 The multiplicity of indices, even when a restriction to special sub-classes may be justified by axiomatic characterization, raises a serious problem for applications. How can one make sure that a distribution is more or less unequal, or has more or less poverty, than another without checking an infinite number of indices? Although this may look like a purely practical issue, it has given rise to a broad range of deep results, relating the statistical concept of stochastic dominance to general properties of social welfare functions and to the satisfaction of transfer axioms by inequality and poverty indices. This approach, in particular, justifies the widespread use of Lorenz curves in the empirical studies of inequality. The Lorenz curve depicts the percentage of the total amount of whatever is measured, income, wealth or well-being, possessed by any given percentage of the poorest among the population. For instance, according to the Census Bureau, in 2006 the poorest 20%’s share of total income was 3.7%, the poorest 40%’s share was 13.1%, the poorest 60%’s share was 28.1%, the poorest 80%’s share was 50.6%, while the top 5%’s share was 22.2%. This indicates that the Lorenz curve is approximately as in the following figure.