Ranking dynamics and volatility

Scientific journals are ordered by their impact factor while countries, institutions or researchers can be ranked by their scientific production, impact or by other simple or composite indicators as in the case of university rankings. In this paper, the theoretical framework proposed in Criado, R., Garcia, E., Pedroche, F. & Romance, M. (2013). A new method for comparing rankings through complex networks: Model and analysis of competitiveness of major European soccer leagues. Chaos, 23, 043114 for football competitions is used as a starting point to define a general index describing the dynamics or its opposite, stability, of rankings. Some characteristics to study rankings, ranking dynamics measures and axioms for such indices are presented. Furthermore, the notion of volatility of elements in rankings is introduced. Our study includes rankings with ties, entrants and leavers. Finally, some worked out examples are shown.