Coherence of inequality measures with respect to partial orderings of income distributions

This paper investigates the coherence of a new class of ratio-based inequality indices introduced in Chan (2022) with respect to certain partial orderings of the underlying income distributions. While coherence with respect to stochastic dominance has been extensively studied, the appropriate partial ordering for this new class of indices is quantile ratio dominance. This paper also establishes coherence with respect to quantile ratio dominance for some other classes of inequality indices which have been introduced by other authors. Finally, some connections between the notion of coherence and transfer principles are explored.