An axiomatic approach to bibliometric rankings and indices

Abstract

This paper analyzes several well-known bibliometric indices using an axiomatic approach. We concentrate on indices aiming at capturing the global impact of a scientific output and do not investigate indices aiming at capturing an average impact. Hence, the indices that we study are designed to evaluate authors or groups of authors but not journals. The bibliometric indices that are studied include classic ones such as the number of highly cited papers as well as more recent ones such as the h-index and the g-index. We give conditions that characterize these indices, up to the multiplication by a positive constant. We also study the bibliometric rankings that are induced by these indices. Hence, we provide a general framework for the comparison of bibliometric rankings and indices.

Ranking authors using fractional counting of citations: An axiomatic approach

“…Indeed, it is satisfied by all brfs that are of common use (e.g., all those studied in Bouyssou and Marchant, 2014). It is violated by ranking methods in which the position of the author of the citing paper in the ranking has an influence on the value of citations made, e.g., ranking methods in which a citation coming from a highly ranked author has more "value" than a citation coming a lowly ranked author (see, e.g., West, Jensen, Dandrea, Gordon, and Bergstrom, 2013).…”

“…This is a standard bibliometric index (see, e.g., van Raan, 2006). It has been studied from an axiomatic point of view by Marchant (2009a) and Bouyssou and Marchant (2014), using a setting that is different from the one used here. This leads to associating with each profile G = (P, S, C) on A and with each author a ∈ A the index:…”

“…Although there are other characterizations of c (see Bouyssou and Marchant, 2010) and Bouyssou and Marchant (2014), Marchant (2009a), these works use settings that are different from the one used here (see Section 6). The one used in Bouyssou and Marchant (2014), Marchant (2009a) is simpler than the one used here and does not allow to tackle the question of field normalization. The one used in Bouyssou and Marchant (2010) is more complex since it also involves journals and co-authors.…”

“…It is satisfied by all brfs that are of common use (e.g., all those studied in Bouyssou and Marchant, 2014). It is violated by ranking methods in which self-citations are not treated as ordinary citations.…”

“…One may think that going from rankings to indices is not difficult. Indeed, Bouyssou and Marchant (2014) have shown that, whenever two consecutive equivalence classes of the ranking are always "equally spaced" in terms of the index, a characterization of the index is easily derived from a characterization of the ranking. This is not so here, for at least two reasons.…”