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An Axiomatization of the Multigroup Atkinson Segregation Indices

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  • Frankel, David M.
  • Volij, Oscar

Abstract

This paper gives an axiomatic characterization of the multigroup Atkinson indices of segregation relying entirely on ordinal axioms. We show that the Symmetric Atkinson index represents the unique ordering that treats ethnic groups symmetrically, that is invariant to population growth rates that differ among ethnic groups, that regards school districts as more segregated when schools in them are subdivided (unless the new schools have the exact same ethnic distribution), and that satisfy an independence property. If symmetry among ethnic groups is dropped, one obtains the family of orderings that are represented by the Asymmetric Atkinson indices. The latter result requires the addition of a continuity axiom.

Suggested Citation

  • Frankel, David M. & Volij, Oscar, 2008. "An Axiomatization of the Multigroup Atkinson Segregation Indices," Staff General Research Papers Archive 12902, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genres:12902
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    File URL: http://www2.econ.iastate.edu/papers/p3879-2008-04-14.pdf
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    References listed on IDEAS

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    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
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    10. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
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    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.

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    More about this item

    Keywords

    education; Segregation; schools; diversity;
    All these keywords.

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General

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