Complex Adaptive Systems: An Introduction to Computational Models of Social Life (Princeton Studies in Complexity Book 14)

by John H. Miller

It is the interest in between stasis and utter chaos. The world tends not to be completely frozen or random, but rather it exists in between these two states. We want to know when and why productive systems emerge and how they can persist.

Unfortunately, using these same tools to understand complex worlds fails, because it becomes impossible to reduce the system without killing it.

The result of such a system is that agent interactions become highly nonlinear, the system becomes difficult to decompose, and complexity ensues.

If heterogeneity is a key feature of complex systems, then traditional social science tools—with their emphases on average behavior being representative of the whole—may be incomplete or even misleading.

While differences can cancel out, making the average a good predictor of the whole, this is not always the case. In complex systems we often see differences interacting with one another, resulting in behavior that deviates remarkably from the average.

The difference of response between the two systems is due to feedback. In the temperature system, heterogeneity introduces a negative feedback loop into the system: when one bee takes action, it makes the other bees less likely to act. In the defense system, we have a positive feedback loop: when one bee takes action, it makes the other bees more likely to act.

The model also demonstrates how a social system can get locked into an inferior outcome and how, with the introduction of noise or different behavioral rules, it can break out of such outcomes and reconfigure itself into a better arrangement.

The formal mathematical approach works best for static, homogeneous, equilibrating worlds. Even in our very simple example, we are beginning to violate these desiderata. Thus, if we want to investigate richer, more dynamic worlds, we need to pursue other modeling approaches. The trade-off, of course, is that we must weigh the potential to generate new insights against the cost of having less exacting analytics.

Heating metal tends to disrupt the alignment of (add noise to) the individual atoms contained in a metal; then, by slowly cooling the metal, the atoms can align better with one another, resulting in a more coherent structure.

More often than not, the essential culture of that organization retains a remarkable amount of consistency over long periods of time, even though the underlying cast of characters is constantly changing and new outside forces are continually introduced. We see a similar effect in the human body: typical cells are replaced on scales of months, yet individuals retain a very consistent and coherent form across decades. Despite a wide variety of both internal and external forces, somehow the decentralized system controlling the trillions of ever changing cells in your body allows you to be easily recognized by someone you have not seen in twenty years.

While it is easy to specify behavior at the extremes, as we move into the middle ground, we are suddenly surrounded by a vast zoo of curious adaptive creatures.

Theoretical work in economics suggests that optimizing agents out for their own benefit can, without intention, lead a market system toward efficiency under the right conditions. Moreover, experimental and computational work suggests that such outcomes are possible even with nonoptimizing agents.

The role of control on social worlds is also of interest. The ability to direct the global behavior of a system via local control is perhaps one of the most impressive, yet mysterious, features of many social systems.

A model requires choices of both the equivalence classes and the transition function, and the art of modeling lies in judicious choices of both.

This continual chasing of the “ideal” model results in a Schumpeterian cycle of scientific creative destruction. Modelers attempt to reduce the world to a fundamental set of elements (equivalence classes) and laws (transition functions), and on this basis they hope to better understand and predict key aspects of the world. The ever present quest for refining old, and discovering new, ways to represent the world drives the process of scientific creative destruction.

Even if we know the fundamentals of a particular system, we may not be able to use that knowledge to reconstruct higher-level systems. It may be, as Anderson says, that “the whole becomes not only more than but very different from the sum of its parts.”

emergence is a phenomenon whereby well-formulated aggregate behavior arises from localized, individual behavior. Moreover, such aggregate patterns should be immune to reasonable variations in the individual behavior.

Similarly, while predicting the motion of a planet surrounded by a few neighbors is difficult, it is easy to calculate its motion when it is among a sea of other planets, as the various gravitational forces that come into play begin to cancel one another out, and soon only the mean force becomes important.

Agent intention can also alter the patterns that emerge in complex systems. In the case of the Sand Pile model, if we give the falling grains of sand a bit of control on where they land and some desires (like maximizing the size of the resulting avalanche), the system is no longer governed by a power law and instead enters a bizarre periodic cycle. As we give agents even more strategic ability, we often see elaborate dances of strategies, with good and bad epochs, cycles, and crashes.

These patterns are so coherent at times that we can ignore the underlying microlevel rules that generated them and instead rely on the resulting global structures to predict systemwide behavior

Under organized complexity, the relationships among the agents are such that through various feedbacks and structural contingencies, agent variations no longer cancel one another out but, rather, become reinforcing.

The flexibility and creativity embodied in computer models often seduce practitioners to continually add features to their work—a practice that must be moderated if good-quality models are to be maintained.

