Polarization measurement for ordinal data
- 311 Downloads
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.
KeywordsPolarization Inequality measurement Ordinal data Atkinson’s Theorem Dominance
Unable to display preview. Download preview PDF.
- 3.Abul Naga, R.H., Yalcin, T.: Median Independent Inequality Orderings, University of Aberdeen Business School working paper series Vol 3, pp. 1–25 (2010)Google Scholar
- 8.Blackburn, M., Bloom, D.: What is happening to the middle class. Am. Demogr. 7 (1), 19–25 (1985)Google Scholar
- 10.Diener, E., Lucas, R.E.: Personality and subjective well-being. In: Kahneman, D., Diener, E., chwarz, N. (eds.) (1999)Google Scholar
- 13.Esteban, J., Ray, D.: Comparing polarization measures. In: Garfinkel, M.R., Skaperdas, S. (eds.) The Oxford Handbook of the Economics of Peace and Conflict, Chapter 7. Oxford University Press, New York (2012)Google Scholar
- 14.Foster, J., Wolfson, M.: Polarization and the decline of the middle class: Canada and the US. J. Econ. Inequal. 8(2), 247–273 (2010)Google Scholar
- 15.Frey, B.S., Stutzer, A.: Happiness and Economics. Princeton University Press, Princeton, NJ (2002)Google Scholar
- 19.Layard, R.: Happiness. Lessons from a New Science, London: Allen Lane (2005)Google Scholar
- 21.Levy, F., Murnane, R.J.: U.S. Earnings Levels and Earnings Inequality: A Review of Recent Trends and Proposed Explanations. J. Econ. Lit. 30 (3), 1333–1381 (1992)Google Scholar
- 23.Parker, D.S., Ram, P.: Greed and majorization, Tech. Report. Department of Computer Science, University of California, Los Angeles (1997)Google Scholar
- 27.Wolfson, M.C.: When inequalities diverge. Am. Econ. Rev. P&P 94, 353–358 (1994)Google Scholar