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# Gini coefficient

A statistic conventionally used in order to describe in summary form the degree of inequality in distributions (usually of income and wealth). It is calculated by determining the area between a Lorenz curve of the distribution (that is a graph of the cumulative income share against the cumulative share of recipients) and the line of perfect equality. This area is then expressed as a percentage of the whole triangular area under the diagonal. The resulting statistic reduces the position of the curve to a single figure. A distribution of perfectly equal incomes has a Gini coefficient of zero. As inequality increases, and the actual Lorenz curve bellies out, the Gini coefficient moves towards its maximum value of 1 (only one recipient receives all income).
The Gini coefficient is one of several measures of inequality (others include the coefficient of variation and inter-decile ratio) which purport to rest exclusively on the mathematical properties of a distribution. Such indices tend to give conflicting answers when they are asked to determine whether any particular distribution is more unequal than another. For example, one statistic may be more sensitive than another to a scatter of low incomes, and each indicator tends to attach different weights to different forms of inequality within the distribution. More sophisticated measures-such as the Theil index and Atkinson index-have therefore been devised, which attempt to express in a single number the degree of inequality in a distribution as a whole, but in ways which explicitly weight inequalities in different parts of the distribution-in line (for example) with the observer's judgements about the relative value of each additional unit of currency accruing to a rich as against a poor person. (Atkinson's formula for his index contains a coefficient which expresses the researcher's aversion to inequality.)
A good account of the various properties of the different measures will be found in, Egalitarianism and the Generation of Inequality (1988). See also income distribution.

Dictionary of sociology. 2013.

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