Norm-Based Measures of Inequality: A Property-Focused Evaluation

Norm-based inequality measures are developed within the UD/RUD framework by applying L ₁ and squared L ₂ norms to the CDQF, QF, and their joint CDQF representations. All six indices satisfy scale, replication, and translation invariance, as well as anonymity, and their behavior under Pigou-Dalton transfers and subgroup decomposition is characterized analytically. CDQF-based indices combine the vertical and horizontal gaps, giving them representation decomposability and making L _1,cq and L ² _2,cq the most informative overall measures of inequality. A Monte Carlo study on six contrasting income distributions corroborates these theoretical advantages, confirming finite, stable values even for mixed-sign and heavy-tailed supports. JEL Classification: C43 , D31 , D63