Computational Legal Studies™

This week’s issue of the Economist has an interesting article entitled Riders on a Swarm. Among other things, the article discusses how attempts to computationally model ant, bee and bird behavior have offered insight into major problems in artificial intelligence.

For those not familiar, the examples discussed within the article are classic models in the science of complex systems. For example, here is the Netlogo implementation of bird flocking. It will run in your browser but requires Java 4.1 or higher. If you decide to take a look — please click setup – then go to make the model run. Once inside the Netlogo GUI, you can explore how various parameter configurations impact the model’s outcomes.

One of the major insights of the bird flocking model is how random starting conditions and local behavioral rules can lead to the emergence of observed behavioral patterns that appear (at least on first glance) to be orchestrated by some sort of top down command structure.

This is, of course, not the case. The model is bottom up and not top down. Both the simplicity and the bottom up flavor of the model are apparent when you explore the model’s code. For those interested, I will take a second and plug the slides from my ICPSR class. In the class, I dedicated about an hour of class time to bird flocking model. Click here for the slides. In the slides, I walk through some of the important features of the code (discussion starts on slide 16).

Diversity is one the major topics of interest here at Michigan Center for the Study of Complex Systems.  This includes diversity as experienced in physical as well as in social systems. On this topic, here is a lecture that one of my dissertation advisors, Scott Page gave earlier this year at the Darden School of Business at Virginia. This lecture is related to his book about the power of diversity entitled: The Difference: How The Power of Diversity Creates Better Groups, Firms, Schools, and Societies.  Although I realize it is roughly a 90 minute talk, I believe that you will find that it is well worth the time!

This summer, I am teaching the Introduction to Computing for Complex Systems course at the ICPSR 2010 Program in Quantitative Methods. On the first day of class, I previously blogged about the course and thus if you are interested in additional details — feel free to consult the prior post.

For those interested in an introductory course that does not assume significant prior preparation, I did want to put up another post highlighting that all of course material (to date) is now freely available online.  This includes course slides, model examples and assignments.

In this introductory course, I highlight several environments designed to explore the field of complex systems.  These include Netlogo (agent based models and network models),  Vensim (system dynamics / ecological modeling) and Pajek (empirical network analysis).  Although, we do not work with more advanced languages within the course, those who need to conduct complex analysis are directed to alternatives such as R, Python, Java.

In the course slides, I offer a history of the science of complex systems and walk step-by-step through the process of model development and implementation. The slides and associated materials are designed to be a complete self-teaching environment where an individual who follows along carefully should be able to bring him or herself up to speed. More material will be added over the balance of the four-week session.  So, please check back for more … including slides from our guest speakers!

This summer I will be teaching a summer course entitled Introduction to Computing for the Study of Complex Systems at the ICPSR Summer Program in Quantitative Methods.  For those not familiar, ICSPR has been offering summer classes in methods since 1963. The Summer Program current features dozens of courses including basic and advanced econometrics, bayesian statistics, game theory, complex systems, network analysis, quantitative analysis of crime, etc.

The Complex Systems Computing Module runs together with the Complex Systems lectures offered by Ken Kollman (Michigan), Scott E. Page (Michigan), P.J. Lamberson (MIT-Sloan) and Kate Anderson (Carnegie Mellon).  Here is the syllabus for the lecture.

The first computing session is tonight from 6-8pm at the ICPSR Computer Lab.  If you click here or click on the image above you will be taken to a dedicated page that will host the syllabus and course slides!  Note: The slides and assignments will not be posted until the conclusion of each class.

Those who know me are well aware of my obsession with fractals (see here).  But why listen to me when you can here from the man himself —  Benoît Mandelbrot!

As highlighted on Marginal Revolution, economist Herb Gintis has authored an Amazon.com review of the book ”Meltdown: A Free-Market Look at Why the Stock Market Collapsed, the Economy Tanked, and Government Bailouts Will Make Things Worse” by Thomas E. Woods Jr.  Suffice to say, the review is not flattering.  Those interested in the direct attack on the book can read the full review here.  Our particular interest in his review lies in the last third of the text where Professor Gintis highlights the genuine weaknesses of current macroeconomic theory. Below is the relevant text:

“I am often asked why macroeconomic theory is in such an awful state. The answer is simple. The basic model of the market economy was laid out by Leon Walras in the 1870′s, and its equilibrium properties were well established by the mid-1960′s. However, no one has succeeded in establishing its dynamical properties out of equilibrium. But macroeconomic theory is about dynamics, not equilibrium, and hence macroeconomics has managed to subsist only by ignoring general equilibrium in favor of toy models with a few actors and a couple of goods. Macroeconomics exists today because we desperately need macro models for policy purposes, so we invent toy models with zero predictive value that allow us to tell reasonable policy stories, the cogency of which are based on historical experience, not theory.

I think it likely that macroeconomics will not become scientifically presentable until we realize that a market economy is a complex dynamic nonlinear system, and we start to use the techniques of complexity analysis to model it. I present my arguments in Herbert Gintis, “The Dynamics of General Equilibrium“, Economic Journal 117 (2007):1289-1309.

