Decomposing bivariate dominance for social welfare comparisons

The principal dominance concept for inequality-averse multidimensional social welfare comparisons, commonly known as lower orthant dominance, entails less or equal mass on all lower hyperrectangles of outcomes. Recently, it was shown that bivariate lower orthant dominance can be characterized in terms of two elementary mass transfer operations: diminishing mass transfer (reducing welfare) and correlation-increasing switches (increasing inequality). In this paper we provide a constructive algorithm, which decomposes the mass transfers into such welfare reductions and inequality increases.