Bill Zwicker: John Nash meets Jorge Hirsch: Scale Invariant Citation Indices

10 novembre 21

Séminaire de Bill Zwicker, mercredi 17 novembre 2021 en salle A707.

Title: John Nash meets Jorge Hirsch: Scale Invariant Citation Indices

Abstract: 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 that strike some balance between productivity (number of papers published) and impact (frequency with which those papers are cited). We propose several new citation indices, each resting on the notion of scale invariance, as introduced by John Nash in his solution of the two-person bargaining problem. Our main focus is on one of these—a scale invariant version of the Hirsch index, which has been independently proposed by Levene et al as the \Chi-index. We argue that it produces fairer rankings within subdisciplines, is more decisive, and is more dynamic.  Simulations with Poisson noise suggest that scale invariance reduces the number of "accidental" reversals, wherein random irregularities cause researcher A to receive a lower index value than B, although A's productivity and impact are both slightly higher than B's. Moreover, we provide an axiomatic characterization of the scale invariant Hirsch index, via axioms that bear a close relationship, in discrete analogue, to those used by Nash. This argues for the mathematical naturality of the new index.

by Josep Freixas, Roger Hoerl, and William S Zwicker