While we do not necessarily agree with every point made in his review, the general thrust of the above argument is directly in line with the thinking of many here at the Center for the Study of Complex Systems. Indeed, the rebuke offered above could be extended and applied to other work in Economics and Political Science. A significant part of the problem is that the analytical apparatus in question is simply not up to the complexity of the relevant problems. Most of the current approaches derive from an era when a CPU had a transistor count of less than 10k and memory was exceedingly expensive. It is not as though leading scholars of the day were completely unaware that most systems are far more intricate than a “few actors and a few goods.”  However, tractability concerns created a strong incentive to develop models which could be solved analytically.

Moderately high-end machines now have transistor counts of greater than 2,000,000,000 and memory is incredibly cheap (see generally Moore’s Law). No need to impose fixed point equilibrium assumptions when there is no qualitative justification for eliminating the possibility that limit cycle attractors, strange attractors or some class of dynamics are, in fact, the genuine dynamics of the system. We have previously highlighted the press release “What Computer Science Can Teach Economics“ (and other social sciences). This is really important work.  However, it is really only the beginning.

More realistic representations of these complex systems are possible, however, it requires scholars to consider jettisoning analytical approaches/solutions. When modeling complex adaptive systems far more granularity is possible but this requires a direct consideration of questions of computation and computational complexity. The use of a computational heuristic is really not that problematic and it can help sidestep truly hard problems (i.e. NP Complete and the like).  The difficult question is how and under what conditions one should select among the available set of such heuristics.

It is important to note, the dominant paradigm was itself a heuristic representation of agent behavior (and a useful one). While there are still some true believers, a declining number of serious scholars still assert that individuals are actually perfect rational maximizers. At best, this assumption is a useful guidepost for agent behavior and is one which can be subjected to revision by continued work in behavioral economics and neuroeconomics.

For those looking for a genuine intellectual arbitrage opportunity … the path is clear … devote your time to filling the space as this is a space with significant potential returns.  The way forward is to remix traditional approaches with leading findings in neuroscience, psychology, institutional analysis and most importantly computer science … winner gets a call from Sweden in about t+25.

Robert Axelrod’s 1997 Culture Model is a complex systems classic.  Several versions of the model are available including one in Repast J. Perhaps the most user friendly version has recently been posted to Netlogo’s “community models” page. Those interested in experimenting with this Netlogo version of the model can click on the image above (provided you have Java 4.1 or higher installed).

For those not previously familiar with the model … Figure 1 from the article is featured to the left and demonstrates a model run through 80,000 events.  Those results are generated in the following manner:

“Patches are assigned a list of num-features integers which can each take on one of num-traits values. Each tag is called a feature, while it’s value is called the trait. The links in the view represent walls between patches where solid black walls mean there is no cultural similarity, and white walls mean the neighbors have the same culture.

The order of actions is as follows:
1) At random, pick a site to be active, and pick one of it’s neighbors
2) With probability equal to their cultural similarity, these sites interact. The active site replaces one of the features on which they differ (if any) with the corresponding trait of the neighbor.”

Those looking for the original article … here is the both the citation and a link: Robert Axelrod, The Dissemination of Culture: A Model with Local Convergence and Global Polarization, J. Conflict Res, 41, 203 (1997).

In the years following its release, several important extensions or applications have been offered. These include contributions from scholars in a wide number of disciplines including applied math, political science, economics and physics. Indeed, while many more articles are available in outlets such as the arXiv … here is a subset for your consideration ….

Damon Centola, Juan Carlos González-Avella, Víctor M. Eguíluz & Maxi San Miguel, Homophily, Cultural Drift and the Co-Evolution of Cultural Groups, J. Conflict Res. 51, 905 (2007).

Konstantin Klemm, Victor M. Eguíluz, Raul Toral, Maxi San Miguel, Globalization, Polarization and Cultural Drift, J. Economic Dynamics & Control 29, 321 (2005).

Konstantin Klemm, Victor M. Eguíluz, Raul Toral & Maxi San Miguel, Role of Dimensionality in Axelrod’s Model for the Dissemination of Culture, Physica A 327, 1 (2003).

As a member of the Society for Evolutionary Analysis in Law (SEAL), I have had the oppurtunity to see a number of interesting presentations by Gregory Todd Jones. Gregory is a Faculty Research Fellow and Adjunct Professor of Law at the Georgia State University College of Law as well as Senior Director of Research and Principal Scientist at the Network for Collaborative Problem Solving. Of particular interest to readers of this blog, he is also the founding director of the Computational Laboratory for Complex Adaptive Systems at Georgia State Law School.

Above is a recent talk by Gregory at the TedX Atlanta in which he (1) assembles a model of sustainability based on collaboration and (2) discusses species behavior … from slugs to chimpanzees.  If you are interested in learning more … Gregory has launched a really cool blog … Cooperation Science Blog … Check it out!