Scale-invariant citation indices

A number of citation indices have been proposed for measuring and ranking the research publication records of scholars. Some of the best known indices are designed to reward most highly those records x that strike some balance between impact I and productivity P ; a large number of publications with few citations per paper will not score well, nor will a very small number of heavily cited papers. Implicit in a number of the best-known indices, however, is a single optimal trade-off ratio r of productivity to impact. In terms of the P × I graph of x, we can think of r as a fixed scale factor relating the size of a unit on the I axis to one on the P axis. We argue that scholars, or entire disciplines, are assigned higher index values if their publication records have better “fit” with r, and that this effect can scramble the relative ordering of scholars within a discipline, in an undesirable way. In an approach modeled loosely on John Nash’s solution to the bargaining problem, we propose four scale-invariant indices, two of which are variants of known indices. While preserving some degree of impact-productivity balance, these indices in effect adjust r on a case-by-case basis, to best fit the publication record of each scholar. We argue that these indices have certain advantages, and discuss axioms intended to capture the ideal of scale invariance. JEL classification: I23, C78.