The Gini coefficient: Majority voting and social welfare

Majority voting and social evaluation functions are the main alternatives proposed in the literature for aggregating individual preferences. Despite these being very different, this paper shows that the ranking of income distributions, symmetric under the same transformation, by S-Gini consistent social evaluation functions and majority voting coincide if and only if the inequality index under consideration is the Gini coefficient. In this case, we show that the equally distributed equivalent income is equal to the median of the distribution. In addition, we find that the Gini coefficient is just an affine function of the median-mean ratio.