An axiomatic characterization of a class of rank mobility measures

  • Roberto Ghiselli RicciEmail author
Original Paper


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.



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.


  1. Bossert W, Can B, D’Ambrosio C (2016) Measuring rank mobility with variable population size. Soc Choice Welf 46(4):917–931CrossRefGoogle Scholar
  2. Chakravarty SR, Dutta B, Weymark JA (1985) Ethical indices of income mobility. Soc Choice Welf 2:1–21CrossRefGoogle Scholar
  3. Cook WD, Seiford LM (1978) Priority ranking and consensus formation. Manag Sci 24(16):1721–1732CrossRefGoogle Scholar
  4. Critchlow DE (2012) Metric methods for analyzing partially ranked data, vol 34. Springer Science & Business Media, BerlinGoogle Scholar
  5. Dardanoni V (1993) Measuring social mobility. J Econ Theory 61:372–94CrossRefGoogle Scholar
  6. D’Agostino M, Dardanoni V (2009) The measurement of rank mobility. J Econ Theory 144:1783–1803CrossRefGoogle Scholar
  7. Debreu G (1954) Representation of a preference ordering by a numerical function. In: Coombs CH, Thrall RM, Davis RL (eds) Decision processes. Wiley, New YorkGoogle Scholar
  8. Diaconis P (1988) Group representations in probability and statistics. Institute of Mathematical Statistics, HaywardGoogle Scholar
  9. Dowrick S, Dunlop Y, Quiggin J (2003) Social indicators and comparisons of living standards. J Dev Econ 70(2):501–529CrossRefGoogle Scholar
  10. Emond EJ, Mason DW (2002) A new rank correlation coefficient with application to the consensus ranking problem. J Multi-Criteria Decis Anal 11(1):17–28CrossRefGoogle Scholar
  11. Fagin R, Kumar R, Sivakumar D (2003) Comparing top k lists. SIAM J Discrete Math 17(1):134–160CrossRefGoogle Scholar
  12. Fields GS, Ok E (1996) The meaning and measurement of income mobility. J Econ Theory 71:349–77CrossRefGoogle Scholar
  13. Fields GS, Ok E (1999) The measurement of income mobility. In: Silber J (ed) Handbook of income inequality measurement. Kluwer Academic Publishers, DordrechtGoogle Scholar
  14. Foster JE, Shorrocks AF (1991) Subgroup consistent poverty indices. Econometrica 59:687–709CrossRefGoogle Scholar
  15. Jäntti M, Jenkins SP (1997) Income mobility. In: Atkinson AB, Bourguignon F (eds) Handbook on income distribution. Elsevier, AmsterdamGoogle Scholar
  16. Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591Google Scholar
  17. Kemeny JG, Snell JL (1962) Mathematical models in the social sciences. Ginn Publishing Inc., BostonGoogle Scholar
  18. Kendall M, Gibbons JD (1990) Rank correlation methods. Edward Arnold, LondonGoogle Scholar
  19. Maasoumi E (1998) On mobility. In: Giles D, Ullah A (eds) The handbook of economic statistics. Marcel Dekker, New YorkGoogle Scholar
  20. Mitra T, Ok E (1998) The measurement of income mobility: a partial ordering approach. Econ Theory 12:77–102CrossRefGoogle Scholar
  21. Permanyer I (2012) Uncertainty and robustness in composite indices rankings. Oxf Econ Pap 64:57–79CrossRefGoogle Scholar
  22. Pečarić JE, Proschan F, Tong YL (1992) Convex functions, partial orderings and statistical applications. Academic Press Inc., New YorkGoogle Scholar
  23. Ruiz-Castillo J (2004) The measurement of structural and exchange mobility. J Econ Inequal 2:219–228CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Economia e ManagementUniversitá di FerraraFerraraItaly

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