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.