Inequality orderings and unit consistency

摘要

The paper examines the implications of the newly proposed unit consistency axiom for partial inequality orderings. We first show that some intermediate Lorenz dominance conditions violate the axiom. We then characterize a class of intermediate Lorenz orderings and demonstrate that the only unit-consistent member is the one related to Krtscha (Models and measurement of welfare and inequality. Springer, Heidelberg, 1994)’s intermediate notion of inequality which has recently been investigated by Zoli (A surplus sharing approach to the measurement of inequality. Discussion paper no. 98/25, University of York, 1998; Logic, game, theory and social choice. Tilburg University Press, Tilburg, 1999) and Yoshida (Soc Choice Welf 24:557–574, 2005). Finally, we provide a general characterization for unit-consistent Lorenz orderings and the Krtscha-type dominance again turns out to be the only one that is intermediate and unit-consistent.