An axiomatization of the iterated h-index and applications to sport rankings

Sylvain Béal (1) , Eric Rémila (2) , Philippe Solal (2) , Sylvain Ferrières (1)

1 CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190)
2 GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne

A variant of the h-index introduced in García-Pérez (2009), called the iterated h-index, is studied to evaluate the productivity of scholars. It consists of successive applications of the h-index so as to obtain a vector of h-indices. In particular, the iterated h-index fixes a drawback of the h-index since it allows for (lexicographic) comparisons of scholars with the same h-index. Two types or results are presented. Firstly, we provide an axiomatic characterization of the iterated h-index, which rests on a new axiom of consistency and extensions of axioms in the literature to a richer framework. Secondly, we apply the h-index and iterated h-index to offer alternative sport rankings in tennis, football and basketball. These applications clearly demonstrate that the iterated h-index is much more appropriate than the classical h-index.

Mots clés: h-index; iterated h-index; axioms; sports ranking

Domaines: Microstructure des marchés [q-fin.TR]; Applications [stat.AP]

Sylvain Béal, Eric Rémila, Philippe Solal, Sylvain Ferrières. An axiomatization of the iterated h-index and applications to sport rankings. 2016. ⟨hal-01394818⟩