Revisiting comparisons of income inequality when Lorenz curves intersect

The main contribution of Davies and Hoy (Am Econ Rev 85:980–986, 1995) was a “necessary and sufficient” condition for comparing inequality between income distributions according to the principle of transfer sensitivity (PTS). Chiu (Soc Choice Welf 28:375–399, 2007) showed that although the condition is sufficient, it is not necessary. In this paper, we provide the correct necessary and sufficient condition, and demonstrate with a simple example how the corrected condition allows for more pairs of distributions to be ranked by PTS. The correction clarifies the connection between Lorenz curve comparisons and inequality rankings when the curves intersect.