Minimum inequality taxation, average and minimally progressive taxations and depolarization

An inequality minimizing taxation (IMT) policy addresses the problem of procuring a certain amount of tax from a given set of persons in an inequality minimizing manner by maintaining rank orders of the individuals in the pre- and post-tax situations and without imposing any notion of inequality invariance. In this article we demonstrate analytically that the newly introduced IMT policy is sufficient but not necessary for average progressive and minimally progressive taxation principles. Using a recent result from the literature we then show that an IMT scheme also implies but is not implied by depolarizing (bipolarization reducing) and bipolarization minimizing taxation policies. An empirical illustration of our results is provided using income data collected by the Center for Monitoring Indian Economy.