January 22, 2010
"For Dummies" Version of Properties of the United States Code Citation Network Needed!
Hat tip to Paul Lomio, Legal Research Plus, for calling attention to Properties of the United States Code Citation Network [SSRN] by Michael James Bommarito II and Daniel Martin Katz. I gave it my best shot during the holidays but my small brain just failed. Hopefully Paul or Robert Richards can give me a "for dummies" explanation. Knowing that LLB readers are much smarter than me, here's the paper's abstract:
The United States Code is a body of documents that collectively comprises the statutory law of the United States. In this short paper, we investigate the properties of the network of citations contained within the Code - most notably its degree distribution. Acknowledging the text contained within each of the Code's section nodes, we adjust our interpretation of the nodes to control for section length. Though we find a number of interesting properties in these degree distributions, we demonstrate that a power law distribution is not an appropriate model for this system.
Wonderful job of explaining the original idea. However, the original contains a faulty definition: "The United States Code is a body of documents that collectively comprises the statutory law of the United States." The code is emphatically NOT the statutory law in a plain sense. It is the PRESUMPTIVE statutory law of the United States. The true statutory law is that found in the Statutes at Large (Public Laws), except instances where the U.S. Code has been affirmatively codified (enacted) by Congress. This is very important to remember--since certain federal laws are NOT codified, but found only in the Statutes at Large. And if the code varies from the statutes, the statutes control.
Posted by: John Hightower | Jan 25, 2010 6:00:16 AM
I can take a stab at it. (My B.S. is in Computer Science, although now my head is full of law school.)
The authors are trying to get a feel for how the U.S.C. cites to itself; i.e., are there patterns in the code? If so, is there a way we can categorize them? The author's result: haven't found a way to describe the pattern yet. :-)
Here's what they did. They took one approach that makes a lot of sense: They created a "Graph" of the statutes and the citations. This is a particular kind of graph - it's basically a web consisting of "nodes" and "edges". (There's a good picture at http://en.wikipedia.org/wiki/Graph_theory)
Once they had this graph representation, it was easy (relatively) to do any number of interesting mathematical analyses. For this article, they calculated the number of outgoing and incoming references (citations) on each node (statute). Once they had these huge lists of counts of connections, they looked to see if the connection counts followed any well known patterns. E.g., a bell curve? A straight line? Etc.
They noticed right away that there was a lot of "skewness" in the connection counts. This means that the values were bunched up at one end, instead of looking evenly distributed, like a bell curve, were they to be plotted.
The high skewness suggested that the Power Law might be at work, which would have been cool and made sense. All sorts of things in nature follow the Power Law. For example, Google website rankings. There's a zillion bad websites, and very few - a long tail - of good ones. The graph would look like a concave bowl-like curve that tapers to zero on the right side.
Or, on a "log log" graph (the kind they used in the article), the Power Law looks like a straight line. (A log-log graph just means that both axes increase exponentially (10, 100, 1000, etc.); it's good for dealing with a set of data that has huge extremes.)
And so, the final charts compared their data to this straight line of the Power Law, and it didn't really match up. So the search for a characterization of the pattern continues...
-- Robb, thanks much! This I understand! And for some reason, what they were looking for reminds me of Plato's later work on Laws. -- Joe
Posted by: Robb Shecter | Jan 22, 2010 11:12:09 PM