Poverty Dominance

Abstract

To see how the material of Chapter 9 can be used practically to test for the robustness of poverty comparisons, we focus for simplicity on classes of additive poverty indices denoted as Π^s(z ⁺), where s stands again for the “ethical order” of the class and where z ⁺ will stand for the upper bound of the range of all of the poverty lines that can reasonably be envisaged. The additive poverty indices P(z) that are members of that class can be expressed as

$$ P(z) = \smallint _0^1 \pi (Q(p);z) dp, $$

(10.1)

where z is a poverty line and π(Q(p); z) is an indicator of the poverty status of someone with income Q(p).