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On the measurement of polarization for ordinal data

Martyna Kobus

No 325, Working Papers from ECINEQ, Society for the Study of Economic Inequality

Abstract: Atkinson’s Theorem (Atkinson, 1970) is a classic result in inequality measurement. It establishes Lorenz dominance as a useful criterion for comparative judgements of inequality between distributions. If a Lorenz distribution A 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, 2008), such as self-reported health status or educational attainment. A new theory in development (Apouey, 2007; Abul Naga and Yalcin, 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 (AF) (2004). We characterize classes of polarization measures equivalent to the AF relation analogously to Atkinson’s original approach.

Keywords: Polarization; Inequality measurement; Ordinal data; Atkinson’s Theorem; Dominance. (search for similar items in EconPapers)
JEL-codes: D3 D6 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2014-03
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