Measuring rank mobility with variable population size

We provide characterizations of a class of rank-mobility measures and of a specific member of this class. These measures are based on the Kemeny distance for orderings. We use the well-known replication-invariance property to ensure that our measures are applicable in variable-population settings. The rank-based approach to mobility has a natural connection with the study of social status. Rank-based measures are widely applied in empirical research but their theoretical foundation is still in need of further investigation, and we consider our approach to be a contribution towards this objective.