Abstract
This paper identifies a paradox for inequality indices which is similar to the well known Simpson paradox in statistics. For the Gini and Bonferroni indices, concrete examples of the paradox are provided and general methods are described for obtaining examples of the paradox for arbitrary size population. Sufficient conditions for the paradox not to hold are developed. The paradox, however, vanishes if we measure inequality by the absolute Gini and Bonferroni indices of inequality.
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