We enjoyed today’s discussion at the Harambeenet Conference here in the Duke Computer Science Department. The conference is centered upon network science and computer science education. It features lots of interdisciplinary scholarship and applications of computer science techniques in novel domains.
We are looking forward to an interesting final day of discussion and hope to participate in allied future conferences.
The visual above is drawn from the Netlogo Simulation of preferential attachment. “In the model, a given node prefers to connect to other nodes that already display high indegree. As the number of connections a given agent displays is a function of the number the agent possessed in earlier time periods, the distribution of connections is highly susceptible to the initial starting conditions. For instance, consider a network that has four nodes A, B, C and D where A is connected to B and C is connected to D. If node E enters the network, assume the initial probability of attachment to the AB community is equal to that of the CD community. Once E connects to either the AB or CD community, subsequent entrants such as node F, G and beyond are more likely to connect with the community selected by E.” The model offers one of the generative processes responsible for creating a network with a power law distribution.
There are important differences between the abstract model as initially described in Albert-László Barabási & Reka Albert, Emergence of Scaling in Random Networks, 286 Science 509 (1999) and the dynamics of broader social world. While a number of extensions of the model have been authored in the period following the original article, what is striking is how much leverage on basic dynamics can be gleaned from the graph analog of a Yule process.
For purposes of positive legal theory consider the following passage … “In order to contextualize what a particular observed network structure implies, it is critical to remember that the social landscape need not take any particular form. Scaffolding could indeed assume a variety of flavors and there are causal mechanisms that act at the micro-level to produce the observed macro-architecture.” While such distributions have been documented in a variety of context relevant for positive legal theory, it is important to note this distribution of social authority is by no means a given. Specifically, as we described in Social Architecture, Judicial Peer Effects and the ‘Evolution’ of the Law: Toward a Positive Theory of Judicial Social Structure social systems can embrace a wide variety of architectures. Thus, we believe the documented tendency of common law and its constitutive systems to generate such highly skewed distributions is highly relevant.
In Part II of this post, we will highlight the current state of the relevant applied legal literature. This includes not only our work but also important studies by a wide number of other legal scholars. To preview, check out this post from a few days ago…
It has been light blogging while we finish some projects here in Ann Arbor. In the meantime, here is an interesting visual offered by CDC website. Also, check out an important paper in this vein by Nicholas Christakis & James Fowler entitled The Spread of Obesity in a Large Social Network Over 32 Years (Click to the Left to Link to the Original Movie). Anyway, more to come later in the week…
Here at the CSCS Lab, we are working hard to finish up some projects. In the meantime, we wanted to highlight one of our favorite articles, an article we previously highlighted on the blog. Some of you might ask “what does this have to do with law or social science?” (1) We believe the taxonomy outlined in this article could potentially be applied to a wide set of social phenomena (2) As we say around here, if you are not reading outside your discipline, you are far less likely to be able to innovate within your discipline. So we suggest you consider downloading this paper….
This article in a recent issue of Science Magazine — authored by some of the leaders in field including Gary King, James Fowler, David Lazer, Albert-László Barabási, Lada Adamic as well as several others — highlights some of the possibilities of and perils associated with a computational revolution in the social sciences. We believe it is a worthwhile read….
Anton Geist has posted Using Citation Analysis Techniques for Computer-Assisted Legal Research in Continental Jurisdictions to the SSRN. While this is certainly longer than most papers, we believe it offers a good review of the broader information retrieval and law literature. In addition, it offers some empirical insight into citation patterns within continental jurisdictions. The findings in this paper are similar to those shown in important papers by Thomas Smith in The Web of the Law and by David Post & Michael Eisen in How Long is the Coastline of Law? Thoughts on the Fractal Nature of Legal Systems.
In our view, the next step for this research is to determine whether the pattern does indeed follow a power law distribution. Specifically, there exists a Maximum Likelihood based test developed in the applied physics paper Power-law Distributions in Empirical Data by Aaron Clauset, Cosma Shalizi and Mark Newman which can help adjudicate whether the detected pattern represents a highly skewed distribution or is indeed a power law.
Either way, we are excited by this paper as we believe comparative research is absolutely critical to broader theory development.
We wanted to highlight a couple of very interesting posts by Drew Conway of Zero Intelligence Agents. While not simple, the programming language python offers significant returns upon investment. From a data acquisition standpoint, python has made what seemed impossible quite possible. As a side note, this code looks like our first Bommarito led Ann Arbor Python Club effort to download and process NBA Box Scores…. you know it is all about trying to win the fantasy league…!
This is the third installment of posts related to our paper Law as a Seamless Web? Comparison of Various Network Representations of the United States Supreme Court Corpus (1791-2005) previous posts can be found (here) and (here). As previewed in the earlier posts, we believe comparing the Union, the Intersect and the Compliment of the SCOTUS semantic and citation networks is at the heart of an empirical evaluation of Law as a Seamless Web …. from the paper….
“Though law is almost certainly a web, questions regarding its interconnectedness remain. Building upon themes of Maitland, Professor Solum has properly raised questions as to whether or not the web of law is “seamless”. By leveraging the tools of computer science and applied graph theory, we believe that an empirical evaluation of this question is at last possible. In that vein, consider Figure 9, which offers several possible topological locations that might be populated by components of the graphs discussed herein. We believe future research should consider the relevant information contained in the union, intersection, and complement of our citation and semantic networks.
While we leave a detailed substantive interpretation for subsequent work, it is worth broadly considering the information defined in Figure 9. For example, the intersect (∩) displayed in Figure 9 defines the set of cases that feature both semantic similarity and a direct citation linkage. In general, these are likely communities of well-defined topical domains. Of greater interest to an empirical evaluation of the law as a seamless web, is likely the magnitude and composition of the Citation Only and Semantic Only subsets. Subject to future empirical investigation, we believe the Citation Only components of the graph may represent the exact type of concept exportation to and from particular semantic domains that would indeed make the law a seamless web.”
Earlier in the month, there was a very interesting discussion over at Flowing Data entitled the Rise of the Data Scientist. We decided to highlight it in this post because it raises important issues regarding the relationship between Computational Legal Studies and other movements within law.
As we consider ourselves empiricists, we are strong supporters of the Empirical Legal Studies movement. For those not familiar, the vast majority of existing Empirical Legal studies employ the use of econometric techniques. For some substantive questions, these approaches are perfectly appropriate. While for others, we believe techniques such as network analysis, computational linguistics, etc. are better suited. Even when appropriately employed, as displayed above, we believe the use of traditional statistical approaches should be seen as nested within a larger process. Namely, for a certain class of substantive questions, there exists tremendous amounts of readily available data. Thus, on the front end, the use of computer science techniques such as web scraping and text parsing could help unlock existing large-N data sources thereby improving the quality of inferences collectively produced. On the back end, the use of various methods of information visualization could democratize the scholarship by making the key insights available to a much wider audience.
It is worth noting that our commitment to Computational Legal Studies actually embraces a second important prong. From a mathematical modeling/formal theory perspective, at least for a certain range of questions, agent based models/computational models ≥ closed form analytical models. In other words, we are concerned that many paper & pencil game theoretic models fail to incorporate interactions between components or the underlying heterogeneity of agents. Alternatively, they demonstrate the existence of a P* without concern of whether such an equilibrium is obtained on a timescale of interest. In some instances, these complications do not necessarily matter but in other cases they are deeply consequential.