Bonferroni and De Vergottini are back: New subgroup decompositions and bipolarization measures

This paper proposes new bipolarization indices based on the Bonferroni and De Vergottini indices of inequality. These new indices follow the approach of Foster and Wolfson and are based on a new subgroup decomposition of the Bonferroni and De Vergottini indices of inequality. We also provide the conditions under which the new polarization indices satisfy the Increased Spread and Increased Bipolarity axioms. Finally, a simulation study is performed to compare the different sensitivity of the new bipolarization indices to progressive transfers. An empirical application based on EU-SILC data for Italy in the period 2007-2011 also shows the appeal of our proposal.