By Satya R. Chakravarty

ISBN-10: 8132221656

ISBN-13: 9788132221654

ISBN-10: 8132221664

ISBN-13: 9788132221661

This monograph at the beginning bargains a scientific remedy of the idea and method of other notions of source of revenue polarization and similar matters. It then is going directly to examine social polarization, ordinal polarization, and the kinfolk among inequality polarization, fractionalization and chance of conflicts. Axiomatic methods to the dimension of polarization from assorted views are analyzed carefully. in an effort to comprehend the adaptation among inequality and polarization, a dialogue on source of revenue inequality can also be included.

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Ii) x^ À can be obtained from y^ À by a sequence of spread-increasing movements away from the median and/or bipolarity increasing progressive transfers; and/or x^ þ can be obtained from y^ þ by a sequence of spread-increasing movements away from the median and/or bipolarity increasing progressive transfers. (iii) x^ À y^ À A1 and/or y^ þ A2 x^ þ , for some bistochastic matrices A1 and A2 of appropriate orders. , . , . , M2q } of finitely many Pigou–Dalton matrices of appropriate orders such that x^ À y^ À M11 M12 .

Xk . The population here has been partitioned into k ! 2 subgroups with respect to some characteristic, where k is arbitrary. SUD provides a breakdown of overall inequality into within-group and betweengroup terms. The between-group component I ðλ1 1n1 , λ2 1n2 , . . , λk 1nk Þ is the level of inequality that would arise if each individual in a subgroup enjoys the mean income k À Á P of the subgroup, and the within-group component wi λ, n I ðxi Þ is the weighted i¼1 sum of inequalities within different subgroups.

Often we assume that a bipolarization index is normalized. That is, it takes on the value zero when incomes are distributed equally. Formally, 40 2 On the Measurement of Income Bipolarization Normalization (NM) For all n 2 N, x 2 Dn ; PðxÞ ¼ 0 if x ¼ c1n , where c > 0 is any scalar. We conclude this section by demonstrating that the Levy index is a transgressor of IS and IB. For this, consider the income distribution y ¼ ð1; 3; 5; 7; 9; 11; 13; 15; 17; 19Þ, whose median (also mean) is 10. 5. Thus, y is transformed into y1 by increasing spread both below and above the median.

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