mathematical theory, nor does it claim to do so. Nevertheless, Jervis makes a case, and a strong one, that international relations are complex, that interdependence is the rule not the exception, and that feedback can be so elaborate that only a genius or a savant could anticipate the future. In these circumstances, Alice in Wonderland might be a better guide than a book of logic. Suppose you want to maximise your power. (Ignore the fact that power is not a well defined concept like utility or probability.) Then perhaps like Cincinnatus (or Washington - the American version), you should relinquish it. Or suppose that you want to signal to the world that your relationship is on the rocks. You might do as the United States and Japan did prior to Second World War and publicly proclaim the strength of your alliance.
Now of course, these two examples and many of the others provided in the book could be explained using standard game theory. And, one might draw the conclusion that international relations needs a strong dose of Ordeshook (1992). At times, this appears to be what Jervis recommends. I say appears because he muddles the distinction between game theory and complexity. This failure to distinguish between complexity theory and game theory can be maddening - especially to a mathematical theorist who wants each epsilon primed and each delta barred - and it diminishes the book's contribution. On the one hand, Jervis favourably compares game-theoretic and decision-theoretic models. On the other hand, his prose embraces complexity and criticises closed form models. He speaks of aggregate behaviour that is complex and ordered, although not predictable and stable. The latter being the domain of equilibrium theorists.
Let me try to introduce some clarity to the methodological confusion. First, in a decision-theoretic model, an agent takes an action and gets a payoff that may depend upon some random realisation of a state of the world. Suppose I am going to buy an automobile. I choose one based on research, beliefs and personal preference, and I get a realisation: the car might turn out to be a lemon or it could run for decades. In a game-theoretic model, payoffs depend upon the actions of others. If country A invades country B, the payoff to A depends upon the reaction of B, be it acquiescence or retaliation. Jervis seems to think that game theory requires all agents to optimise ex post, that all firms make equilibrium choices at all times, and that all equilibria must be efficient. In fact, the converse appears to be the case, both theoretically and empirically. Most recent game-theoretic models embrace notions of learning, subjectivity, inefficiency, path dependence and the multiplicity of equilibria. However, the game-theoretic approach does emphasise equilibria, equilibria that are often counter-intuitive. To borrow a line of reasoning from George Tsebelis (cited by Jervis), raising fines might not decrease the amount of drug trafficking. Why? Because higher fines could lead to less monitoring in anticipation of less trafficking.
One point of complexity theory is that equilibrium may not always be a meaningful concept. Basketball and soccer games do not seem to be heading towards any equilibrium. Teams continually adapt their strategies. Why don't they just choose the optimal strategy to begin with? Because, in contrast to the world of theory, the game happens too fast. Optimal strategic responses cannot be predicted or, in some cases, even imagined in the time available.
When agents lack this ability to predict equilibria, we enter the realm of complexity theory. To grasp complexity, it is helpful to begin by understanding the concept of difficulty. Difficulty refers to hard decision problems, those with many variables that interact in a non-linear fashion. Difficult problems include curing cancer, designing an efficient combustion engine and creating the perfect hamburger. These problems exist independent of the actions of others. They are not strategic, but they are hard. Most scientific problems are difficult. Those that are not difficult, we have already solved.
Complexity is to game theory what difficulty is to decision theory. In a complex environment, agents take actions that influence the payoffs to other agents. The resulting behavioural dynamics cannot be fully understood by any one agent or set of agents. The agents may comprehend and exploit patterns along some dimension for periods of time, but others remain mysterious. The constant discovery and exploitation of patterns yields new patterns. This elaborate interplay between the micro and the macro never ceases. This does not mean that no equilibria exist, but it does mean that equilibria have little informational value. The evolutionary environment in which we live will ultimately end in heat death for us all, although few use this to predict stock market prices - even in the long run.
