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Identifying the Unique Polarization Index: A Mean-Preserving Axiomatic Approach


  • Difei Geng, Department of Economics, Vanderbilt University, VU Station B #351819, 2301 Vanderbilt Place, Nashville, TN 37235 (

  • I appreciate comments from a co-editor and a referee which helped improve the paper substantially. I am extremely grateful to Shlomo Weber for constant support and guidance. I am especially thankful to Joan Esteban for very constructive comments. I thank Bo Chen, Rajat Deb, Daniel Millimet, Santanu Roy, and Erwan Quintin for helpful comments and discussion. All remaining errors are mine.


In this paper, we propose a new axiomatic approach to identify the unique polarization index from a class of polarization measures proposed by Esteban and Ray. Methodologically, we consider the absolute income or the mean normalized income instead of the logarithm of income, which in our opinion is useful under various circumstances. Accordingly, we propose a set of mean-preserving axioms so that the obfuscating effects of income scale can be removed. We also discuss some properties of the polarization indices based on different types of income differences.