4. Extended bi-polarization and inequality measures

This paper aims to clarify the similarities and differences between the concepts of bi-polarization and inequality by proposing an extended measure of bi-polarization, which is consistent with the second polarization curve. The standard decomposition property of population subgroups for the Gini coefficient can be generalized to the extended Gini coefficients. Then, it is explicitly shown that the Wolfson bi-polarization index can be obtained by subtracting the within-groups from the between-groups Gini coefficients, computed for groups separated by the median value. Moreover, we demonstrate the existence of a critical interval of the sensitivity parameter values (v) of the extended Gini coefficient, within which the second polarization curve can be consistently expressed as the subtraction of the within-groups inequality component from the between-groups inequality component. This critical interval is defined by v ϵ[2, 3]. This approach has the conceptual advantage of viewing inequality and polarization within the same framework.