use inequality indices to compare the degree of inequality across populations (for example, to determine if there is greater income inequality in California than in Texas, or in Brazil versus South Africa). The best-known inequality index is the Gini coefficient; others include the Atkinson measure, the Theil index, the Hoover index (a.k.a. Robin Hood index), and many others. Firebaugh has shown that standard inequality indices reduce to a convenient common form. He begins by noting that perfect equality exists when the inequality ratio, rj = Xj / equals 1.0 for all j units in some population (for example, there is perfect income inequality when everyone’s income Xj equals the mean income , so that rj = 1.0 for everyone). Inequality, then, refers to deviations of the rj from 1.0; the greater the average deviation, the greater the inequality. Inequality indices reflect that fact because they have this common form: Inequality Index = where pj weights the units by their population share (necessary in a cross-country analysis, for example, since countries vary in population), and f(rj) is a function of the deviation of each unit’s rj from 1.0, the point of equality. The important insight of Firebaugh’s general inequality equation is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the rj) from 1.0. Trends in global income inequality Firebaugh was among the first to note that income inequality for the world as a whole leveled off in the last decades of the 20th century, after rising for more than two centuries. Firebaugh describes this important turning point in a 1999 lead article in the American Journal of Sociology and in a 2003 book. While global income inequality is massive, it has remained relatively steady or declined somewhat in recent years due to rapid income growth in China and India. Firebaugh’s findings challenged earlier claims that global income inequality continues to rise rapidly. According to Firebaugh, that claim was based on a flaw: Each country was assigned equal weighting, despite vast differences in population size. When populous countries such as China and India are given their due weight, the data show that global income inequality has not been rising sharply, and most likely is not rising at all. Firebaugh’s findings have been verified by others. As a result, earlier claims by the United Nations and the World Bank of rapidly rising global income inequality