Systems with mostly negative feedback tend to be very stable and predictable. Extraneous factors left out of the model can even be absorbed by the actions of the agents, leading to even less noise than we would expect from a prediction relying on the Central Limit Theorem. However, in systems with positive feedback, we loose some predictability. Small differences can build upon themselves and create large differences, making precise prediction difficult.

A priori, it is not clear that evolution must lead to optimization. Evolutionary systems often get stuck at local optima (for example, many organisms eat and breath through the same tube, even though this often causes them to choke).

Physical systems typically rely on fixed rules, and as we saw in the initial model, such rules may indeed lead to complex behavior. However, adaptation tends to place the system in more interesting regions of that space. Moreover, in adaptive social systems we find that the agents’ rules often respond to the phenomena that they generate, creating multiple layers of feedback that result in a diverse set of emergent behaviors, both for the agents and the system at large.

The idea that imperfection is a productive way to navigate multiple equilibria has been shown in many contexts, such as in simulated annealing. This research indicates that allowing mistakes (especially if they are not too costly or occur early in the search process) helps systems escape less productive outcomes and converge on more productive ones. Less perfection is often more in these types of systems.

The comparative elegance of the omniscient closure model is appealing, but more than likely difficult, if not impossible, to attain in reality. Even if agents could conceive of such a clean solution, the coordination required to jump to it may not be possible. Alas, agents are often left fumbling toward ecstasy, especially in worlds with even a modicum of realism.

There is a universality among computational systems in which, once a certain threshold is passed, each such system is capable of performing the other’s computations.10 Thus, balls colliding with one another on a billiard table, suitably arranged and interpreted, can perform the same computations as a supercomputer or any possible agent-based model. This implies that it is possible for a dumb system (colliding billiard balls) to emulate a smart one (sophisticated agents interacting in a social system).

Class 1 rules quickly evolve to a unique, homogeneous state with identical actions across the agents (as in the “all 1s” rule). Class 2 rules result in separated groups of simple stable or periodic structures (as in the “do the opposite” rule). Class 3 rules imply chaotic patterns (the rule in table 8.1 is a member of this class). Class 4 rules produce complex structures with long transients (thus, coherent patterns arise that can persist across space and time for extended periods) that are hypothesized to be capable of universal computation—that is, able to compute anything that can in principle be computed (Rule 110 meets this criterion).4

Note that randomness does not necessarily imply “random” behavior. Randomness is often a source of order in complex systems.

systems that are too simple are static and those that are too active are chaotic, and thus it is only on the edge between these two behaviors where a system can undertake productive activity.

The “edge” in the edge of chaos is not in phase space but in the space of rules. The idea is that if we slightly perturb a rule that generates complexity we will get a rule that either generates chaos or stasis. Therefore, the search for the edge of chaos focuses on how small changes in a rule impact its behavior.

One hypothesis is that adaptive systems will have a bias toward emphasizing simple structures that resist chaos over more complicated ones that handle difficult situations.

Clearly there are systems, for example, stock markets, in which agents actively adapt and alter the fundamental behavior of the system and, in so doing, force it into new realms of activity. Thus, if stock markets are too predictable, then we would expect adaptation to create agents that can exploit this feature. The emergence of such agents should wipe out the predictability and push the system toward a more chaotic regime (which is essentially the argument driving the efficient-market hypothesis). However, once the market is completely chaotic, the selective pressures on agent behavior become quite neutral, and predictability might again slip back into the system.

It can be shown that even in networks with similar initial distributions of criminals, you can get very different final distributions of criminal behavior: some worlds become crime ridden while others become relatively crime free. This suggests that high crime rates in one area could be an artifact of unfortunate historical accidents rather than some difference in initial criminal behavior.

Power-law distributions are just one member of a class of fat-tailed distributions. A distribution has fat tails if the probabilities of extreme events are “abnormally” high, where by abnormally we mean literally not like a normal distribution. If we assume that a distribution is normal when indeed it is fat-tailed, then we will grossly underestimate the potential for extreme events (and discount those that do happen as rare anomalies).

The key driving force behind self-organized criticality is that microlevel agent behavior tends to cause the system to self-organize and converge to critical points at which small events can have big global impacts. Such critical points are familiar to anyone who has ever built a house of cards; while initially such constructions go quite smoothly, at some point the structure goes critical and even the slightest jiggle causes it to collapse. Similarly, in self-organized critical systems, the agents throughout the system tend to be poised in critical states where small disturbances can trigger large relaxation events that may encompass any number of agents.

In general, mutation is viewed as a way to keep adaptive systems from getting trapped in narrow regions of the search space versus being a constructive way to find good solutions to problems.

