Modeling Citation and Download Data in Legal Scholarship

Abstract

Impact factors among law reviews provide a measure of influence among these journals and the schools that publish them. Downloads from the Social Science Research Network (SSRN) serve a similar function. Bibliometrics is rapidly emerging as a preferred alternative to more subjective assessments of academic prestige and influence. Law should embrace this trend.

This paper evaluates the underlying mathematics of law review impact factors and per-author SSRN download rates by institution. Both of these measures follow the sort of stretched exponential distribution that characterizes many right-skewed distributions found in the natural and social sciences. Indeed, an ordinary exponential distribution — that is, a stretched exponential distribution with an exponent of 1 — generates strikingly accurate, even beautiful, models of both phenomena. Mindful of physicist Hermann Weyl's admonition that any choice between truth and beauty should favor beauty, I freely admit to sacrificing some marginal improvement in the descriptive accuracy of my model in order to develop the elegant mathematics of the ordinary exponential distribution.

Further elaboration of this model of law review impact factors as an exponential distribution yields the Gini coefficient of the secondary legal literature, to the extent that each journal's influence is expressed by its impact factor. An identical analysis applies to law school prestige as measured by per-author download rates on SSRN. The remarkable result of this inequality computation is that the Gini coefficient of legal academia, when prestige in this field is modeled according to an ordinary exponential distribution, is exactly 1/2. That outcome that is determined analytically rather than empirically. The inverse Simpson index similarly reflects an exact twofold reduction in the second-order diversity of law review publishing and academic prestige as measured through SSRN downloads. I conclude that modeling law review impact factors and SSRN download rates according to ordinary exponential distributions gives rise to a powerful mathematical tool for assessing influence among law journals and law schools.

Keywords: impact factor, bibliometrics, rankings, SSRN, downloads, John Doyle, Lambert W function, Gini coefficient, Lorenz area, power law, stretched exponential, Simpson index, Zipf's law, U.S. News, exponential distribution, empirical analysis, calculus

JEL Classification: C00, E25