Google Scholar and the Yule-Simon Model

Stephen J Bensman notsjb at LSU.EDU
Tue Apr 22 09:55:06 EDT 2014

The paper below just posted on arXiv may be of interest to the SIGMETRICs Listserve:

Comparison of the Research Effectiveness of Chemistry Nobelists and Fields Medalist Mathematicians with Google Scholar: the Yule-Simon Model / Stephen J. Bensman, Lawrence J. Smolinsky, Daniel S. Sage.  Available at the arXiv WWW site at:

This paper presents a test of the validity of using Google Scholar (GS) to assess researchers' publication impacts. It does this by using the Yule-Simon model to compare the research effectiveness of chemistry Nobelists and Fields medalist mathematicians as measured by GS inlinks. It finds that GS delivers results that are consistent with the structure of the disciplines and the nature of the prizes. Chemistry is a science, and the Nobel prize is awarded at the end of a chemist's career. Mathematics is a fragmented discipline, more philosophical than scientific in many respects, and the Fields medal is awarded at the beginning of a mathematician's career. Due to these factors, the Yule-Simon better approximates the inlink distributions to the works of the chemists than to those of the mathematicians, which manifest a more random pattern.

Before reading this paper, you should read the following passage I have written about Paul Krugman, winner of the Nobel prize in economics in 2008:

"The above statistical tests will applied Paul Krugman (2008).... Krugman is of the most interest, and his data will be used to explain and demonstrate the tests.  Krugman is interesting for the following three reasons.  First, of all Nobel prizes the one in economics probably has the most societal impact, and Krugman's career reflects this as he has at least three jobs: professor of economics and international affairs at Princeton University; Centenary Professor at the London School of Economics; and his best-known job an op-ed columnist for The New York Times, resulting in his being called "the most important political columnist in America" (, 2014).  Second, in an op-ed piece entitled "Open Science and the Econoblogosphere" Krugman (2012, Jan. 12) stated that the traditional method of submitting, being refereed, and then published in leading journals broke down in economics as far back in the 1980s as being too slow.  Even in those days, according to him, nobody at a top school learned things by reading the journals; it was all done by printed working papers being exchanged among members of informal working groups.  Journals served as tombstones, good for only tenure committees, and the notion of journals as gatekeepers was largely fictional 25 years ago.  Krugman states that the system nowadays still works the same except that the printed working papers have been replaced by rapid-fire exchange via blogs and online working papers, suggesting that GS cites may perhaps be a better measure economists' importance than WoS ones.  And, finally, Krugman was awarded the prize "for his analysis of trade patterns and location of economic activity" (, 2014), and in this work Krugman (1996a; 1996b, pp. 44-46 and 92-97) confronted the problem of using power-law models to analyze the distribution of U.S. cities by size.  He found that the size distribution of U.S. cities is startlingly well described by a simpler power law, i.e., the number of cities whose population exceeds S is proportional to 1/S. For him this simple regularity was puzzling especially as it had apparently remained true for at least the past century. According to Krugman, standard models of urban systems offer no explanation of the power law, but the Yule-Simon model was the best try to date.  However, he stated, while it can explain a power law, it cannot reproduce one with the right exponent, leaving us in the frustrating position of having a striking empirical regularity with no good theory to account for it.  For these reasons Krugman (1996b) considered the Yule-Simon distribution not a model but a "story" (p. 44),  and he stated that, while he had no resolution of the problem, he was convinced of three things: 1) the power law model on city sizes is very real and tells us something very important about our economy; 2) some kind of random growth process Is the most likely explanation; and 3) the Yule-Simon model is so elegant an approach the it is the best game in town (p. 97).  Krugman's experience seems to indicate that we are dealing with a wrong but useful model and that we will not be able to mathematically prove our findings but only determine whether they are logical."

The above passage should indicate where and why I am coming from in the arXiv paper.  If anybody takes the time to read the stuff, I would be interested in your comments.

Stephen J Bensman, Ph.D.
LSU Libraries
Lousiana State University
Baton Rouge, LA 70803

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