The Multi-Threshold Generalized Sufficientarianism and Level-Oligarchy

This paper investigates a class of socialwelfare orderings that satisfy the standard and acceptable axioms in the literature: anonymity, strong Pareto, separability, and Pigou-Dalton transfer (or, convexity). Due to the lack of continuity, we show that the class of social welfare orderings typically has some thresholds satisfying the following property, which we call level-oligarchy: individuals whose utility is less than the value are prioritized over the other individuals whose utility is greater than the value. First, we provide the novel reduced form characterization that a social welfare ordering satisfies anonymity, strong Pareto, separability, and convexity must be either the weak generalized utilitarian or level-oligarchy. Next, by dropping convexity and instead requiring Pigou-Dalton transfer and a mild continuity axiom, we characterize the new class of social welfare orderings, the multi-threshold generalized sufficientarian orderings, which subsumes the leximin, generalized utilitarian, and critical-level sufficientarian social welfare orderings as special cases. Therefore, we can provide a unified characterization for the important class of social welfare orderings only by the permissible axioms. In particular, although the social judgment from both classes of orderings seems quite different, our result implies that the difference between the utilitarian and leximin orderings just comes from the degree of continuity.