Michael Radzicki

Characteristic of Complex Systems #22: The structure of a complex system can sometimes lead to the "paradox of attraction," which is a situation in which the attractiveness of a location eventually causes it to become unattractive. No other than Yogi Berra made this point many years ago when he said: "No one goes there anymore, it's too crowded." An example would be a city with good schools due to a low student-to-teacher ratio. Families with children would be attracted to this city and, ceteris paribus, the influx of students would eventually increase the student-to-teacher ratio to the point at which individual attention to students would suffer.

Characteristic of Complex Systems #21: The structure of a complex system can sometimes lead to "tragedy of the commons" situation in which an unmanaged common resource is overused, and the overuse causes the destruction of the common resource. A common resource is owned by no one, so it is "owned" by everyone.

Characteristic of Complex Systems #20: The structure of a complex system often leads to "limits to growth" behavior. This is also known as Archetype #2. Except for (possibly) the expansion of the universe, complex systems cannot grow infinitely large. Instead, a system's growth (caused by positive feedback processes) is usually constrained by limiting factors (representing negative feedback processes).

Characteristic of Complex Systems #19: The structure of a complex system often leads to a "success to the successful" behavior. This is also known as Archetype #1. In the figure below each arrow represents cause and effect -- the variable at the end of the arrow is the cause and the variable at the head of the arrow is the effect. A plus sign means "same direction" and a minus sign means "opposite direction." All arrows are dawn ceteris paribus -- i.e., assuming that all other factors that can influence a variable are held constant. For the mathematically inclined, this means that each arrow is essentially a picture of a partial derivative.

Characteristic of Complex Systems #18: The behavior of a complex system is often self-organizing. In other words, the dynamics of a complex system can arise spontaneously from its internal structure. In the figure below noise from a normal distribution is turned on in week 10 and shocks the system out of equilibrium. The system then oscillates. This shows that the system’s structure causes it to oscillate. The external shocks “release” the oscillations, but do not “cause” them.

But wait -- Equilibrium is not a dirty word in complex systems modeling. In fact, we routinely put our models, or parts of our models that are under construction, into a state of equilibrium and then shock them out with a variety of exogenous test inputs to determine how they behave. This makes it much easier to ferret out poorly formulated equations, as anything that is not a horizontal line after a shock has to be the response of the system to the shock. And if the response doesn't make sense, corrections can be made. Long story short is that equilibrium formulations, when properly employed, are very useful.

Characteristic of Complex Systems #17: Complex systems exist in a state of disequilibrium. Equilibrium in a dynamic system is quite uninteresting. A time series graph of each variable in a system in equilibrium is simply a horizontal line. Since there is no pressure for change, every variable keeps the same value over time. Of course, graphs of time series data from any living, complex system, do not show a set of variables with constant values. In traditional economics the concept of equilibrium is sacrosanct. Virtually all traditional models in economics either exhibit equilibrium, or a steady state growth path in which the ratio of two model variables is typically a horizontal line over time. This is due to the need for an economic system to be stable -- i.e., shocks displace the system from equilibrium, only to have it return to the same (or a new) equilibrium. BTW: An equilibrium can be "good" or "bad." When markets clear -- good. When a macro economy is stuck with high levels of involuntary unemployment -- bad. Here are two well-known models from economics -- a micro model of a market and the IS-LM macro model -- both of which are (static) equilibrium models:

Here's a couple of simulation experiments utilizing the Polya Process. The first figure shows nine simulations. Of note is that after some initial instability (early in each simulation the advantage between the white and black marbles swings back and forth) each simulation settles down and gets locked into a particular path: i.e., the fraction of the marbles in the jar that are white (1 - this fraction is the fraction of the marbles that are black). The second figure shows thousands of simulations of the same Polya Process and reveals that almost any combination of white and black marbles is possible (although due to the initial conditions there will always be a minimum of one marble of each color in the jar). One take-a-way from all of this is that history matters!

A nice example of a path dependent process is a Polya Process, named for the Hungarian mathematician George Polya (who, incidentally, taught John von Neumann). Consider the following situation...A glass jar is to be filled to the brim with white and black marbles. At time zero there is one white marble and one black marble in the jar. Now follow this rule: Add a white marble if a random number from a uniform distribution (with a maximum value for a random variate of 1 and a minimum value of a random variate of 0) is less than the percent of the marbles in the jar that are white. Otherwise add a black marble. The uniform distribution will generate a series of random variates between 0 and 1, each of which is equally likely. At time zero the percent of the marbles in the jar that are white is .5. There is thus an equal chance that the first random variate generated is less than .5. In other words, there is no initial bias toward white or black marbles. If the first random variate generated is, say, .2 then a white marble is added to the jar. And the percent of the marbles in the jar that are white has increased to .67. This means that the chance that another white marble will be added has increased greatly. The big question is: What will happen if a large sequence of random variates is generated?

Characteristic of Complex Systems #16: The behavior of a complex system is often path dependent. This means that it can get locked into a particular time path, even if the path is less than desirable. For example, we mostly use QWERTY keyboards even though the Dvorak keyboard layout (or other alternative layouts such as Colemak, Workman, Norman, and QGMLWY ) are more efficient. This is because the cost of re-training people (including overcoming muscle memory), and redesigning and replacing the installed base of QWERTY keyboard machines makes it uneconomical to switch to the superior technology. In economics this sort of situation is known as a path dependent process, which is often explained by Gunnar Myrdal's principle of "Circular and Cumulative Causation." In complex systems modeling path dependent processes are explained by stocks and flows and positive feedback loops.

Because the unpredictability of the future trajectory of a complex feedback system, which is heavily influenced by exogenous shocks (which, by definition, are unpredictable), it’s better to spend your modeling time redesigning the structure of the system so that it behaves “well” in response to any external shock, whenever it may arrive.

Characteristic of Complex Systems #15: The behavior of a complex system is almost always unpredictable over any useful time frame. This figure illustrates the concept that an accurate forecast of the future behavior of a complex system can be made in the short run, due to the momentum of the system, but any actions taken at the time of the forecast only influence the system's behavior in the long run, where the system's behavior cannot be forecast.

Characteristic of Complex Systems #14: Complex systems often shift the burden to the intervenor. * Corrective programs imposed on a complex system from the outside can have far less than their intended effect b/c they tend to displace the corresponding internal processes. For example - A person's unaided eyesight is usually worse after they begin wearing glasses, as the glasses take over some of the work previously done by the person's eye muscles. For example - A person's long division skills often degrade if they always use a calculator to solve a quotient. * Probably no active, externally imposed, program is superior to a system modification that changes internal incentives and leaves the burden of system improvement to internal processes. I.O.W. to make the airplane permanently fly better it needs to be redesigned.

Characteristic of Complex Systems #13: Complex systems often drift to low performance. * The bias toward near-term, “better before worse” policy changes lead to short-run improvements, followed by system decline. * But the initial improvements are remembered, and the original policy changes are redoubled. This causes another round of short-run improvement followed by deeper long-run difficulties

More on Better Before Worse or Worse Before Better Behavior and Leverage Points: * Time delays mean that long-run system responses are often different from short-run system responses * High leverage policies often cause worse-before-better behavior * Low leverage policies often generate transitory improvement before the problem gets worse * Voter/shareholder pressure and political expediency tend to incentivize policy changes that favor short-run considerations over long-run considerations and set the stage for long-term degeneration.