Social tension order: A new approach to inequality reduction

We introduce a new order on income distributions that we call "social tension" order, based on the concepts of absolute satisfaction and absolute deprivation, as introduced by Chakravarty (1997) (see also Chateauneuf and Moyes, 2006). Our order postulates that antagonist groups of individuals behave differently when comparing welfare: each "poor" individual compares herself with richer individuals, while each "rich" individual compares herself with poorer ones. We prove that reducing social tension corresponds to fair taxation and provide an explicit algorithm that allows for transitioning from a dominated distribution to a dominating one through a sequence of elementary transfers that respect our order. Additionally, we construct a new index from the "social tension" order, which may better capture the various sources of inequality compared to the Gini index. Lastly, we characterize those expected utility functions that respect our order.