Measuring polarization by reduced-form indices

Abstract

An abbreviated or reduced-form monotonic polarization index is an increasing function of the between-group term and a decreasing function of the within-group term of a population subgroup decomposable inequality index. The between-group term represents the „identification? component of polarization and the within-group term can be regarded as an inverse indicator of the „alienation? component of polarization. An ordering for ranking alternative distributions of income using such polarizations indices has been developed. Several polarization indices of the said type have been characterized using intuitively reasonable axioms. Finally, we also consider the dual problem of retrieving the inequality index from the specified form of a polarization index.Polarization, ordering, axioms, indices, characterization, duality.