Consistent and inconsistent inequality indices for ordinal variables
研究了定序变量不平等比较中，指数是否应受类别排序方式影响的问题，提出一致性性质并刻画了满足该性质的指数类，检验了文献中常见指数的一致性。
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.