In sum, some systems settle into equilibria, others do not. The former can be predicted using game theory. And, unfortunately, the latter cannot be predicted using either game theory or complexity theory. Why? Because pattern awareness usually implies pattern exploitability. This means that complexity theory must have more modest aims than game theory. Even though complexity theory cannot predict exact patterns, it can predict the sorts of patterns that might persist in negative (as opposed to positive) feedback systems. It can provide formal underpinnings for recurrent patterns. For example, how far is William McNeil's historically based "conservation of catastrophe" principle, which Jervis discusses, from Per Bak's (Bak 1996) mathematical concept of "self-organised criticality?" (Not far, I reckon.) And, hopefully, complexity theory can teach us how to construct systems that will be less complex. Or, if that is not possible, it might, at a minimum, allow us to steer the complexity into less problematic domains.
In light of this discussion, the perspective presented by Jervis becomes clearer. He believes that some problems in international relations are complex, and that this is different from saying that all problems are complex. The precise breakdown may be 5% complex and 95% easy. The easy parts can be solved through laws and norms: red means go and green means stop. It is the remaining 5% that occupy our time. He also thinks that strategic reasoning, if not formal game-theoretic models themselves, will go a long way in helping us to understand that complexity. Perhaps the best way to gauge the strength of this argument is by a quick fly over, so here goes.
The first substantive chapter of the book (chapter two) deals with what Jervis calls systems effects. This mantra of this chapter can be phrased in several ways: "the whole does not equal the sum of its parts", "results cannot be predicted from separate actions" or "interactions cannot be understood additively". Jervis means that not only do the actions matter, but so do the connections and the environment. In other words, the connections and the environment do not belong to the whole as commonly conceived in international relations. Whether that is true or not, I cannot say, but Jervis makes a compelling argument for using a wide angled lens in viewing social processes.
For example, you might look at a partially obscured intersection and say: "That's a dangerous stretch of road." But, if everyone recognises the potential for danger, does the stretch remain dangerous after drivers modify their behaviour in response? In some cases it will, in others, it will not. In the former U.S.S.R., managers gave workers bonuses based on output, only to be presented with large quantities of low quality goods. Jervis makes two separate points here and both are good. First, prediction macrobehavior from micro level incentives is a tricky business. This is a point made by Schelling (1978) in greater generality. And second, even predicting individual behaviour from incentives is not easy. Consider the work of Karl Sims, formerly of Thinking Machines, who used a massive computer to evolve artificial species with the goal of propulsion in an environment simulating Newtonian physics. His measure of fitness was displacement in the centre of mass over a fixed period of time. One species that evolved was very tall and fell over, thus moving it's centre of mass a great distance.
These examples show that predicting outcomes and crafting incentives can be a daunting task. You might pass a law requiring safer ladders, thus raising their price and encouraging the use of substitutes - say milk crates on top of chairs - and as a result, create a less safe world. But didn't most of us already know this? Even if we did, we benefit from a reminder. More importantly, this book was written for an international relations audience, and judging by the discussion in chapter three on systematic theories of international politics, I think that this book falls into the "much needed" category. After trudging through Jervis' overview of the bi-polar, multi-polar, first strike, second strike literature, I could only but wonder how any intelligent person would not pay attention to strategic interdependencies when studying international relations. One struggles to imagine how amassing weapons, forging alliances and developing technologies would not induce strategic responses from others.
Chapter four covers positive, negative, and circular feedbacks. As an example of a negative feedback, Jervis introduces the balance of power theory. History tells us that no single state dominates, that there are few total wars, that losers are reintegrated into the international community and that small weak states survive. The infrequency of total war results from increasing opposition in alliance (a negative feedback) against an aspiring world dictator. Positive feedbacks include Schelling's famous racial tipping model (Schelling 1978), the aforementioned domino theory and races to the bottom within federal systems, such as when all states cut welfare benefits.
