Can Acceptable Social Welfare Orderings Show Compassion for Both Relative Inequality and Poverty? A Reexamination of Interpersonal Comparisons of Well-being and Scale Invariance

This study shows that combining the Pareto principle and continuity with scale invariance, which has usually been interpreted as the requirement of interpersonal comparisons of well-being, imposes a major constraint on a functional form of a social welfare ordering. In fact, if the social welfare ordering is required to satisfy cardinal full comparability of well-being, then it must belong to a class of weighted utilitarianisms with variable weights. However, thorough an appropriate reformulation on interpersonal comparisons of well-being, the class of acceptable social welfare orderings is shown to be a rank-dependent generalized utilitarianism that can show compassion for both relative inequality and poverty. If additional conditions are required, we can obtain some refinements of this social welfare ordering such as a rank-weighted generalized utilitarianism and a rank-weighted Atkinson-Blackorby-Donaldson social welfare ordering. Moreover, the rank-weighted generalized utilitarianism is shown to approximately include the well-known three social welfare orderings that have been proposed in ethics: the Pareto egalitarianism, prioritarianism, and sufficientarianism. Therefore, it makes clear that the theoretical difference between the ideas of distributive justice in ethical theory is simply caused by intensity levels for tolerable inequality and poverty. These results can be easily extended to the context of social choice with variable populations.