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Investigating equality: The Rényi spectrum

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  • Eliazar, Iddo

Abstract

An equality index is a score quantifying the socioeconomic egalitarianism of the distribution of wealth in human societies; the score takes values in the unit interval, with the unit upper bound characterizing purely communist societies. In this paper we explore the Rényi spectrum, a continuum of equality indices that: (i) is based on the moments of the societies’ distributions of wealth; (ii) unifies various measures of socioeconomic inequality, including the Theil and Atkinson indices; (iii) displays a collection of amicable analytic properties; (iv) admits multiple Rényi-divergence representations; and (v) provides a high-resolution gauging of egalitarianism that is way beyond what can be offered by the common-practice measures of socioeconomic inequality, the Gini and Pietra indices. At large, the Rényi spectrum is applicable in the context of any distribution of non-negative sizes with a positive mean—yielding a high-resolution gauging of the distribution’s inherent statistical heterogeneity.

Suggested Citation

  • Eliazar, Iddo, 2017. "Investigating equality: The Rényi spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 90-118.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:90-118
    DOI: 10.1016/j.physa.2017.04.003
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    1. François Bourguignon, 2015. "The Globalization of Inequality," Economics Books, Princeton University Press, edition 1, number 10433.
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