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Polarization measurement for ordinal data

An Erratum to this article was published on 30 June 2015

Abstract

Atkinson’s Theorem (Atkinson J. Econ. Theory 2, 244–263, 1970) is a classic result in inequality measurement. It establishes Lorenz dominance as a useful criterion for comparative judgements of inequality between distributions. If distribution A Lorenz dominates distribution B, then all indices in a broad class of measures must confirm A as less unequal than B. Recent research, however, shows that standard inequality theory cannot be applied to ordinal data (Zheng Res. Econ. Inequal. 16, 177–188, 2008), such as self-reported health status or educational attainment. A new theory in development (Abul Naga and Yalcin J. Health Econ. 27(6), 1614–1625, 2008) measures disparity of ordinal data as polarization. Typically a criterion used to compare distributions is the polarization relation as proposed by Allison and Foster (J. Health Econ. 23(3), 505–524, 2004). We characterize classes of polarization measures equivalent to the AF relation analogously to Atkinson’s original approach.

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Correspondence to Martyna Kobus.

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The project was supported by National Science Centre in Poland and by a grant from the CERGE-EI Foundation under a program of the Global Development Network. All opinions expressed are those of the author and have not been endorsed by CERGE-EI or the GDN.

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Kobus, M. Polarization measurement for ordinal data. J Econ Inequal 13, 275–297 (2015). https://doi.org/10.1007/s10888-014-9282-y

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Keywords

  • Polarization
  • Inequality measurement
  • Ordinal data
  • Atkinson’s Theorem
  • Dominance