Merging populations, stochastic dominance and Lorenz curves

In typical comparisons of inequality the condition that the means of the distributions are equal is hardly met. In these cases, the widely used Lorenz curves non-intersection criterion is neither a necessary nor sufficient condition for stochastic dominance. It is suggested to replace the Lorenz curves non-intersection criterion with an absolute Lorenz curves non-intersection criterion. The implications of adopting this criterion are discussed in the context of fixed populations and changing populations.