Relative bipolarization Lorenz curve

This note proposes a relative bipolarization quasi-ordering based on relative bipolarization (RB) Lorenz curves, which is consistent with the quasi-ordering generated by relative bipolarization indices satisfying key axioms. Therefore the quasi-ordering induced by RB Lorenz curves is identical to the one induced by relative bipolarization curves (the second-order curves in Foster and Wolfson (2010)). An appealing trait of RB Lorenz curves is their intuitive and straightforward representation of relative bipolarization situations, including minimum and maximum bipolarization, as well as any intermediate situation of perfect bimodality.