The benefits of crossover stem from the fact that good partial solutions, known as building blocks or schema, are present in the population. The current theory of genetic algorithms suggests that crossover effectively preserves and combines building blocks, allowing good solutions to be built from the bottom up.

The general result of this research is that context matters: how agents play a particular game depends on the collection of the other games in the ensemble. The ultimate implication of this result is that in worlds in which agents have limited cognitive capacity and face multiple games, we should predict very different behavior than that suggested by the standard game-theoretic models.

In general, communication is capable of productively altering the interactions in a social system for a few key reasons. First, communication expands the behavioral repertoire of the agents, allowing new and potentially productive forms of interaction to prevail. With communication, agents can create new actions that allow them to escape the previous behavioral bounds. The greater the potential of communication, proxied in our discussion by processing ability and tokens, the more possibilities that emerge. Second, communication emerges as a mechanism that allows an agent to differentiate “self” from “other.” In the worlds we have explored, agents would like to cooperate in the case of the Prisoner’s Dilemma and hunt stag in the case of the Stag Hunt, but the presence (and inherent incentives) of defectors is an ever present danger to adopting such behavior. Communication emerges as a way either to signal a willingness to be nice or to detect meanness. In these systems, this occurs when a fortuitous mutation gives an agent the ability to “speak” and to respond positively to such communication while avoiding harm from those agents that say nothing. By detecting “self” in such a way, the agent can improve its performance even in nasty worlds.

Indeed, for certain classes of organizations, it is likely to be the case that the problem space quickly overwhelms the solution ability of the underlying organizations. That is, organizations may be productive on only a small set of all possible problems. This may imply that organizations may be more reactive than proactive, working well only when the problems are easily solvable rather than solving whatever problems come their way.

Throughout this work we are finding that adaptation implies more structure, not less. There has been an implicit assumption that because adaptive systems exist in the messy in-between, that the resulting models will be mired in incomprehensible layers of detail. Alas, the opposite appears to be the case: the messy in-between results in a reduction of complex behavior.

The link between the micro and macro is not as clear as we once thought. We must explore a new realm that both acknowledges the microfoundations of macrobehavior while simultaneously recognizing the potential for seemingly magical transformations that link one level to another. Of course, such magic is the impetus for the scientific exploration that in time will eventually lead to understanding.

Wolfram goes on to suggest that his restriction to simple models is an important one. In particular, he finds a natural bound on the computation a system can perform, and once this bound is reached, there is a universal equivalence that can allow one system to emulate another, as long as we are free to manipulate the inputs and reinterpret the outputs. Moreover, the suggestion is made that most systems (including some of the very simple ones he explores) have achieved this equivalence milestone.

Note that this is not saying that emergence occurs when the parts cancel one another out. To the contrary, the parts are aggregating in complex and interesting ways. What they create, the emergent phenomena, has a statistical signature of its own, one that can be predicted more parsimoniously without looking at all of the parts. The concept of emergence has thus made the transition from a metaphor to a measure, from something that could only be identified by ocular magic to something that can be captured using standard statistics.

Complexity can occur at many levels, including time, space, and interactions. Perhaps we are expecting too much if we want a single measure of complexity that captures all of our intuitions. Indeed, not having a uniform definition of, say, architectural beauty has not held back architecture, nor should the lack of a single definition of complexity hold back the science of complex systems.

In a world of thoughtful, interacting agents, complexity might emerge as those agents begin to “game” the system and, eventually, each other. There may be inherent forces in systems that drive out predictability. For example, in stock markets agents have incentives to find, and exploit, any regularities. In these types of systems, the actions of the agents result in the destruction of the regularity, and an increase in complexity.

Modeling how agents simplify complexity so that they can predict and act is an important topic. There are a variety of techniques whereby apparent complexity can be condensed into useful approximations (indeed, the process of modeling itself is one such technique). Moreover, understanding how such simplifications themselves can influence the resultant complexity is also of interest.

Harnessing coevolution is a powerful way to adapt systems. Evolution needs to exploit opportunities inherent in the underlying structure of the world. Unfortunately, for most problems, the space of good structures is much smaller than the space of bad ones. In such a world, most of the feedback takes the form of “bad idea” rather than “good idea,” and thus it is difficult for an evolutionary system to gain enough purchase to make rapid progress. Coevolution, however, lowers the fitness bar initially and, in so doing, allows systems to evolve more rapidly toward good structures. Over time, as the coevolving structures get better, the bar is raised and more selective pressure is exerted in the system. Coevolution allows the evolving entities to “challenge” each other progressively. By slowly, and automatically, ramping up the challenges, rapid evolutionary progress becomes possible.