Abstract
Should inequality comparisons with ordinal variables be sensitive to alternative sorting of the categories? We introduce the consistency property whereby an inequality or bipolarisation index regards frequency distribution r less unequal than s if and only if it ranks the reverse-ordered distribution r ′ less unequal than s ′ for every pair of comparable frequency distributions. We characterise the class of consistent indices with a functional equation that serves as a useful test of the property. Applying the test to the most popular indices in the literature, we identify the respective consistent and inconsistent sets. • The consistency property for inequality comparisons with ordinal variables is introduced. • Consistent inequality comparisons are independent of the order of categorical sorting. • Consistent indices satisfy a functional equation that serves as a test of the property. • Inequality indices from the literature are classified into consistent or not with the test.
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