The Revolution Will Not Be Televised — But Will it Come from HLS or YLS ? A Social Network Analysis of the Legal Academy (Part IV)

Law Prof Diffusion

This is the final installment of posts related to Reproduction of Hierarchy? A Social Network Analysis of the American Law Professoriate. Thanks for your emails.

Here is the plot we provide within the paper.  As a general proposition, we believe this represents an upper bound measure for the intellectual reach of an agenda offered by a given institution.  With respect to our version of the Reed Frost Epidemiological Model, we use the p parameter to model “idea infectiousness.”  When p = 1 every institution “contacted” by the idea is infected with the idea. When p = 0 no institution “contacted” by the idea is infected.  In this version, we use the programming language python to run the model 500 times per institution. The above plot represents an estimate of the “diffusion curve” for each of the 184 institutions in our model. Building off central limit type properties, this leaves a far better estimate of reach than is offered in the single model run from the previous Netlogo GUI.

A cursory review of the above plot demonstrates, we are far from the land of linearity.  Namely, a large number of institutions are able to reach much of the graph with very small changes in the value of p.

In the Structure of Scientific Revolutions, Kuhn quotes from Max Planck:  “a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.” Following Planck, we believe retirement is indeed be an important mechanism.  However, we also argue the nature of the p parameter is a relevant consideration.  In fact, unpacking various dimensions of p is the key to the broader model. Specifically, what are the properties of an idea that generate its infectiousness? Of course, we might like to believe infectiousness is related to a class of normatively attractive properties such as promoting efficiency or justice.  However, it is not clear that this follows.

We took no pass on the question of whether some institutions would be better or worse at producing ideas with greater or lesser values of p. The motivated question for this post considers whether, in general, the institutions which are top producers of law professors are (1) leaders in innovation, (2) subsequent ratifiers of a newly established paradigm or (3) defenders of the status quo. In a deep sense, we are asking how to reasonably model decision making by the heterogeneous agents located at such institutions.  Do institutions reward or punish intellectual risk-taking, search, etc.?

While this is an empirical question beyond the scope of this post, it worth asking because it partially informs the micro-dynamics plausibly responsible for generating the spread of new intellectual paradigms.

Classic Model from Complex Systems: The El Farol Bar Problem

picture-31

I recently attended a conference at the Santa Fe Institute.  During the trip, I made a point of eating at the El Farol Bar & Restaurant. This restaurant holds a special place in the lore of complex systems.  Thus, I thought I would take the opportunity to highlight the model on the CLS blog.  

Here is a subset of the model description…. “The bar is popular — especially on Thursday nights when they offer Irish music — but sometimes becomes overcrowded and unpleasant. In fact, if the patrons of the bar think it will be overcrowded they stay home; otherwise they go enjoy themselves at El Farol. This model explores what happens to the overall attendance at the bar on these popular Thursday evenings, as the patrons use different strategies for determining how crowded they think the bar will be.”   

The original paper written by Brian Arthur is located here. An interesting follow up paper employing reinforcement learning is located here.    This above is a screen print from the Netlogo model.  Netlogo offers an easy interface useful for exploring a variety of agent based models.  

The model will run in your browser provided you have Java 1.4.1+.  

To run the El Farol model, please go here.   

Coming Next Week on CLS Blog

picture-4

 

A Netlogo 3D screenprint of one of the classic agent based models—the Shelling Segregation Model is above. We offer it as a holdover until CLS Blog Returns Sunday Night with more exciting content…..

NEXT WEEK:
(1) Discussion of a New Paper: Computer Programming and the Law
(2) Visualizing the 110th Congress — The House of Representatives
(3) For Law Students and Law Professors — Data on the Law Clerk Tournament
(4) And More …..