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Investigates three ordering criteria for measures of income inequality: Lorenz-ordering, R-ordering, and power-scale ordering. R-ordering is a new criterion based on Wohlstetter and Coleman's ratio of income at quantiles function. The relationship of the three orderings is determined. Then, two new summary measures of income inequality are introduced. Both derive from the ratio of incomes at quantiles function. The first, W, has the properties desired of an inequality measure. The second, omega, is useful for describing the ratio of incomes at quantiles function when it is nearly linear, but lacks the ordering properties needed for a good measure of inequality. Ordering properties are determined for the new measures and for the familiar Gini coefficient, variance of the logarithm, two information measures, and the coefficient of variation. Dichotomous distributions are presented as a convenient family of distributions for providing counter-examples. (See also R-578.)

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