We must be careful here. Feedbacks by themselves do not imply complexity. Predicting which domino falls next isn't hard. In my opinion, Jervis' case for complexity through feedback hinges on the role of expectations and mental models. He mentions only the former. Dominoes heed only gravity. People and governments possess the freedom to choose. These choices depend on our models of the world. Expectations matter depending on how they interact with these mental models. If, as I would expect Jervis believes, we cannot anticipate the international patterns that occur during our time on the world stage, then rather simple theories - of the domino and the balance of power - may help determine our actions. These theories may prove powerful, but owing to the multi-dimensionality of volitional action, they will never attain the accuracy of physical laws. Complexity reigns.
Complexity will also prevail in the relations among states, the subject of chapter five. Power depends upon relations among adversaries. Pivotal positions depend upon multiple factors: geography, technology, resources and so on. Thus, these positions will be transient. This is not to say that alignments will not exist and occasionally persist, but that the strength and extent of ties depend upon other ties. For example, in 1971, when India and the U.S.S.R. forged a closer alliance, China and Pakistan also became friendlier with each other.
Jervis raises several interesting points in this chapter that present opportunities for formal complexity models. To name just one, conflicts typically involve only two alliances. Three way fights between states are almost non-existent (though they can happen within states). Deeper theoretical foundations for complexity theory may explain why such phenomena occur.
The final chapter of the book addresses acting within a system. By showing that political actors can constrain the actions of others, anticipate their reactions, compensate accordingly and correct for the multiplicity of consequences, Jervis strikes an optimistic chord. Peace has a chance. But, at its core, his argument relies on a sort of circular reasoning. Consider the Lijphart effect, which says that any undesirable natural outcome can be foreseen and prevented. Thus, the Netherlands, which according to most theories should be unstable remains a political entity. How? Its leaders are aware of the potential for instability and take actions which circumvent it. Similarly, knowing the domino theory, we quickly grab the second domino to prevent the cascade. Thus, the compromise which Kennedy made on Laos may have led to the engagement in Vietnam. In both cases, the political actors understand the world well enough to prevent bad outcomes as a result of the complexity.
Jervis believes that catastrophe also can be avoided by taking actions in pairs - President Truman fires MacArthur, but enacts the General's policies - by advocating indirect approaches such as separation of powers and political parties, by occasionally moving in the opposite direction and by doing one more thing: not relying on a single policy. All of these "solutions" implicitly assume either that we know what will happen next - something Jervis spends an entire book telling us we cannot do - or that by making the system more complex (directly or indirectly), we can prevent bad outcomes, an equally dubious proposition.
I cannot help but come to different conclusions. Firstly, if we can gauge predictability, we have hope. Preferred policies, coalitions and alignments depend not only on the state of the world and on how we arrived there, but also on our confidence level about predictions for the future. Natural bad outcomes seldom occur for the same reason that I rarely step into a known hole. By definition, the location of an unknown hole is no common knowledge, but we might know if we know that a hole exists somewhere. Secondly, complexity can never be circumvented, short of some Brave New World. New ideas, technologies, metaphors and resources arise daily to feed the complexity engine. If we are headed toward an equilibrium (other than heat death) someone keeps moving the darned thing. Thus, our goal should be to channel the complexity of a world comprised of states with distinct cultures, governments, geographies and resources into non-violent dimensions. Thirdly, although we will never predict all of the patterns in the political system, and wouldn't want to, we may be able to construct institutions that preclude undesirable patterns.
In sum, I highly recommend this book. At times, the writing and argumentation are inspired. The book supports its main arguments with relevant examples. Given the scope of the project, to ask for much more would be unfair. The book raises big questions and attempts to answer them. To borrow a Herbert Simon quote from Jervis: "Everything is connected. Some things more than others." And, as this book shows, international politics clearly belongs to the latter category.
BAK P. 1996. How Nature Works: The Science of Self Organized Criticality, Springer-Verlag, New York, NY.
ORDESHOOK P. 1992. A Primer in Political Theory, Routledge, London.
SCHELLING T. C. 1978. Micromotives and Macrobehaviour, W. W. Norton, New York, NY.
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