Poverty orderings: A graphical illustration

This note graphically illustrates the power of various poverty ordering conditions. Using the Kolm three-person simplex, we are able to show that (1) for a fixed poverty line the power may be increased as higher degrees of stochastic dominance are considered, (2) for a single but variable poverty line the power is reduced as the line increases, and (3) for a range of poverty lines the power of the third degree ordering condition may be reduced to that of the second degree if the lower bound poverty line is arbitrarily close to zero.