# An axiomatic characterization of a class of rank mobility measures

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## Abstract

In this paper we provide an axiomatic characterization of a total preorder for assessing the mobility associated with any pair of rankings relative to a same group by means of a new class of rank-mobility measures. These measures constitute a strong generalization of Spearman’s \(\rho \) index. The problem of dealing with mobility of subgroups, which is a pressing issue in several and various applicative contexts ranging from the use of socio-economic indicators to information retrieval, is addressed in terms of *partial permutations* which include standard permutations as a special case. Literature is lacking in a theoretical discussion for comparing mobility of variable-size subgroups: we show that our axiomatic approach fills this gap.

## Notes

### Acknowledgements

We would like to thank the anonymous referees for their careful reading and valuable comments that have been helpful for providing a much improved version of the present work.

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