The Journal of Economic Inequality

, Volume 13, Issue 2, pp 275–297 | Cite as

Polarization measurement for ordinal data

  • Martyna Kobus


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.


Polarization Inequality measurement Ordinal data Atkinson’s Theorem Dominance 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of EconomicsPolish Academy of SciencesWarsawPoland

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